[EM] PR methods and Quotas
Like Jameson and Toby, I have spent some time thinking about how to make a median-based PR system. The system I came up with is similar to Jameson's, but simpler, and uses the Hare quota! Say there are 100 voters and you're going to elect ten representatives. Each representative should represent 10 people, so why not choose the first one by choosing the candidate who makes 10 people the happiest? (The one whose tenth highest grade is the highest.) Then, take the 10 voters who helped elect this candidate and eliminate their ballots. (There might be more than ten and you'd have to choose ten or use fractional voters. I have ideas for that, but lets gloss over that issue for now.) You can even tell those 10 voters who their representative is. Electing the next seat should be the same way. Choose someone who is the best representative for 10 people. Repeat. The only problem is when you get down to the last representative. If you follow this pattern, the last candidate is the one whose LOWEST grade among the remaining ballots is the highest, which is rather unorthodox. You could change the rules and just use the median on the last seat, but using the highest minimum grade does have a certain attraction to it. You're going to force those last ten voters to have some representative. It makes some sense to choose the one who maximizes the happiness of the least happy voter. (Though ties at a grade of 0 may be common.) But this system doesn't reduce to median voting. Which got me thinking... Is there anything that special about the 50th percentile in the single-winner case anyways? I can imagine lots of single-winner situations where it's more egalitarian to choose a lower percentile. In a small and friendly group, even choosing the winner with the highest minimum grade is a good social choice method. It's like giving each person veto power and still hoping you can find something everyone can live with. This is the method we tend to use (informally) when I'm in a group choosing where to go to lunch together. Thoughts? Andy Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] PR-SODA? Try 2 (and 3)
On Thu, Jul 21, 2011 at 9:45 AM, Jameson Quinn jameson.qu...@gmail.comwrote: So, here's the simpler procedure: While there are more uneliminated candidates than empty seats: Divide each ballot by the number of uneliminated candidates it approves If there are any candidates with more than a Droop quota: Elect the one with the highest score (previously unique ballots) Discard a Droop quota of randomly-chosen ballots which approve the elected candidate, starting with the ones delegated to that candidate Assign that candidates pre-declared approvals on any undiscarded delegated ballots for that candidate Otherwise: Eliminate the candidate with the lowest score Assign that candidates pre-declared approvals on any delegated ballots for that candidate Elect all remaining candidates to fill the seats. Okay, I really love how simple this is. From the description, it sounds like it would be explainable and would work well. I wonder how it does in simulations and if we can find any problematic scenarios. Questions: - Is there a bullet vote but don't delegate option like normal SODA? - Would it work just as well with the Hare quota? - Without the delegation, is it the same as any other PR-with-approval-ballots method in existence? Suggestions: - When a candidate is elected and you need to discard ballots, you could specify a more detailed preference order: 1. Ballots which delegated to that candidate 2. Ballots which bullet voted that candidate and didn't delegate 3. Ballots which approved two candidates 4. Ballots which approved three candidates 5. Ballots which approved four candidates 6. And so on. This eliminates ballots first which approve fewer candidates. You may still have to select randomly within these tiers, but it gives an incentive for people to approve more candidates, which helps the method work better. Right? - Andy Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] PR methods and Quotas
Andy Jennings wrote:
Like Jameson and Toby, I have spent some time thinking about how to make
a median-based PR system.
The system I came up with is similar to Jameson's, but simpler, and uses
the Hare quota!
How about clustering logic? Say you have an electorate of n voters, and
you want k seats. The method would be combinatorial: you'd check a
prospective slate. Say the slate is {ABC...}. Then that means you make a
group of n/k voters and assign A to this gorup, another group of n/k
other voters and assign B to that group, and so on.
The score of each slate is equal to the sum of the median scores for
each assigned candidate, when considering only the voters in the
assigned candidate's group. That is, A's median score when considering
the voters of the first group, plus B's median score when considering
the voters of the second group, and so on. The voters are moved into
groups so that this sum is maximized.
Actually determining where to move each voter to optimize this might be
quite hard, though. But if you could make it work, then that would seem
to do what you wanted: it gives one candidate to represent the first
n/k, one candidate to represent the next n/k, etc, and picks the council
that makes these people most happy.
Say there are 100 voters and you're going to elect ten representatives.
Each representative should represent 10 people, so why not choose the
first one by choosing the candidate who makes 10 people the happiest?
(The one whose tenth highest grade is the highest.) Then, take the 10
voters who helped elect this candidate and eliminate their ballots.
(There might be more than ten and you'd have to choose ten or use
fractional voters. I have ideas for that, but lets gloss over that
issue for now.) You can even tell those 10 voters who their
representative is.
I imagine you could eliminate the voters directly, though that would
have some path dependence problems (which was why I suggested the
above). Say you make use of highest tenth grade. Then you know which
voters voted the candidate in question that high. Eliminate these. Find
the highest tenth with those voters elminated, among uneliminated
candidates. Again, you know the 10 voters who voted the next winner at
that level or higher. Eliminate *them*. And so on down.
Is that what you're suggesting? Then the last candidate is only the one
with the best worst votes in the sense that there are only ten voters left.
How about using the midpoint? That is, you find the 5th voter down, not
the 10th. Then when you're down to the last 10 voters, the 5th voter
down is the median. Doing so would seem to reduce it to median ratings
in the single-winner case, since 100/1 = 100, so you'd pick the
midpoint, i.e. at the 50th voter, which is the median.
Electing the next seat should be the same way. Choose someone who is
the best representative for 10 people. Repeat.
The only problem is when you get down to the last representative. If
you follow this pattern, the last candidate is the one whose LOWEST
grade among the remaining ballots is the highest, which is rather
unorthodox. You could change the rules and just use the median on the
last seat, but using the highest minimum grade does have a certain
attraction to it. You're going to force those last ten voters to have
some representative. It makes some sense to choose the one who
maximizes the happiness of the least happy voter. (Though ties at a
grade of 0 may be common.)
But this system doesn't reduce to median voting. Which got me
thinking... Is there anything that special about the 50th percentile in
the single-winner case anyways? I can imagine lots of single-winner
situations where it's more egalitarian to choose a lower percentile. In
a small and friendly group, even choosing the winner with the highest
minimum grade is a good social choice method. It's like giving each
person veto power and still hoping you can find something everyone can
live with. This is the method we tend to use (informally) when I'm in a
group choosing where to go to lunch together.
I think the median is used because it's robust. If you assume unlimited
ratings, the maximum and minimum could be altered by a single voter
(whoever's at the min or max), as could the mean (by any outlier).
However, the median is robust to distorted values - quite a number of
voters would have to change their votes to alter the median.
In one way, then, the median is a way of robustly estimating a property
related to the shape of the function given by the voters' ratings, even
in the presence of noise (or strategy). To keep this reasoning for
multiwinner, one should find out what properties one want to know about
for multiwinner elections, then find a way of robustly estimating these.
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Single Contest
On Sat, Jul 23, 2011 at 11:28 AM, fsimm...@pcc.edu wrote: If one of the finalists is chosen by a method that satisfies the majority criterion, then you can skip step one, and the method becomes smoother. Here are some possibilities for the method that satisfies the majority criterion: DSC, Bucklin, and the following range ballot based method: Elect the candidate X with the greatest value of p such that more than p/2 percent of the ballots rate X at least p percent of the maxRange value. Forest, Can you clarify your definition of the majority criterion? I don't think this method satisfies it. As a general example, suppose there are two candidates, A and B. The voting range is 0-100 and there are 5 voters: 1 voter: A=10 B=30 1 voter: A=30 B=50 1 voter: A=50 B=70 1 voter: A=70 B=90 1 voter: A=90 B=10 B is strictly preferred to A by 4 out of 5 voters, but these two candidates have the exact same set of votes. Any method which forgets which voter gave which vote must consider them exactly tied. This includes score (range) voting, majority judgement, the chiastic median, and any of the other generalized medians. Thus, with only some minor perturbation, A can defeat B in any of these methods. In the chiastic median (or the majority judgement), both candidates have societal grades of 50, but if you change A=50 to A=51 for the third voter, A's societal grade becomes 51 and A defeats B, despite strong majority opposition. In the p/2 system, 40% of the voters gave grades of 70 or above and 20% of the voters gave grades strictly above 70, so both candidates get a societal grade of 70. But if you change A=70 to A=71 for the fourth voter, A's societal grade becomes 71 and A defeats B, again despite a strong majority opposition. I think any method which forgets which voter gave which vote will never satisfy the majority criterion. - Andy Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Weighted voting systems for proportional representation
Kathy Dopp wrote: The system you describe *is* still precinct summable in the sense of reporting the sums for each possible slate of candidates for each precinct or polling location - this is at least a whole lot fewer sums than the number of possible ballot choice permutations including partially filled out ballots that IRV/STV would require to be reported and sampled to be precinct summable (reporting all individual ballots' choices would be less to report in most cases). To be summable, this system would require reporting (N choose S) sums where N is the number of total candidates in the contest and S is the number of seats being elected. This is a lot of sums - but could, I imagine, be mathematically sampled and audited to limit the risk of certifying the wrong slate much more easily than IRV methods could be - but I'm not certain about that until I have the time to think about it more (not any time soon). Ah, yes. This leads me back to an older thought that perhaps the criterion of summability should be refined for multiwinner methods by turning it into two criteria. These criteria would be: - Weak summability: If the number of seats is fixed, one can find the winner of the method according to precinct sums, where the amount of data required for these sums grows as a polynomial with respect to the number of candidates, and as a polylogarithmic function with respect to the number of voters. - Strong summability: Same as weak, but without the number of seats being fixed or known in advance. To my knowledge, Schulze STV is weakly summable, as is this method, because if you fix S, N choose S is bounded by a polynomial. When people here talk about summability for multiwinner methods, they usually mean strong summability, though. This is like SNTV or party list. If you have the Plurality counts for SNTV, it doesn't matter how many seats you want, you can just read off the n first Plurality winners. Similarly, for party list, you can just run the Sainte-Laguë method n times for n seats with the same input data. Do you think weak summability is sufficient to audit multiwinner methods? Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] PR methods and Quotas
Kristofer Munsterhjelm wrote:
Andy Jennings wrote:
Like Jameson and Toby, I have spent some time thinking about how to make a
median-based PR system.
The system I came up with is similar to Jameson's, but simpler, and uses
the Hare quota!
How about clustering logic? Say you have an electorate of n voters, and you
want k seats. The method would be combinatorial: you'd check a prospective
slate. Say the slate is {ABC...}. Then that means you make a group of n/k
voters and assign A to this gorup, another group of n/k other voters and
assign B to that group, and so on.
The score of each slate is equal to the sum of the median scores for each
assigned candidate, when considering only the voters in the assigned
candidate's group. That is, A's median score when considering the voters of
the first group, plus B's median score when considering the voters of the
second group, and so on. The voters are moved into groups so that this sum
is maximized.
The median is not what you want for clustering like this, because it
basically ignores the scores of half the voters assigned to each candidate.
That is, if I'm assigning 11 voters to each candidate, I can assign 6
voters who love that candidate and 5 voters who hate the candidate and still
have a very high median.
Say there are 100 voters and you're going to elect ten representatives.
Each representative should represent 10 people, so why not choose the first
one by choosing the candidate who makes 10 people the happiest? (The one
whose tenth highest grade is the highest.) Then, take the 10 voters who
helped elect this candidate and eliminate their ballots. (There might be
more than ten and you'd have to choose ten or use fractional voters. I have
ideas for that, but lets gloss over that issue for now.) You can even tell
those 10 voters who their representative is.
I imagine you could eliminate the voters directly, though that would have
some path dependence problems (which was why I suggested the above). Say you
make use of highest tenth grade. Then you know which voters voted the
candidate in question that high. Eliminate these. Find the highest tenth
with those voters elminated, among uneliminated candidates. Again, you know
the 10 voters who voted the next winner at that level or higher. Eliminate
*them*. And so on down.
Is that what you're suggesting?
Yes, this is what I'm suggesting.
Then the last candidate is only the one with the best worst votes in the
sense that there are only ten voters left.
How about using the midpoint? That is, you find the 5th voter down, not the
10th. Then when you're down to the last 10 voters, the 5th voter down is the
median. Doing so would seem to reduce it to median ratings in the
single-winner case, since 100/1 = 100, so you'd pick the midpoint, i.e. at
the 50th voter, which is the median.
True, but in filling the first seat, I don't think we should take a
candidate loved by 5 and hated by 95 as the first choice to represent
one-tenth of the population.
But this system doesn't reduce to median voting. Which got me thinking...
Is there anything that special about the 50th percentile in the
single-winner case anyways? I can imagine lots of single-winner situations
where it's more egalitarian to choose a lower percentile. In a small and
friendly group, even choosing the winner with the highest minimum grade is a
good social choice method. It's like giving each person veto power and
still hoping you can find something everyone can live with. This is the
method we tend to use (informally) when I'm in a group choosing where to go
to lunch together.
I think the median is used because it's robust. If you assume unlimited
ratings, the maximum and minimum could be altered by a single voter
(whoever's at the min or max), as could the mean (by any outlier). However,
the median is robust to distorted values - quite a number of voters would
have to change their votes to alter the median.
With any finite number of voters, the median is still the score of one
voter, who can change the median by changing his vote. But you are right
that if the scores follow a normal distribution, then he probably can't
change the median very much before he crosses another voter's score and is
not the median vote anymore. But that's not true for a bimodal
distribution.
- Andy
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] PR methods and Quotas
Andy Jennings wrote:
Kristofer Munsterhjelm wrote:
Andy Jennings wrote:
Like Jameson and Toby, I have spent some time thinking about how
to make a median-based PR system.
The system I came up with is similar to Jameson's, but simpler,
and uses the Hare quota!
How about clustering logic? Say you have an electorate of n voters,
and you want k seats. The method would be combinatorial: you'd check
a prospective slate. Say the slate is {ABC...}. Then that means you
make a group of n/k voters and assign A to this gorup, another group
of n/k other voters and assign B to that group, and so on.
The score of each slate is equal to the sum of the median scores for
each assigned candidate, when considering only the voters in the
assigned candidate's group. That is, A's median score when
considering the voters of the first group, plus B's median score
when considering the voters of the second group, and so on. The
voters are moved into groups so that this sum is maximized.
The median is not what you want for clustering like this, because it
basically ignores the scores of half the voters assigned to each
candidate. That is, if I'm assigning 11 voters to each candidate, I can
assign 6 voters who love that candidate and 5 voters who hate the
candidate and still have a very high median.
Well, yes, but the same thing holds for median ratings in general. If
you want to find someone who represents the whole population, median
ratings can pick someone who is loved by 51% and hated by 49%, rather
than someone that 80% think are okay (and I think Warren have made
arguments to the effect that this makes Range better than median).
The question then is: what makes that logic okay when you're electing a
single representative for the whole population, but not okay when you're
electing one of ten representatives for 10% of the population? Is it the
fluid nature of the clustering - that the optimizer could try to
artificially inflate the scores by packing hate A voters into the A-group?
Then the last candidate is only the one with the best worst votes in
the sense that there are only ten voters left.
How about using the midpoint? That is, you find the 5th voter down,
not the 10th. Then when you're down to the last 10 voters, the 5th
voter down is the median. Doing so would seem to reduce it to median
ratings in the single-winner case, since 100/1 = 100, so you'd pick
the midpoint, i.e. at the 50th voter, which is the median.
True, but in filling the first seat, I don't think we should take a
candidate loved by 5 and hated by 95 as the first choice to represent
one-tenth of the population.
I guess you could be more gentle by placing the point at 50% (1/2) for
one winner, 1/3 for two, 1/4 for three ... 1/11 for ten. That would be
more Droop-like and less Hare-like. But then you can't simply eliminate
those who contributed to the voting, I think.
With any finite number of voters, the median is still the score of one
voter, who can change the median by changing his vote. But you are
right that if the scores follow a normal distribution, then he probably
can't change the median very much before he crosses another voter's
score and is not the median vote anymore. But that's not true for a
bimodal distribution.
He can't alter the median to an arbitrary extent, however. An outlier at
the mean can do so by setting his score arbitrarily high (or low), and
the max or min voter can do so, but to a limited extent, by raising his
score (if he's max) or lowering his score (if he's min). If the median
voter alters his score by too much, he's no longer the median voter.
That may change the median result by some amount (unless the new median
voter expresses the same score as the old one used to), but it's limited.
Ah, there is a term for this reasoning.
https://secure.wikimedia.org/wikipedia/en/wiki/Breakdown_point#Breakdown_point
I haven't investigated it in detail though :-)
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] How to make a summable version of STV
fsimm...@pcc.edu wrote: Kristopfer. Look at it this way, the process of amalgamating the factions is a low pass filter that gets rid of some fo the noise. So why not consider the resulting ballots as the true ballots, and the associated weights tell how many of them there are of each kinsd. STV can be done with these new true ballots, Droop quotas and all. Sure, but these reformulated criteria are less useful than the ordinary criteria. For instance, the Droop proportionality criterion means that voters don't have to coordinate the ordering of their preferred set (except regarding vote management). In the case of an absolutely preferred candidate like X, if your low-pass filter is in place, the voters now have to remember to not rank X top, which weakens the guarantee given by the DPC. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Automated Approval methods (was Single Contest)
Kevin Venzke wrote: I also tried implementing the most obvious (I suppose) method: Take the ratings and conduct simulated approval polling, either for some determined or semi-random number of iterations, or until someone wins twice in a row. This doesn't test as well as I thought it would though. What Approval strategy do you use? Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] PR methods and Quotas
Kristofer Munsterhjelm wrote:
Andy Jennings wrote:
Kristofer Munsterhjelm wrote:
Andy Jennings wrote:
Like Jameson and Toby, I have spent some time thinking about how
to make a median-based PR system.
The system I came up with is similar to Jameson's, but simpler,
and uses the Hare quota!
How about clustering logic? Say you have an electorate of n voters,
and you want k seats. The method would be combinatorial: you'd check
a prospective slate. Say the slate is {ABC...}. Then that means you
make a group of n/k voters and assign A to this gorup, another group
of n/k other voters and assign B to that group, and so on.
The score of each slate is equal to the sum of the median scores for
each assigned candidate, when considering only the voters in the
assigned candidate's group. That is, A's median score when
considering the voters of the first group, plus B's median score
when considering the voters of the second group, and so on. The
voters are moved into groups so that this sum is maximized.
The median is not what you want for clustering like this, because it
basically ignores the scores of half the voters assigned to each candidate.
That is, if I'm assigning 11 voters to each candidate, I can assign 6
voters who love that candidate and 5 voters who hate the candidate and still
have a very high median.
Well, yes, but the same thing holds for median ratings in general. If you
want to find someone who represents the whole population, median ratings can
pick someone who is loved by 51% and hated by 49%, rather than someone that
80% think are okay (and I think Warren have made arguments to the effect
that this makes Range better than median).
Exactly. This is why I'm questioning the median even for single-winner
elections. Maybe you're right and we should be using the 20th percentile,
which would give us the candidate that some 80% of the population liked
best. I tried to point out some arguments that highest minimum might be a
good method even in some single-winner environments. It does give everyone
veto power. But that's okay if everyone is committed to finding a solution
that's acceptable to everyone. (In a public method, obviously, you'd have
to have some tie-breaker, like electing the candidate vetoed by the fewest
voters.)
The question then is: what makes that logic okay when you're electing a
single representative for the whole population, but not okay when you're
electing one of ten representatives for 10% of the population? Is it the
fluid nature of the clustering - that the optimizer could try to
artificially inflate the scores by packing hate A voters into the A-group?
Yes, the fluid nature makes it much worse. Say there are 110 voters and
we're choosing 10 winners. Here's the voter profile:
50 people love A and noone else
6 people love B and noone else
6 people love C and noone else
...
6 people love K and noone else
If A were a political party, it would be entitled to at least 4 out of the
ten seats. As a candidate, you would expect A to get a seat. But we can
cluster the voters into:
6 voters who love B and 5 voters who love A
6 voters who love C and 5 voters who love A
...
6 voters who love K and 5 voters who love A
And then we elect B,C,..., and K, each with a perfect median in their
cluster.
Clustering with the median in each cluster is way too under-determined.
Then the last candidate is only the one with the best worst votes in
the sense that there are only ten voters left.
How about using the midpoint? That is, you find the 5th voter down,
not the 10th. Then when you're down to the last 10 voters, the 5th
voter down is the median. Doing so would seem to reduce it to median
ratings in the single-winner case, since 100/1 = 100, so you'd pick
the midpoint, i.e. at the 50th voter, which is the median.
True, but in filling the first seat, I don't think we should take a
candidate loved by 5 and hated by 95 as the first choice to represent
one-tenth of the population.
I guess you could be more gentle by placing the point at 50% (1/2) for one
winner, 1/3 for two, 1/4 for three ... 1/11 for ten. That would be more
Droop-like and less Hare-like. But then you can't simply eliminate those who
contributed to the voting, I think.
Yes, it is much more Droop-like. It seems arbitrary, though, to leave one
eleventh of the voters completely unrepresented. (With STV, Droop is
natural, but with cardinal inputs, I see no justification for it.)
With any finite number of voters, the median is still the score of one
voter, who can change the median by changing his vote. But you are right
that if the scores follow a normal distribution, then he probably can't
change the median very much before he crosses another voter's score and is
not the median vote anymore. But that's not true for a bimodal
distribution.
He can't alter the
Re: [EM] Weighted voting systems for proportional representation
One approach to summability and auditing is to say that the target is to allow the district to count the votes and later check that at the top level their votes (or the votes of all districts) were counted correctly, AND to allow the top level to check that the districts will report their results correctly (they may e.g. want the districts to tell their final results before they hear what the results of the other districts were). In addition to these also the general public and independent auditors will benefit of having the results in a format that allows them to recount and check the results and that allows them to audit all the districts (and subdistricts, and top level) independently one by one. The key point is thus to provide transparency and easy and local checks in all directions. If this is what we want, then an interesting new feature is the new information society and its technical capabilities. That makes almost all methods summable in the above mentioned sense. Let's say we use STV. With current technology it is not a big problem to require all poll stations to record all their ballots in some digital format. And it is easy to check, if needed, that the physical ballots actually correspond to the reported results. It is also easy to check at the top level that the results are correct since the digital space taken by few million STV ballots is not that big, and the time that computers take to check the results is not that big. One may thus say that current digital storage, transport and computation capabilities can make almost any method summable in the discussed way. But there are still some problems left. One could say that the summability criterion also includes a requirement of being able to sum up the votes so that the summed up votes will hide details of the individual votes. This may be needed to provide privacy and to avoid unwanted phenomena like coercion and vote selling. In this sense the above mentioned treatment of the STV votes may not be sufficient. The number of candidates may be high enough and the length of the ballots high enough to allow identification of individual ballots. If we want to guarantee also privacy some additional tricks are needed in this case. My point was anyway that it isa also possible to divide this summability / auditing / privacy requirement in two parts so that it will consist of the 1) easy verifiability and 2) privacy parts. New information technology may redefine the rules to some extent. Verification is easier, but on the other hand privacy may be more problematic since it is now easier to share all the information (partially intentionally to guarantee better verifiability). The tricky part is actually the privacy part. We may nowadays have e.g. interest to break the individual ballots in smaller and more numerous parts instead of trying to sum them up in smaller space. Juho On 24.7.2011, at 11.53, Kristofer Munsterhjelm wrote: Kathy Dopp wrote: The system you describe *is* still precinct summable in the sense of reporting the sums for each possible slate of candidates for each precinct or polling location - this is at least a whole lot fewer sums than the number of possible ballot choice permutations including partially filled out ballots that IRV/STV would require to be reported and sampled to be precinct summable (reporting all individual ballots' choices would be less to report in most cases). To be summable, this system would require reporting (N choose S) sums where N is the number of total candidates in the contest and S is the number of seats being elected. This is a lot of sums - but could, I imagine, be mathematically sampled and audited to limit the risk of certifying the wrong slate much more easily than IRV methods could be - but I'm not certain about that until I have the time to think about it more (not any time soon). Ah, yes. This leads me back to an older thought that perhaps the criterion of summability should be refined for multiwinner methods by turning it into two criteria. These criteria would be: - Weak summability: If the number of seats is fixed, one can find the winner of the method according to precinct sums, where the amount of data required for these sums grows as a polynomial with respect to the number of candidates, and as a polylogarithmic function with respect to the number of voters. - Strong summability: Same as weak, but without the number of seats being fixed or known in advance. To my knowledge, Schulze STV is weakly summable, as is this method, because if you fix S, N choose S is bounded by a polynomial. When people here talk about summability for multiwinner methods, they usually mean strong summability, though. This is like SNTV or party list. If you have the Plurality counts for SNTV, it doesn't matter how many seats you want, you can just read off the n first Plurality winners. Similarly, for party list, you
Re: [EM] PR for USA or UK
2011/7/23 Andy Jennings electi...@jenningsstory.com On Sat, Jul 23, 2011 at 7:45 AM, Jameson Quinn jameson.qu...@gmail.comwrote: And so I'd like to suggest that we should be looking for a PR system which satisfies the following criteria: c1. Truly proportional (of course). I would be willing to support a not-truly-proportional system, but I'm not everyone. Egregious compromises on this issue will simply reduce the activist base, to no benefit. c2. Includes a geographical aspect. People are attached to the local representation feature of FPTP, whether that's rational or not. c3. No closed list. A party should not be able to completely shield any member from the voters. In general, voter power is preferable to party power, insofar as it's compatible with the next criterion. c4. Simple ballots. A reasonably-thorough voter should not have to mark more than, say, 5 candidates or options, and an average ballot should not list more than 20 candidates or options. Those are extreme limits; simpler is better, all the way down to around 7 options (of which only around half will be salient and/or viable). c5. Ideally, the smoothest transition possible. If existing single-winner districts can be used unchanged, all the better. c6. Insofar as it's compatible with the criteria above, greater freedom in voting is better. For instance, if ballots are printed with only in-district candidates, a system which allows out-of-district write-ins is better than one which doesn't, all other things being equal. I'm interested both in systems which satisfy 2 and those that don't. If we could identify a good, truly proportional, at-large system, then a state with a bicameral legislature (like Arizona) could leave one house as geographical and change one to be at-large proportional. I agree that if you were designing a democracy from scratch, non-geographical systems deserve attention. My purpose here is to support a system or systems that have some chance of passage in the US or UK. In my experience, that means that activists should unify behind a system which represents a minimal change. Whatever reform you propose will have opposition, both from people who are honestly and naturally skeptical of anything new, and from whichever major party currently benefits from the distortions of the current system. It's better to push a smaller reform which gives such people fewer arguments to use against you, than a more-complete one which can never pass. That's why I included criteria 2 and 5, and I stand behind them. This same argument applies to Kathy Dopp's suggestion that states like AZ could have their bicameral legislatures function using one PR body and one geographical body. It's a great idea, and I'd happily and enthusiastically support it; but it's a more-radical reform, so I think something which meets my criteria would be more attainable. At least, I'd like to settle on something which meets my criteria, so that if I'm right, we still have a chance. My proposal for SODA-PR satisfies and surpasses all 5 criteria. Other systems which do reasonably well: -I've seen a proposal for single-member districts and open party lists. This is similar to my SODA-PR system, except that it requires that all candidates in a party approve the same party set. As such, it is strictly worse on criterion 3, without being notably better on any of the other criteria. It is more conventional, though. -Multimember districts, with some system inside each district. -Mixed member systems. We should add Fair Majority Voting, by Balinski. ( http://mathaware.org/mam/08/EliminateGerrymandering.pdf) Here's the summary: Parties run one candidate in each district and voters vote for one candidate in the race in their district. The votes are totaled nationwide by party and an apportionment method is used to decide how many seats each party deserves. Each party is assigned a multiplier and the winner in each district is the one whose (vote total times party multiplier) is highest. The multipliers can be chosen so that the final total seats won by each party matches the number of seats assigned by the apportionment method. It definitely satisfies your criteria 1,2,4, and 5. I'd say it mostly satisfies 3. Don't know how to evaluate 6. The main thing I don't like about it is that it conflates voting for a candidate with voting for his party. What if I like the candidate but not the party, or vice versa? But since so many things in the legislature happen on a party basis, I've decided that this is not as bad as it first seems. FMV is equivalent to the single-member districts and open party lists system I was talking about, although I remember seeing it under some different name (some two-letter acronym with a U, I seem to recall). In the end, FMV can be considered a limited special case of SODA-PR. Thus, using the more-general terminology of SODA-PR to discuss them both, the differences are:
Re: [EM] Weighted voting systems for proportional representation
I agree with Juho's argument that all methods are summable these days. However, I'd suggest a few vaguely-defined related criteria. The general one is auditable - is it possible to gain confidence that the result is correct through some process besides a full recount? This breaks down into human-auditable (can you gain confidence through some simple arithmetic process which doesn't require a computer? Such a process can involve summary-statistics.); and sampling-auditable (can you gain an arbitrary degree of confidence in the result by recounting a random sample of the votes? Are the sample sizes required reasonable?). STV does pretty poorly on these criteria. Since a tie at any stage can have extreme effects on later stages; and electing A,B,C is likely to lead to different results later on than electing C,B,A; the system is unstable. The number of possible ties at all stages is order N³, the cube of the number of candidates. And the voters divide into N camps at each stage. Thus, in general, if there are fewer than about N⁴ voters, you can expect to come arbitrarily close to a tie at some stage, which would mean that you have to recount all the votes to be confident of the result. Party list systems do the best on all these criteria, because they are traditionally summable. Things like Schulze-STV, AT-TV, and SODA-PR fall somewhere in the middle. If summary statistics of votes are published, there are some easy sanity checks which would catch the clumsier frauds in the counting process. And a sampled recount would be enough to confirm the validity of these summary statistics. Some forms of fraud would still take a full recount to detect; but in general, such frauds would be logistically difficult. I'm doing a lot of hand-waving in that last paragraph, though. The fact is, to really be fully auditable in both senses, you need a system which is summable in the traditional, low-order-polynomial-of-candidates, sense. JQ 2011/7/24 Juho Laatu juho4...@yahoo.co.uk One approach to summability and auditing is to say that the target is to allow the district to count the votes and later check that at the top level their votes (or the votes of all districts) were counted correctly, AND to allow the top level to check that the districts will report their results correctly (they may e.g. want the districts to tell their final results before they hear what the results of the other districts were). In addition to these also the general public and independent auditors will benefit of having the results in a format that allows them to recount and check the results and that allows them to audit all the districts (and subdistricts, and top level) independently one by one. The key point is thus to provide transparency and easy and local checks in all directions. If this is what we want, then an interesting new feature is the new information society and its technical capabilities. That makes almost all methods summable in the above mentioned sense. Let's say we use STV. With current technology it is not a big problem to require all poll stations to record all their ballots in some digital format. And it is easy to check, if needed, that the physical ballots actually correspond to the reported results. It is also easy to check at the top level that the results are correct since the digital space taken by few million STV ballots is not that big, and the time that computers take to check the results is not that big. One may thus say that current digital storage, transport and computation capabilities can make almost any method summable in the discussed way. But there are still some problems left. One could say that the summability criterion also includes a requirement of being able to sum up the votes so that the summed up votes will hide details of the individual votes. This may be needed to provide privacy and to avoid unwanted phenomena like coercion and vote selling. In this sense the above mentioned treatment of the STV votes may not be sufficient. The number of candidates may be high enough and the length of the ballots high enough to allow identification of individual ballots. If we want to guarantee also privacy some additional tricks are needed in this case. My point was anyway that it isa also possible to divide this summability / auditing / privacy requirement in two parts so that it will consist of the 1) easy verifiability and 2) privacy parts. New information technology may redefine the rules to some extent. Verification is easier, but on the other hand privacy may be more problematic since it is now easier to share all the information (partially intentionally to guarantee better verifiability). The tricky part is actually the privacy part. We may nowadays have e.g. interest to break the individual ballots in smaller and more numerous parts instead of trying to sum them up in smaller space. Juho On 24.7.2011, at 11.53, Kristofer Munsterhjelm wrote: Kathy
Re: [EM] PR methods and Quotas
2011/7/24 Andy Jennings electi...@jenningsstory.com Like Jameson and Toby, I have spent some time thinking about how to make a median-based PR system. The system I came up with is similar to Jameson's, but simpler, and uses the Hare quota! Say there are 100 voters and you're going to elect ten representatives. Each representative should represent 10 people, so why not choose the first one by choosing the candidate who makes 10 people the happiest? (The one whose tenth highest grade is the highest.) Then, take the 10 voters who helped elect this candidate and eliminate their ballots. (There might be more than ten and you'd have to choose ten or use fractional voters. I have ideas for that, but lets gloss over that issue for now.) You can even tell those 10 voters who their representative is. Glossing-over noted. I'd like to hear your ideas, but I agree that they should not be part of the basic definition of the system. Also, this hard elimination is where your method differs from AT-TV. Your method certainly has a stronger free-riding incentive than AT-TV. It is radically simpler, though, so perhaps AT-TV is adding too much complication in an attempt to minimize the (fundamentally inevitable) free-rider incentive. Electing the next seat should be the same way. Choose someone who is the best representative for 10 people. Repeat. The only problem is when you get down to the last representative. If you follow this pattern, the last candidate is the one whose LOWEST grade among the remaining ballots is the highest, which is rather unorthodox. You could change the rules and just use the median on the last seat, but using the highest minimum grade does have a certain attraction to it. You're going to force those last ten voters to have some representative. It makes some sense to choose the one who maximizes the happiness of the least happy voter. (Though ties at a grade of 0 may be common.) If you use the Droop quota instead of the Hare, ties at 0 will be less likely. In general, I think that with the Hare quota, ties at 0 wouldn't just be common, they'd be universal; and they'd still be common with the Droop quota. In either case, the obvious solution (and the one which AT-TV uses) is to elect the candidate with the fewest 0 votes. But this system doesn't reduce to median voting. Right, it doesn't. But it does if you use the Droop quota. Which got me thinking... Is there anything that special about the 50th percentile in the single-winner case anyways? I can imagine lots of single-winner situations where it's more egalitarian to choose a lower percentile. In a small and friendly group, even choosing the winner with the highest minimum grade is a good social choice method. It's like giving each person veto power and still hoping you can find something everyone can live with. This is the method we tend to use (informally) when I'm in a group choosing where to go to lunch together. The Droop quota reduces to the median. The Hare quota reduces to the highest minimum grade. You could also use any number in between. (I note that modified Saint-Lague is, I think, actually used in some places, and amounts to a similar compromise idea.) The higher the quota (up to Hare), the smaller a group of strategic voters can be and still determine the result (if everyone else is honest). I'd argue that this makes pure Hare a poor solution. I am open to compromises. 2/(2N+1), the quota half way between Droop and Hare (I bet it already has a name, but I don't know it), reduces to the ~33rd percentile in the single-winner case. From what I've seen of supermajority requirements in contentious high-stakes contexts (California tax hikes, US senate filibusters), 2/3 is the highest reasonable supermajority requirement, and may already be too high. But, as you say, a higher requirement may make sense for smaller, friendlier decision-making. In sum: I like your method. It is certainly similar to, but simpler than, AT-TV. I prefer it with the Droop quota. What do you call it? (It would be good if you had terms for both the Droop and Hare versions). JQ Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Single Contest
The ranked majority criterion is: if one candidate is top-ranked by a majority of voters, that candidate must win. To me, the natural extension of that to rated systems is: if only one candidate is top-rated by any majority of voters, that candidate must win. You are suggesting that we use the ranked majority criterion for rated systems. If we do so, you are right that broad classes of rated systems (including range, median, and chiastic) can never pass. But if we use my definition of the criterion, then median systems pass, trivially. JQ 2011/7/24 Andy Jennings electi...@jenningsstory.com On Sat, Jul 23, 2011 at 11:28 AM, fsimm...@pcc.edu wrote: If one of the finalists is chosen by a method that satisfies the majority criterion, then you can skip step one, and the method becomes smoother. Here are some possibilities for the method that satisfies the majority criterion: DSC, Bucklin, and the following range ballot based method: Elect the candidate X with the greatest value of p such that more than p/2 percent of the ballots rate X at least p percent of the maxRange value. Forest, Can you clarify your definition of the majority criterion? I don't think this method satisfies it. As a general example, suppose there are two candidates, A and B. The voting range is 0-100 and there are 5 voters: 1 voter: A=10 B=30 1 voter: A=30 B=50 1 voter: A=50 B=70 1 voter: A=70 B=90 1 voter: A=90 B=10 B is strictly preferred to A by 4 out of 5 voters, but these two candidates have the exact same set of votes. Any method which forgets which voter gave which vote must consider them exactly tied. This includes score (range) voting, majority judgement, the chiastic median, and any of the other generalized medians. Thus, with only some minor perturbation, A can defeat B in any of these methods. In the chiastic median (or the majority judgement), both candidates have societal grades of 50, but if you change A=50 to A=51 for the third voter, A's societal grade becomes 51 and A defeats B, despite strong majority opposition. In the p/2 system, 40% of the voters gave grades of 70 or above and 20% of the voters gave grades strictly above 70, so both candidates get a societal grade of 70. But if you change A=70 to A=71 for the fourth voter, A's societal grade becomes 71 and A defeats B, again despite a strong majority opposition. I think any method which forgets which voter gave which vote will never satisfy the majority criterion. - Andy Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] PR-SODA? Try 2 (and 3)
2011/7/24 Andy Jennings electi...@jenningsstory.com On Thu, Jul 21, 2011 at 9:45 AM, Jameson Quinn jameson.qu...@gmail.comwrote: So, here's the simpler procedure: While there are more uneliminated candidates than empty seats: Divide each ballot by the number of uneliminated candidates it approves If there are any candidates with more than a Droop quota: Elect the one with the highest score (previously unique ballots) Discard a Droop quota of randomly-chosen ballots which approve the elected candidate, starting with the ones delegated to that candidate Assign that candidates pre-declared approvals on any undiscarded delegated ballots for that candidate Otherwise: Eliminate the candidate with the lowest score Assign that candidates pre-declared approvals on any delegated ballots for that candidate Elect all remaining candidates to fill the seats. Okay, I really love how simple this is. From the description, it sounds like it would be explainable and would work well. I wonder how it does in simulations and if we can find any problematic scenarios. Questions: - Is there a bullet vote but don't delegate option like normal SODA? Yes, but it's pretty useless. In general, your vote will be more likely to be decisive in some context, the closer to half of the candidates you approve. Voting for just one candidate is pretty unlikely to have any effect on results. - Would it work just as well with the Hare quota? Yes, but see my other message about your median-based system. For contentious elections, I prefer the Droop quota. With the Hare quota, the last candidate elected is likely to have about half the support of all the rest. And in the single-winner case it amounts to a supermajority requirement; and these don't have an illustrious history in my view. (I suppose that you could have an explicit tiebreaker representative, with only half a vote. But that amounts to same voting power as everyone else, unless an odd number of people abstain, which is just silly.) - Without the delegation, is it the same as any other PR-with-approval-ballots method in existence? I expect that non-delegated votes will be rarer than in plain SODA, for the reasons I mentioned above relating to bullet votes. So it's not too important. But without delegation, this method reduces to the same approval-based method as two-rating-level AT-TV. This system is to me an obvious case - it's the simplest form of sequential representative approval voting - and so I would not be surprised to learn that someone has already named it, but if so, I'm not aware of that. I guess I'd call it SRAV if it needs a name, see previous sentence. Suggestions: - When a candidate is elected and you need to discard ballots, you could specify a more detailed preference order: 1. Ballots which delegated to that candidate 2. Ballots which bullet voted that candidate and didn't delegate 3. Ballots which approved two candidates 4. Ballots which approved three candidates 5. Ballots which approved four candidates 6. And so on. This eliminates ballots first which approve fewer candidates. You may still have to select randomly within these tiers, but it gives an incentive for people to approve more candidates, which helps the method work better. Right? Well, up to a point. The problem would be if people approved a no-hope candidate, just to puff up the number of approvals on their ballot. This is a form of Woodall free riding, and it could lead to DH3-type pathologies in the worst case. I'd rather not go there. JQ Election-Methods mailing list - see http://electorama.com/em for list info
[EM] SODA page updated with SODA-PR
Just to alert those who may be interested, I've added SODA-PR to the SODA page on electowikihttp://wiki.electorama.com/wiki/Simple_Optionally-Delegated_Approval#SODA-PR_.28proportional_representation_version_of_SODA.29 . It includes some minor adjustments since the last time I expounded it here: Simplifying the ballot by including same-district candidates in a larger font, nearby-district candidates in a smaller font, and far-away candidates as write-ins only, is now part of the system by default. Random discards are repeated until the next candidate to be elected is the same twice in a row. That is intended as a compromise between the mathematical simplicity of ballot discarding and the deterministic nature of fractional reweighting. In most cases, it will not affect the result. Intercandidate can be conditional on being mutual, but not conditional on anything else. That should allow a reasonable, but not excessive, level of party discipline. It also notes the circumstances when this will give the same results as plurality, to argue that existing plurality winners will find this to be a relatively-good PR system. JQ Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] PR for USA or UK
I've replied to Jameson and Kevin in the same post here, so hopefully it's come out alright! From: Jameson Quinn jameson.qu...@gmail.com To: Toby Pereira tdp2...@yahoo.co.uk Cc: EM election-methods@lists.electorama.com Sent: Sun, 24 July, 2011 2:50:12 Subject: Re: [EM] PR for USA or UK I agree that PRV would give better results, with sophisticated voters, than most forms of PR. However, it does fail my criterion 4 (simple ballots) and do worse than SODA-PR on criteria 5(smooth transition) and even arguably 1(true proportionality - because separate districts spoil the proportionality). If you don't think these criteria are reasonable, you should give that argument. I started out with a list of criteria because I think that's the right place to start when you're looking for a practical system. JQ I don't necessarily think sophisticated voters are required in order to ensure reasonable PR under PRV. I think as long as you don't get some candidates who have much better strategic voters than others, it should do OK. I would argue that my system doesn't fail on simple ballots. It's not all or nothing. Yes, there are simpler ballots, but if I was rating simplicity of ballots approval style, I'd approve range ballots! But seriously, scores out of 6 is quite simple, and it could be made quite clear that you only need to rate candidates that you have any positive feeling towards. Blanks would count as zero. Some may argue for an average score to be given to blanks, but I think that would actually encourage people to fill out a load of zeros anyway. SODA-PR is probably simpler, but I think the delegable/non-delegable thing would be a bit confusing for voters and so wouldn't be simple in their minds. I know that it's arguably better to have the one vote and let your favourite candidate delegate (given that they probably have similar views to you) than dilute with several approvals, but why not just let candidates have their own delegation list - i.e. STV - and do away with the approval aspect completely (since you don't approve of voters actually voting approval style under your system yourself)? Smooth transition - yes, PRV a bigger step from FPTP in some ways than SODA-PR (giving candidates a score is further from a single X than approval-style votes), but the idea of giving your vote to the candidates to delegate is a pretty big paradigm shift in itself, and arguably causes it to fail on this criterion. Still, if we ever were to have PR in the UK, it would probably be STV anyway (don't know about in the US), which I would argue is no more or less smooth a transition than PRV from the starting point of FPTP. So for smooth transition, I don't think PRV fails, because I think it ties with the realistic (UK) frontrunner. Separate constituencies do spoil proportionality to an extent, yes. There would only be a certain number of seats available in each. If it was six, then a party with constant 10% support across the county would struggle to get anything. What's the alternative? We could have bigger constituencies, but that means bigger ballots, or party lists, but I don't like them. I'm not sure I get your district/co-district thing though. In any case, I think this is a problem of how we sort out districts/constituencies, rather than anything against PRV per se. Also, I don't get the whole thing about write-ins. Maybe it's a UK/US divide thing, but surely if you want to be elected then you stand for election. Therefore your name would be on the ballot. From: Kevin Venzke step...@yahoo.fr To: election-meth...@electorama.com Sent: Sun, 24 July, 2011 5:38:18 Subject: Re: [EM] PR for USA or UK Hi Toby, Hello. I really don't know what dishonest results means. Judging by your example below it apparently requires comparing two different methods. So, I can make any method give dishonest results just by inventing a different method that requires dishonesty from everyone. Now every other method in the world is cheating. I suppose what I mean is that by transferrig your vote for you, STV ends up producing the same result (in my simple case) as PRV with strategic voting, and to me it's an ugly result. It's not a bad description that strategy-resistant systems do the strategy for you. This has important results: 1. The voters do not need to do the strategy 2. So the playing field is leveled 3. So votes should have correct effect in proportion to the number, meaning the outcome is more accurate. That is, it reflects better the overall preferences of the electorate. Strategy-resistant systems do have certain advantages as you say, but in the single-winner case it would end up reducing range to a Condorcet method, which arguably isn't as good, and ends up pushing out a better-liked candidate for one that strictly more people prefer. And this is what I like about range - it's not
Re: [EM] Automated Approval methods (was Single Contest)
Hi Kristofer, --- En date de : Dim 24.7.11, Kristofer Munsterhjelm km_el...@lavabit.com a écrit : I also tried implementing the most obvious (I suppose) method: Take the ratings and conduct simulated approval polling, either for some determined or semi-random number of iterations, or until someone wins twice in a row. This doesn't test as well as I thought it would though. What Approval strategy do you use? I always use better than expectation when it is allowed to assume the voters know the method is approval. (Which is just to say that the main sim, when during pure Approval, can't use better than expectation.) I put a tiny amount of average utility of all candidates into the expectation just to try to avoid the situation where your favorite won all the polls so therefore you don't approve him. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] PR for USA or UK
On 23.7.2011, at 17.45, Jameson Quinn wrote: We had a discussion about the best practical single-winner proposal, which, while it certainly wasn't as conclusive as I'd hoped, seemed productive to me. I think we should have a similar discussion about PR. Obviously, the situations in the UK and in the USA are very different in this regard. The UK is, as far as I know, the origin of the PR movement (in the 1860s and 1870s, liberals gained seats disproportionately as the franchise was extended, and Conservatives looked for a fairer system to recoup their losses). And it's part of Europe, where people have experience with PR. But both the UK and the US currently elect their principal representative bodies by district-based FPTP/plurality. And so I'd like to suggest that we should be looking for a PR system which satisfies the following criteria: 1. Truly proportional (of course). I would be willing to support a not-truly-proportional system, but I'm not everyone. Egregious compromises on this issue will simply reduce the activist base, to no benefit. What is a not-truly-proportional system? That could range from being close to proportional (= only few seats difference to full PR) to being close to what the system is today in the USA (= gives one or two seats to third parties). 2. Includes a geographical aspect. People are attached to the local representation feature of FPTP, whether that's rational or not. That may well make sense also in a PR system. Proportional geographical representation is a different and separate target, not necessarily a relic. 3. No closed list. A party should not be able to completely shield any member from the voters. In general, voter power is preferable to party power, insofar as it's compatible with the next criterion. 4. Simple ballots. A reasonably-thorough voter should not have to mark more than, say, 5 candidates or options, and an average ballot should not list more than 20 candidates or options. Those are extreme limits; simpler is better, all the way down to around 7 options (of which only around half will be salient and/or viable). I hope you don't assume that all the candidates must be listed on the ballot. One could have also ballots where the voters write the number(s) of their favourite candidate. That approach allows high number of candidates. Let's say that there are 100 seats. In a fully proportional system a party with more than 1% support would be entitled to one seat. If you want the voters to decide who wins instead of letting the party decide you need several candidates to choose from. Let's say that this party has 5 candidates. If other parties have similar rights to nominate candidates you could end up having e.g. 100*5 candidates. That is not an exact formula and I ignored the impact of districts, but the point is that if you want to support small parties and ability to select from multiple candidates the total number of candidates and the total number of candidates per district may grow large. Does number 20 above limit the number of candidates per district? 5. Ideally, the smoothest transition possible. If existing single-winner districts can be used unchanged, all the better. Having both pure single-winner districts (not e.g. MMP) and full PR is possible but then you have to accept considerable inaccuracy in electing the most liked candidate in each district. I guess what you are looking for is a good balance between these incompatible (but positive) requirements. Maybe this is one reason why you would accept also less than perfect PR. 6. Insofar as it's compatible with the criteria above, greater freedom in voting is better. For instance, if ballots are printed with only in-district candidates, a system which allows out-of-district write-ins is better than one which doesn't, all other things being equal. Is the old American tradition of allowing write-in candidates included in your list of requirements? My proposal for SODA-PR satisfies and surpasses all 5 criteria. Other systems which do reasonably well: -I've seen a proposal for single-member districts and open party lists. This is similar to my SODA-PR system, except that it requires that all candidates in a party approve the same party set. As such, it is strictly worse on criterion 3, without being notably better on any of the other criteria. It is more conventional, though. -Multimember districts, with some system inside each district. -Mixed member systems. One possible approach (with accurate PR) is to first allocate the seats to parties at national level and then allocate those seats to (probably multimember) districts (in a geographically proportional way). One approach that allows high number of candidates and simple ballots is to allow voters to rank candidates of one single party in one single region only. One may also limit the maximum number of ranked candidates heavily since
Re: [EM] PR for USA or UK
Hi Toby, --- En date de : Dim 24.7.11, Toby Pereira tdp2...@yahoo.co.uk a écrit : Strategy-resistant systems do have certain advantages as you say, but in the single-winner case it would end up reducing range to a Condorcet method, which arguably isn't as good, and ends up pushing out a better-liked candidate for one that strictly more people prefer. And this is what I like about range - it's not just about which candidates you prefer to which other ones, but by how much. I think the Range method itself is pretty incapable of this, but you could do it either with rated ballots or with a rank ballot that has truncation incentive. And as long as strategy isn't performed better by voters of some candidates than others, the fact that there would still be some honest voters would mean that the advantages of range would still remain to an extent, meaning that overall better-liked candidates stand a better chance, and it therefore reflects better the overall preferences of the electorate! That paragraph makes sense if you're comparing Range to Approval, but not Range to anything else. If large numbers of voters use strategy in Range (and I'm pretty sure they would be encouraged to; personally I wouldn't need any encouraging) this will destroy so much information that the only way Range will win out is if the rank methods you compare it to contain even more destructive incentives than Range has. [begin quote] On my website I give an example where party A has 68% of the support and party B 32%. There are two seats and so each party fields two Of course party A voters could coordinate themselves and split into two factions of 34% to take both seats, but this would be very hard for them to achieve. STV (Droop quota anyway) would transfer the votes above the quota accordingly so that party A would win both seats, and give what I would regard as the less fair result. Ok, but it's not obvious that it is less fair. You are according a privilege to the weaker party just because it is a different party. I'm not according them a privilege because they are a different party, but because I would see it as logical and fair that 75% is a reasonable cut-off. If a system made the cut-off at 80%, I'd argue that it was unfair in favour of the smaller party. [end quote] Can you explain your position without saying party? Because if you didn't see the parties, and only saw voters, it would be indefensible to give a seat to the 32%. There would be nothing special about that group. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] PR for USA or UK
2011/7/24 Juho Laatu juho4...@yahoo.co.uk On 23.7.2011, at 17.45, Jameson Quinn wrote: We had a discussion about the best practical single-winner proposal, which, while it certainly wasn't as conclusive as I'd hoped, seemed productive to me. I think we should have a similar discussion about PR. Obviously, the situations in the UK and in the USA are very different in this regard. The UK is, as far as I know, the origin of the PR movement (in the 1860s and 1870s, liberals gained seats disproportionately as the franchise was extended, and Conservatives looked for a fairer system to recoup their losses). And it's part of Europe, where people have experience with PR. But both the UK and the US currently elect their principal representative bodies by district-based FPTP/plurality. And so I'd like to suggest that we should be looking for a PR system which satisfies the following criteria: 1. Truly proportional (of course). I would be willing to support a not-truly-proportional system, but I'm not everyone. Egregious compromises on this issue will simply reduce the activist base, to no benefit. What is a not-truly-proportional system? That could range from being close to proportional (= only few seats difference to full PR) to being close to what the system is today in the USA (= gives one or two seats to third parties). I was thinking of things like limited vote as somewhat-proportional systems. These would be an improvement, but the activist base for these half-measure reforms is I think always smaller than that of true PR. 2. Includes a geographical aspect. People are attached to the local representation feature of FPTP, whether that's rational or not. That may well make sense also in a PR system. Proportional geographical representation is a different and separate target, not necessarily a relic. Note that SODA-PR is not perfect here. It would tend to elect about one candidate per district, but there would be a possibility that some districts would get 2 and some would get 0. 3. No closed list. A party should not be able to completely shield any member from the voters. In general, voter power is preferable to party power, insofar as it's compatible with the next criterion. 4. Simple ballots. A reasonably-thorough voter should not have to mark more than, say, 5 candidates or options, and an average ballot should not list more than 20 candidates or options. Those are extreme limits; simpler is better, all the way down to around 7 options (of which only around half will be salient and/or viable). I hope you don't assume that all the candidates must be listed on the ballot. One could have also ballots where the voters write the number(s) of their favourite candidate. That approach allows high number of candidates. Let's say that there are 100 seats. In a fully proportional system a party with more than 1% support would be entitled to one seat. If you want the voters to decide who wins instead of letting the party decide you need several candidates to choose from. Let's say that this party has 5 candidates. If other parties have similar rights to nominate candidates you could end up having e.g. 100*5 candidates. That is not an exact formula and I ignored the impact of districts, but the point is that if you want to support small parties and ability to select from multiple candidates the total number of candidates and the total number of candidates per district may grow large. Does number 20 above limit the number of candidates per district? I understand that large numbers like this are possible; that's the reason for this criterion. A system (like SODA-PR) which allows legal, useful votes for the full candidate set, but which only explicitly lists some (district-based) subset on any given ballot, would pass this criterion in my view. 5. Ideally, the smoothest transition possible. If existing single-winner districts can be used unchanged, all the better. Having both pure single-winner districts (not e.g. MMP) and full PR is possible but then you have to accept considerable inaccuracy in electing the most liked candidate in each district. I guess what you are looking for is a good balance between these incompatible (but positive) requirements. Maybe this is one reason why you would accept also less than perfect PR. I said I'd personally accept it, but it's not what I'm looking for in this thread. But yes, it's a balancing act here. 6. Insofar as it's compatible with the criteria above, greater freedom in voting is better. For instance, if ballots are printed with only in-district candidates, a system which allows out-of-district write-ins is better than one which doesn't, all other things being equal. Is the old American tradition of allowing write-in candidates included in your list of requirements? No. In this case the write-in capability is a way to list fewer candidates than the full allowed set, as a way to
Re: [EM] PR for USA or UK
From: Kevin Venzke step...@yahoo.fr To: election-meth...@electorama.com Sent: Sun, 24 July, 2011 20:34:33 Subject: Re: [EM] PR for USA or UK Hello again. --- En date de : Dim 24.7.11, Toby Pereira tdp2...@yahoo.co.uk a écrit : Strategy-resistant systems do have certain advantages as you say, but in the single-winner case it would end up reducing range to a Condorcet method, which arguably isn't as good, and ends up pushing out a better-liked candidate for one that strictly more people prefer. And this is what I like about range - it's not just about which candidates you prefer to which other ones, but by how much. I think the Range method itself is pretty incapable of this, but you could do it either with rated ballots or with a rank ballot that has truncation incentive. Is a range ballot not a rated ballot? And as long as strategy isn't performed better by voters of some candidates than others, the fact that there would still be some honest voters would mean that the advantages of range would still remain to an extent, meaning that overall better-liked candidates stand a better chance, and it therefore reflects better the overall preferences of the electorate! That paragraph makes sense if you're comparing Range to Approval, but not Range to anything else. If large numbers of voters use strategy in Range (and I'm pretty sure they would be encouraged to; personally I wouldn't need any encouraging) this will destroy so much information that the only way Range will win out is if the rank methods you compare it to contain even more destructive incentives than Range has. With a single-winner election, the full strategy option is to vote approval style, but I'm not sure if this is as clear for PR. You say you wouldn't need any encouraging to vote strategically - I wouldn't either to be honest - but what is the optimal strategy? In any case, if range does turn out to be problematic, proportional approval voting would be my next choice. I don't like ranked ballots because you don't know how much the voter actually likes each candidate or whether they like them at all. Can you explain your position without saying party? Because if you didn't see the parties, and only saw voters, it would be indefensible to give a seat to the 32%. There would be nothing special about that group. Candidates A and B are both fairly similar and 68% of voters vote for both of these approval-style and no-one else. Candidates C and D are also similar to each other and 32% of voters vote for both of these approval style and no-one else. That's the example set out without parties. And it's the same as before - if 50% of the voters voted for A and B it would be exactly the right proportion (without rounding due to a specific number of seats) for one of A or B to be elected, and if 100% voted for them, it would eb exactly the right proportion for both seats. 75% is halfway. Hi Toby, Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] PR for USA or UK
From: Jameson Quinn jameson.qu...@gmail.com To: Toby Pereira tdp2...@yahoo.co.uk Cc: EM election-methods@lists.electorama.com Sent: Sun, 24 July, 2011 19:45:06 Subject: Re: [EM] PR for USA or UK I don't necessarily think sophisticated voters are required in order to ensure reasonable PR under PRV. I think as long as you don't get some candidates who have much better strategic voters than others, it should do OK. You should read some of Schulze's papers about the history of free riding. It seems clear from those examples that there are examples of parties with better or worse free-riding vote-management capabilities. So I would worry about this distorting results. OK, I might look into it. But you could probably legislate against blatant suggestions to vote in a specific way from certain parties. It would still exit unofficially with discussions online and elsewhere but anyone would have access to the information. I'm sure Warren's got an answer too. ;) Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Another approach to geographical proportionality and single-winner districts (was: PR for USA or UK)
One feature of single-winner district based political systems is that voters will have a clearly named own representative that is as local as possible. In a PR context with multiple parties one could redefine this idea so that people should have a known representative that represents them in the assembly. A two-party / single-winner district system has the problem that often the local representative is from the wrong party. The requirement could be modified so that the idea is to have a local representative of one's *own* party. With that approach we will lose some of the locality, but on the other hand we may get more natural local representatives. This kind of methods could work for example so that first the number of seats that each party gets will be determined at national level (to provide perfect proportionality between parties). The country is divided in small voting areas. We know the number of votes from each voting area to each party and the location of each voting area. (Votes are summed up in voting areas instead of using individual votes directly in order to guarantee voter privacy.) Also candidates have a location. That location could be approximate and it could be used only to indicate that the intention of the candidate is to represent certain region. Voters will then vote for the candidates. The system could allow only bullet votes or one could user ranked or rated ballots too. Then we need an algorithm that takes the votes to some party and their geographical distribution, and the geographical distribution of the votes to different candidates of the party into account. The whole country will be divided in (party specific) regions, and one candidate (of this party) will be elected in each region. Now all supporters of this party will have a single own representative of their own party. The size of the regions should reflect the density (or sparseness) of votes from that region. The size of each district would be about the same in terms of votes received from that region. One could allow also disjoint regions, but if one wants the regions not to be too fragmented, one could add some parameter that favours compact regions. One should form such a set of regions and set of representatives in them that the overall happiness of the voters (of this party) is maximized (= local representatives having local support etc.). One could develop also systems with no party structure (with ranked or rated ballots). In such systems each geographical spot could have exactly one representative. Or alternatively one could agree some (small) number of representatives that each spot should have (= layers). That would allow every voter to have a local representative from their own wing at least. Also in this approach different layers could have different regions, and the size of the regions could reflect the popularity distribution of that candidate. (Actually the layers need not be separate layers. It is enough if each representative has a region, and each geographical spot is included in the agreed number of regions. The end result so far is thus a mixture of strict political and geographical proportionality requirements, leading to electing a fixed number of representatives for each geographic spot. But of course one could still give up the idea of keeping the number of representatives per spot constant :-). One could instead optimize the number of representatives per spot so that it reflects the uniformity of opinion in each location. If some place has only small number of different opinions it could have only a small number of very local representatives, while another place (with similar population density) could have numerous but less local representatives. I guess we will keep the requirement of all representatives having in their regions about equal number of supporters to represent. One problem of systems without clear district structure and geographic proportionality is that candidates from the capital region and other major cities and television tend to become overrepresented. The discussed system above had no clear fixed district borders (although it could have) and it may allow voters to vote also distant candidates, but it may still maintain regional representation quite well (also without limiting the area where each candidate can collect votes) since individual candidates are more likely to be elected if they get their votes from a region size geographical area. I wrote this mail as a response to the PR for USA or UK mail stream, and particularly to the question how to offer good political proportionality, geographic proportionality and local representation at the same time. This model is however not a very concrete and practical proposal for the needs of that mail stream. If one looks for a practical implementations of this approach, maybe the party based approach with one party representative for each spot is closest to being a
Re: [EM] Single Contest
Jameson Quinn wrote: The ranked majority criterion is: if one candidate is top-ranked by a majority of voters, that candidate must win. To me, the natural extension of that to rated systems is: if only one candidate is top-rated by any majority of voters, that candidate must win. That must be the definition Forest is using. Thanks. Any strategic median which assigns the MaxGrade if at least 50% of the electorate rated the candidate at MaxGrade will indeed pass this criterion. You are suggesting that we use the ranked majority criterion for rated systems. If we do so, you are right that broad classes of rated systems (including range, median, and chiastic) can never pass. But if we use my definition of the criterion, then median systems pass, trivially. You are probably aware the median systems pass a stronger criterion: If for some grade X, only one candidate is rated at X or above by any majority of voters, then that candidate must win. In other words, it doesn't just have to be top-rated, it can be any grade. - Andy Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] PR for USA or UK
Hi Toby, --- En date de : Dim 24.7.11, Toby Pereira tdp2...@yahoo.co.uk a écrit : [begin quote] Strategy-resistant systems do have certain advantages as you say, but in the single-winner case it would end up reducing range to a Condorcet method, which arguably isn't as good, and ends up pushing out a better-liked candidate for one that strictly more people prefer. And this is what I like about range - it's not just about which candidates you prefer to which other ones, but by how much. I think the Range method itself is pretty incapable of this, but you could do it either with rated ballots or with a rank ballot that has truncation incentive. Is a range ballot not a rated ballot? [end quote] Sorry, I mean, I don't believe it is hopeless to try doing what you want with a rated ballot. Range does use a rated ballot. Off the top of my head I don't have any really great method suggestions here, because it seems to me to be extremely difficult to design a method so that it maximizes utility. If the method is strategy-proof, it will tend to elect the sincere Condorcet winner. If it's not strategy-proof, you can't fully trust the information you collect. Something in-between seems to be needed, but I would bet nobody will feel very happy with whatever is invented. [begin quote] And as long as strategy isn't performed better by voters of some candidates than others, the fact that there would still be some honest voters would mean that the advantages of range would still remain to an extent, meaning that overall better-liked candidates stand a better chance, and it therefore reflects better the overall preferences of the electorate! That paragraph makes sense if you're comparing Range to Approval, but not Range to anything else. If large numbers of voters use strategy in Range (and I'm pretty sure they would be encouraged to; personally I wouldn't need any encouraging) this will destroy so much information that the only way Range will win out is if the rank methods you compare it to contain even more destructive incentives than Range has. With a single-winner election, the full strategy option is to vote approval style, but I'm not sure if this is as clear for PR. [end quote] No, I have no comment on any PR versions. I wouldn't assume any similarity. You say you wouldn't need any encouraging to vote strategically - I wouldn't either to be honest - but what is the optimal strategy? I have heard and tend to agree with approve everyone better than what you expect on average the outcome to be. If there are two frontrunners with perceived-to-be equal odds of winning, that would mean approving every candidate better than the average of the two. Experimentally there usually are two frontrunners that emerge from pre-election polling. In my own simulations, the ideal strategy is determined by the voters within the specific situation they find themselves in. So it's not easy to describe what strategy they are choosing, but it must be something close. In any case, if range does turn out to be problematic, proportional approval voting would be my next choice. I don't like ranked ballots because you don't know how much the voter actually likes each candidate or whether they like them at all. Generally I have liked rank methods where voters are not thought to be supposed to rank candidates they don't really like. This may start to turn it into Approval, but with some ranking information retained. Can you explain your position without saying party? Because if you didn't see the parties, and only saw voters, it would be indefensible to give a seat to the 32%. There would be nothing special about that group. Candidates A and B are both fairly similar and 68% of voters vote for both of these approval-style and no-one else. Candidates C and D are also similar to each other and 32% of voters vote for both of these approval style and no-one else. That's the example set out without parties. Ok. It sounds like you want to represent more types of voters. The 68% cannot have both seats because they're the same type. If they were different types then it would be OK. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] PR for USA or UK
Jameson Quinn wrote: 2011/7/23 Andy Jennings electi...@jenningsstory.com On Sat, Jul 23, 2011 at 7:45 AM, Jameson Quinn jameson.qu...@gmail.comwrote: And so I'd like to suggest that we should be looking for a PR system which satisfies the following criteria: c1. Truly proportional (of course). I would be willing to support a not-truly-proportional system, but I'm not everyone. Egregious compromises on this issue will simply reduce the activist base, to no benefit. c2. Includes a geographical aspect. People are attached to the local representation feature of FPTP, whether that's rational or not. c3. No closed list. A party should not be able to completely shield any member from the voters. In general, voter power is preferable to party power, insofar as it's compatible with the next criterion. c4. Simple ballots. A reasonably-thorough voter should not have to mark more than, say, 5 candidates or options, and an average ballot should not list more than 20 candidates or options. Those are extreme limits; simpler is better, all the way down to around 7 options (of which only around half will be salient and/or viable). c5. Ideally, the smoothest transition possible. If existing single-winner districts can be used unchanged, all the better. c6. Insofar as it's compatible with the criteria above, greater freedom in voting is better. For instance, if ballots are printed with only in-district candidates, a system which allows out-of-district write-ins is better than one which doesn't, all other things being equal. I'm interested both in systems which satisfy 2 and those that don't. If we could identify a good, truly proportional, at-large system, then a state with a bicameral legislature (like Arizona) could leave one house as geographical and change one to be at-large proportional. I agree that if you were designing a democracy from scratch, non-geographical systems deserve attention. My purpose here is to support a system or systems that have some chance of passage in the US or UK. In my experience, that means that activists should unify behind a system which represents a minimal change. Whatever reform you propose will have opposition, both from people who are honestly and naturally skeptical of anything new, and from whichever major party currently benefits from the distortions of the current system. It's better to push a smaller reform which gives such people fewer arguments to use against you, than a more-complete one which can never pass. That's why I included criteria 2 and 5, and I stand behind them. This same argument applies to Kathy Dopp's suggestion that states like AZ could have their bicameral legislatures function using one PR body and one geographical body. It's a great idea, and I'd happily and enthusiastically support it; but it's a more-radical reform, so I think something which meets my criteria would be more attainable. At least, I'd like to settle on something which meets my criteria, so that if I'm right, we still have a chance. Agree on both counts, but I live in AZ so the bicameral option doesn't seem so radical. :) My proposal for SODA-PR satisfies and surpasses all 5 criteria. Other systems which do reasonably well: -I've seen a proposal for single-member districts and open party lists. This is similar to my SODA-PR system, except that it requires that all candidates in a party approve the same party set. As such, it is strictly worse on criterion 3, without being notably better on any of the other criteria. It is more conventional, though. -Multimember districts, with some system inside each district. -Mixed member systems. We should add Fair Majority Voting, by Balinski. ( http://mathaware.org/mam/08/EliminateGerrymandering.pdf) Here's the summary: Parties run one candidate in each district and voters vote for one candidate in the race in their district. The votes are totaled nationwide by party and an apportionment method is used to decide how many seats each party deserves. Each party is assigned a multiplier and the winner in each district is the one whose (vote total times party multiplier) is highest. The multipliers can be chosen so that the final total seats won by each party matches the number of seats assigned by the apportionment method. It definitely satisfies your criteria 1,2,4, and 5. I'd say it mostly satisfies 3. Don't know how to evaluate 6. The main thing I don't like about it is that it conflates voting for a candidate with voting for his party. What if I like the candidate but not the party, or vice versa? But since so many things in the legislature happen on a party basis, I've decided that this is not as bad as it first seems. FMV is equivalent to the single-member districts and open party lists system I was talking about, although I remember seeing it under some different name (some two-letter acronym with a U, I seem to recall). In the end, FMV can be
Re: [EM] Automated Approval methods (was Single Contest)
This kind of approach has been experimented with for a long time by Rob LeGrand, and there doesn't seem to be any good way to make it monotone. Here's a very conservative and simple approach that may have some value in some context, if not this one: For each rating ballot b approve the top N candidates where N is the (rounded) sum of the ballot b ratings of all of the candidates divided by the maxRange value Let S be the sum over candidates X of the ballot ratings b(X) . Then N is S divided by maxRange, rounded to the nearest whole number (or rounded to even when exactly halfway between floor and ceiling of S/maxRange). The N highest rated candidates on ballot b are approved. If these approvals are used to elect an approval winner, the method is montone and as clone free as possible for automated approval. (It can split clone sets at the approval boundary on a ballot). Here is a possible heuristic for the method: If the ballot b ratings are normalized (by dividing by maxRange) and taken to represent probabilities, so that b(X) is the probability that candiadte X would correctly represent the ballot b voter on a random question, then the sum S is the expected number of candidates that would agree with this voter on a random question. So why not approve the top S voters, since they are the most likely to be the ones that would agree with the voter? Note that this is a zero information strategy, and for all I know, it could well be zero-info-optimal by some criterion or other. The usual zero info strategy is to assume that all of the candidates are equally likely to win, and to approve above expectation on that basis, but the insertion of lots of clones can radically change those probabilities. This kind of reminds me of the rule that Kristofer suggested for how many winners there should be in a PR election when that number hasn't been decided ahead of time. Date: Sun, 24 Jul 2011 20:01:48 +0100 (BST) From: Kevin Venzke Hi Kristofer, --- En date de?: Dim 24.7.11, Kristofer Munsterhjelm a ?crit?: I also tried implementing the most obvious (I suppose) method: Take the ratings and conduct simulated approval polling, either for some determined or semi-random number of iterations, or until someone wins twice in a row. This doesn't test as well as I thought it would though. What Approval strategy do you use? I always use better than expectation when it is allowed to assume the voters know the method is approval. (Which is just to say that the main sim, when during pure Approval, can't use better than expectation.) I put a tiny amount of average utility of all candidates into the expectation just to try to avoid the situation where your favorite won all the polls so therefore you don't approve him. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] [COVoterChoice] RB gives an equal chance of winning to not just all parties, but all combinations of programs,
I assume this is from Colorado, and have no idea who else has seen it. I see it as worth considering the thinking, although I AM NOT signing on as backing any of it. On Jul 23, 2011, at 11:32 PM, Dave Ketchum wrote: Knowing of IRV and Condorcet methods of counting ballots, the first paragraph below makes me wonder how valid the the author's claims may be. The very last few lines help. . STV - not used here - THANKS . Condorcet - also not used here - think more whether this is better. On Jul 23, 2011, at 3:59 PM, preferentiality wrote: Ranked Ballot (voters ranking candidates in order of preference) will give us (PRACTICABLE!) Instant TRUE Democracy for ALL the World, even put an end to all war forever. Because it gives an equal chance of winning to not just all parties, but all combinations of programs, “RB” is the only thing that’s truly both just free. Because it always elects the candidate most exactly in the middle of all voting, RB is top-dead-center counter extremist, thus more anti-terrorist than all the many recent retrenchments combined thus will even disallow the tendency of (virtually two- party) parliamentary systems to give the top to the biggest gang on the block, sometimes with violently extremist results. Worth reading more - I am not buying the author's claims of achieving perfection. There are many topics for which more than two possible choices seem worth debating possible value. Dave Ketchum RB is the sole unchangeable plank bylaw of a Ranked Ballot Party, the only practicable third party.) We imagine running on the single issue of RB, promising a citizens’ advisory board based on Organized Communications, “OC”, small randomly assigned discussion groups electing reps to higher higher randomly assigned levels, by means of RB, ‘til one small group, most exactly in the middle of all voting, remains at the top, to guide us in the rest, which group by its merest invitation to speak inevitably names the perfect compromise next winner That’s the instant part. You do the same, from the most local on up. By the power of its example alone, RB will give us practicable instant worldwide true democracy. Virtually no democracy has ever been attacked by another. In a world of only democracies, there would no longer be need of the counter-productive wastefulness of armies, war or the preparation for war. RB will bring us that all else: a real solution to terror, a perfect marriage of Freedom Justice, Tradition Modernity, Palestinian Jew, Free Market Communalism, all the fairness, payback make-up one could wish for, clean back to the Cro- Magnons, ecologically sustainable politics, what’s best for all workers, instant global women’s liberation, world-wide luxury, a rationalization of the drug wars, human unity, the Freedom of Justice the Justice of Freedom, perhaps the only possible solution to the world’s only real problem, the Israeli/Palestinian conflict (once they both are made to have to adopt RB), even integrity. RB is to the horse buggy two-party system as shopping in the Mall of America is to shopping in Soviet Russia. The majority of the problems we face are due to the heavy-footedness of the two party system. RB lessens the power of the extremes, whether authoritarian, economic or sectarian, except through what they can gain by persuasion, which is only what’s just. While it would be equally useful for all else, RB’s real power is perhaps most clearly shown in the case of Iraq. Unless its Parliament comes to select the Prime Minister by means of RB, it may not hold the country, region world will be in danger of going to war over some ancient grudge, oil well, multi-ethnic city, or sabotaged pipeline. While the new constitution does call for the selection of the President by a 2/3 vote in the first round (even if only by the parliament not the people) (who may then decide who will form the new government) then by a run-off between the top two vote getters in the second round, if that fails to move all three tribes to nominate centrists, then the resulting handful of old men in a back room will fall far short of RB’s ultimate retail politics. RB would be equally useful for all electoral systems (parliamentary or presidential, the parliaments choosing their PMs by RB from among their members, lest they produce another Hitler or other extreme) coops, collective leaderships, tribal groupings, religious confessions, political parties, associations or, even cabals. Whoever gets there first wins. For leaders to best represent their country, or district, whether chosen at large or by a representative body, they must be the perfect compromise, most exactly in the middle, as is given by RB. Yet because it gives minorities a real say in which member of the plurality/majority gets chosen, RB is the only thing that will lead Iraqis, or anyone else, to support any plan more than inadequate
Re: [EM] Weighted voting systems for proportional representation
On Sun, Jul 24, 2011 at 4:53 AM, Kristofer Munsterhjelm km_el...@lavabit.com wrote: Ah, yes. This leads me back to an older thought that perhaps the criterion of summability should be refined for multiwinner methods by turning it into two criteria. These criteria would be: - Weak summability: If the number of seats is fixed, one can find the winner of the method according to precinct sums, where the amount of data required for these sums grows as a polynomial with respect to the number of candidates, and as a polylogarithmic function with respect to the number of voters. - Strong summability: Same as weak, but without the number of seats being fixed or known in advance. To my knowledge, Schulze STV is weakly summable, as is this method, because if you fix S, N choose S is bounded by a polynomial. When people here talk about summability for multiwinner methods, they usually mean strong summability, though. This is like SNTV or party list. If you have the Plurality counts for SNTV, it doesn't matter how many seats you want, you can just read off the n first Plurality winners. Similarly, for party list, you can just run the Sainte-Laguë method n times for n seats with the same input data. Do you think weak summability is sufficient to audit multiwinner methods? Your definitions do not differentiate between the enormous difference between the difficulty of summing STV vs. the far more summable voting method you were proposing! That is an enormous difference - regardless of whether the number of seats is known in advance or not. I was only considering contests where the # of seats are known in my remarks. Thus, I do not think that your definitions are sufficient for evaluating methods. -- Kathy Dopp http://electionmathematics.org Town of Colonie, NY 12304 One of the best ways to keep any conversation civil is to support the discussion with true facts. Fundamentals of Verifiable Elections http://kathydopp.com/wordpress/?p=174 View some of my research on my SSRN Author page: http://ssrn.com/author=1451051 Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] [COVoterChoice] RB gives an equal chance of winning to not just all parties, but all combinations of programs,
Hi, --- En date de : Dim 24.7.11, Dave Ketchum da...@clarityconnect.com a écrit : De: Dave Ketchum da...@clarityconnect.com Objet: Re: [EM] [COVoterChoice] RB gives an equal chance of winning to not just all parties, but all combinations of programs, À: electionscience Foundation electionscie...@googlegroups.com Cc: preferentiality preferential...@gmail.com, EM election-methods@lists.electorama.com Date: Dimanche 24 juillet 2011, 19h42 I assume this is from Colorado, and have no idea who else has seen it. I see it as worth considering the thinking, although I AM NOT signing on as backing any of it. I have trouble finding any description in the post. I wonder if RB is intended to mean Random Ballot (RB) as the message subject would almost make sense in that case. Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Automated Approval methods (was Single Contest)
Hi Forest, --- En date de : Dim 24.7.11, fsimm...@pcc.edu fsimm...@pcc.edu a écrit : This kind of approach has been experimented with for a long time by Rob LeGrand, and there doesn't seem to be any good way to make it monotone. Yes, but if it were strategy-free somehow, I think it would be worth it. Real life isn't monotone. I don't imagine that all the prettier Yee diagrams would really look like that if voters were using information and strategy! No time to say more... Kevin Venzke Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] PR for USA or UK
On Jul 24, 2011, at 5:01 PM, Toby Pereira wrote: From: Kevin Venzke step...@yahoo.fr ... I think the Range method itself is pretty incapable of this, but you could do it either with rated ballots or with a rank ballot that has truncation incentive. Is a range ballot not a rated ballot? well, i don't know precisely what is meant by a rated ballot, but Range or Score Voting is not the same as the *ranked* ballot nor really a subset of it. i guess any score ballot can default to a ranked ballot, where the candidate ranks are listed in the same order as the candidate scores. but Range or Score requires more information than the ranked ballot. and i don't think voters would be entirely consistent between the two types of ballots. it might be that a voter thinks that both Candidates B and C are scum (compared to A) and would score B and C at 0 with A at 10 whereas, since the ranked ballot, if the voter thinks that B, while scum, is preferable to C and they might rank B higher than C, which doesn't hurt A at all. whereas with score, bumping B up from 0 to 1 (or anything non-zero) to express the voters preference of B to C will numerically hurt this voters preference of A to B. i have to admit, i don't like Score voting (i still don't see any of the single-winner alternatives beating Condorcet, for the most part). i think, while requiring more precise information from the voter than with the ranked ballot (how much more do you prefer A over C than do you prefer A over B?), i think it can lead a voter to act, to vote in a less expressive way than with the ranked ballot. and i think that if voters (especially those that hate IRV and the ranked ballot) will use their Score ballot like a traditional ballot, except for the scaling. that voter will give the single candidate of their choice a 10 and all other candidates a 0. that becomes like a First-Past-The- Post election. -- r b-j r...@audioimagination.com Imagination is more important than knowledge. Election-Methods mailing list - see http://electorama.com/em for list info
