Re: [EM] Amalgamation details, hijacking, and free-riding
Well, kinda; but in a sense, that pushes the strategy into the tree-building. 2011/8/6 Juho Laatu juho4...@yahoo.co.uk On 4.8.2011, at 2.09, Jameson Quinn wrote: Free riding in some form is inevitable in a good system. (That is, any system which avoids free riding entirely would be horribly warped by that necessity). How about tree methods? If candidates are ordered as a binary tree (instead of an open list), then there are no choices between three or more branches, and related free riding becomes impossible. Juho 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] Amalgamation details, hijacking, and free-riding
Tree building could be voluntary or mandatory. If voluntary, then parties and wings can stop free riding in their own area. If mandatory, then the most difficult part is to organize the parties as a tree (= party external tree). One should have rules on how to build a tree also in the case when there is no consensus on what the structure of the tree should be. One simple approach would be to allow the already agreed (= voluntary) binary branches (= trees of a forest) to join themselves (or the bigger trees that they are already part of) into other trees of the forest in random order. Or maybe largest ones first into the largest tree, starting from the third largest, after joining the two largest ones together first. I assumed that the voluntary branches (that were agreed already before the forced phase) would be considered atomic (= no joining inside them). Did you mean that there would be concrete strategic opportunities in the tree-bulding phase, or that one just needs to think a bit on how to form the tree or how to force the tree to be formed? Sincere strategy seems quite good to me. Or maybe one could nominate fake parties next to one's strongest competitors in the hope of making some of the voters of the competing party vote for the wrong party (that could get a seat if many enough voters make that mistake). Juho P.S. I might come back with a proposal of considering trees to be a good method that is simple and understandable to the voters, very strategy free, and even close to but better than plurality. On 6.8.2011, at 10.46, Jameson Quinn wrote: Well, kinda; but in a sense, that pushes the strategy into the tree-building. 2011/8/6 Juho Laatu juho4...@yahoo.co.uk On 4.8.2011, at 2.09, Jameson Quinn wrote: Free riding in some form is inevitable in a good system. (That is, any system which avoids free riding entirely would be horribly warped by that necessity). How about tree methods? If candidates are ordered as a binary tree (instead of an open list), then there are no choices between three or more branches, and related free riding becomes impossible. Juho 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] Amalgamation details, hijacking, and free-riding
- Original Message - From: Jameson Quinn Date: Wednesday, August 3, 2011 4:10 pm Subject: Re: Amalgamation details, hijacking, and free-riding To: fsimm...@pcc.edu Cc: election-methods@lists.electorama.com 2011/8/3 So if the true preferences are 20 AB 45 C? 35 (something else), the C supporters could spare 21 voters to vote AC so that the amalgamated factions would become 41 AC 24 C? 35 (something else) . I can see where it is possible for such a move to payoff, but it seems fairly innocuos compared to other strategy problems like burial, compromising, chicken, etc. Not to me. I would be livid to find out my vote had been hijacked. All the other strategies you mention at least use a voter's own vote. Highjacking sounds bad, but it is just one form of over-riding votes. At least it doesn't over-ride your first place preference like the compromising incentive twists your arm to do. Every method eventually over-rides various preferences at some point in the process. Compromising is a form of extortion that blackmails you into expressing a false preference. That's the most egregious form. In other words, compromising forces you to either lie or lose. If somebody else highjacks, they lie to take advantage of you, but with much more risk than the liar who buries to take advantage of the CW supporters. For this kind of highjacking to work, the highjacking faction would have to have more than three times the support of the highjacked faction, as can be seen from the above example (which lacking that much support in the hijacking faction gives an obvious first place advantage to A). That kind of superiority is more than enough to over-ride pairwise wins in ranked pairs, river, beatpath, etc. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Amalgamation details, hijacking, and free-riding
2011/8/4 fsimm...@pcc.edu - Original Message - From: Jameson Quinn Date: Wednesday, August 3, 2011 4:10 pm Subject: Re: Amalgamation details, hijacking, and free-riding To: fsimm...@pcc.edu Cc: election-methods@lists.electorama.com 2011/8/3 So if the true preferences are 20 AB 45 C? 35 (something else), the C supporters could spare 21 voters to vote AC so that the amalgamated factions would become 41 AC 24 C? 35 (something else) . I can see where it is possible for such a move to payoff, but it seems fairly innocuos compared to other strategy problems like burial, compromising, chicken, etc. Not to me. I would be livid to find out my vote had been hijacked. All the other strategies you mention at least use a voter's own vote. Highjacking sounds bad, but it is just one form of over-riding votes. At least it doesn't over-ride your first place preference like the compromising incentive twists your arm to do. Every method eventually over-rides various preferences at some point in the process. Compromising is a form of extortion that blackmails you into expressing a false preference. That's the most egregious form. In other words, compromising forces you to either lie or lose. If somebody else highjacks, they lie to take advantage of you, but with much more risk than the liar who buries to take advantage of the CW supporters. For this kind of highjacking to work, the highjacking faction would have to have more than three times the support of the highjacked faction, as can be seen from the above example (which lacking that much support in the hijacking faction gives an obvious first place advantage to A). That kind of superiority is more than enough to over-ride pairwise wins in ranked pairs, river, beatpath, etc. This is only true if you define the hijacking faction in terms of the ultimate beneficiary, the winner. But a minor faction could hijack another minor faction to shift the frontrunner. I agree, it's unlikely. But the very possibility, to me, rankles more than the average strategy. In fact, I suspect it would open the process to legal challenges. Anyway, I don't see why it's necessary. All it gains you is summability; which is nice, but in the age of fast data pipelines it is not a necessity. JQ Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Amalgamation details, hijacking, and free-riding
So if the true preferences are
20 AB
45 C?
35 (something else),
the C supporters could spare 21 voters to vote AC so that the amalgamated
factions would become
41 AC
24 C?
35 (something else) .
I can see where it is possible for such a move to payoff, but it seems fairly
innocuos compared to other
strategy problems like burial, compromising, chicken, etc.
In any case, it can only be a problem in methods that forget the ratings after
the amalgamation and use
only the rankings (like DSC), because when two candidates are rated closely a
small hijacking effort
could tip the balance and reverse the ranking of the two candidates in question.
On the free rider problem of some PR methods, what do you think about the
following?
Because of its free riding problem Plurality is a fairly decent PR method in
a perfect information
setting, as long as voters agree to randomize in order to take advantage of the
free riding effect. For
example in a three winner election where the voter preferences are
60 A1A2
25 B
15 C
If the A supporters agreed to toss coins and vote A! or A2 in the case of heads
or tails, respectively,
then the winning slate would be {A1, A2, B}, the best possible outcome in this
case.
So, in at least one PR method, the free-riding possibilities are essential
for the fairness of the method.
In fact, that is the basic principle of Asset voting (for PR); the candidates
share their assets so that
none will be wasted unnecessarily. Whether the voters or the candidates do the
redistribution doesn't
natter in the perfect info case.
In the zero info case, free-riding doesn't work, so it can neither harm nor
help.
So, I don't worry too much about it.
From: Jameson Quinn
OK, that's what I thought. So, candidate hijacking does not work
for any
amalgamated ballot blind method, that is, a method which
forgets which
rating came from which ballot. However, on a non-ballot-blind system,
including the ranking-based DSC which was the next step in your
SODA-inspired sequential play method, it can work. Basically,
it involves
finding a faction a bit smaller than yours, and ranking its favorite
candidate first. Since your faction is larger, you will be able
to set the
ranking of the remaining candidates, and you will gain the
ballot weight of
the smaller faction. Of course, you must be sure that the false flag
candidate does not win. This is similar to Wodall free riding in PR.
JQ
2011/8/1
To amalgamate factions so that there is at most one faction
per candidate X
(in the context of range
style ballots) take a weighted average of all of the ballots
that give X
top rating, where each ballot has
weight equal to one over the number of candidates rated equal
top on that
ballot. The total weight of the
resulting faction rating vector for candidate X is the sum
of the weights
that that were used for the
weighted average.
Note that these faction rating vectors are efficiently
summable. A running
sum (together with its weight)
is kept for each candidate. Any single ballot is incorporated
by taking a
weighted average of the running
sum and the ballot, where the respective weights are those
mentioned above.
For the running sum it is
the running sum weight. For the ballot it is zero if the
candidate is not
rated top, and 1/k if it is rated top
with (k-1) other candidates..
To combine two running sums for the same candidate take a
weighted average
of the two using the
running sum weights, and then add these weights together to
get the
combined running sum weight.
If you multiply each faction rating vector by its weight and
add up all
such products, you get the vector of
range totals.
Of course Range as a method is summable more efficiently without
amalgamating factions, but other
non-summable methods, when willing to accept amalgamated
factions, thereby
become summable.
So, for example, we can make a summable form of Dodgson:
(1) Use ratings instead of rankings.
(2) amalgamate the factions.
(3) let each candidate (with help from advisors) propose a
modification of
the ballots that will created a
Condorcet Winner.
(4) the CW that is created with the least total modification
is the winner.
Modifications are measured by how much they change the ratings
on how many
ballots.
For example if you change X's rating by .27 on 10 of the 537
ballots of one
faction, and by .32 on 15
ballots from another faction, then the total modification is
2.7 + 4.8 =
7.5
The reason for the competition is that otherwise the method
would be
NP-complete.
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Amalgamation details, hijacking, and free-riding
2011/8/3 fsimm...@pcc.edu
So if the true preferences are
20 AB
45 C?
35 (something else),
the C supporters could spare 21 voters to vote AC so that the amalgamated
factions would become
41 AC
24 C?
35 (something else) .
I can see where it is possible for such a move to payoff, but it seems
fairly innocuos compared to other
strategy problems like burial, compromising, chicken, etc.
Not to me. I would be livid to find out my vote had been hijacked. All the
other strategies you mention at least use a voter's own vote.
In any case, it can only be a problem in methods that forget the ratings
after the amalgamation and use
only the rankings (like DSC), because when two candidates are rated closely
a small hijacking effort
could tip the balance and reverse the ranking of the two candidates in
question.
On the free rider problem of some PR methods, what do you think about the
following?
Because of its free riding problem Plurality is a fairly decent PR method
in a perfect information
setting, as long as voters agree to randomize in order to take advantage of
the free riding effect. For
example in a three winner election where the voter preferences are
60 A1A2
25 B
15 C
If the A supporters agreed to toss coins and vote A! or A2 in the case of
heads or tails, respectively,
then the winning slate would be {A1, A2, B}, the best possible outcome in
this case.
So, in at least one PR method, the free-riding possibilities are
essential for the fairness of the method.
In fact, that is the basic principle of Asset voting (for PR); the
candidates share their assets so that
none will be wasted unnecessarily. Whether the voters or the candidates do
the redistribution doesn't
natter in the perfect info case.
In the zero info case, free-riding doesn't work, so it can neither harm nor
help.
So, I don't worry too much about it.
Free riding in some form is inevitable in a good system. (That is, any
system which avoids free riding entirely would be horribly warped by that
necessity). So it's a problem to be managed, not avoided. Still, to me it is
worth some thought. I'm not so much worried about successful free
riding/vote management, as about the pernicious effects of failed
strategies. A system should aim to be good enough that most voters do not
bother voting dishonestly in an attempt at free riding. STV is not always
good enough in that sense, but I think that there are systems which are
better. In the end, it's an empirical question.
JQ
From: Jameson Quinn
OK, that's what I thought. So, candidate hijacking does not work
for any
amalgamated ballot blind method, that is, a method which
forgets which
rating came from which ballot. However, on a non-ballot-blind system,
including the ranking-based DSC which was the next step in your
SODA-inspired sequential play method, it can work. Basically,
it involves
finding a faction a bit smaller than yours, and ranking its favorite
candidate first. Since your faction is larger, you will be able
to set the
ranking of the remaining candidates, and you will gain the
ballot weight of
the smaller faction. Of course, you must be sure that the false flag
candidate does not win. This is similar to Wodall free riding in PR.
JQ
2011/8/1
To amalgamate factions so that there is at most one faction
per candidate X
(in the context of range
style ballots) take a weighted average of all of the ballots
that give X
top rating, where each ballot has
weight equal to one over the number of candidates rated equal
top on that
ballot. The total weight of the
resulting faction rating vector for candidate X is the sum
of the weights
that that were used for the
weighted average.
Note that these faction rating vectors are efficiently
summable. A running
sum (together with its weight)
is kept for each candidate. Any single ballot is incorporated
by taking a
weighted average of the running
sum and the ballot, where the respective weights are those
mentioned above.
For the running sum it is
the running sum weight. For the ballot it is zero if the
candidate is not
rated top, and 1/k if it is rated top
with (k-1) other candidates..
To combine two running sums for the same candidate take a
weighted average
of the two using the
running sum weights, and then add these weights together to
get the
combined running sum weight.
If you multiply each faction rating vector by its weight and
add up all
such products, you get the vector of
range totals.
Of course Range as a method is summable more efficiently without
amalgamating factions, but other
non-summable methods, when willing to accept amalgamated
factions, thereby
become summable.
So, for example, we can make a summable form of Dodgson:
(1) Use ratings instead of rankings.
(2) amalgamate the factions.
(3) let each
