At 01:24 PM 4/25/2010, Kevin Venzke wrote:
Hi Abd,
--- En date de : Dim 25.4.10, Abd ul-Rahman
Lomax <a...@lomaxdesign.com> a écrit :
> That's right. But until utility analysis started to be
> done, the arguments had practically no foundation, they were
> just ideas about what democracy should look like, sometimes
> intuitions, and sometimes quite deceptive. Some criteria may
> be positively harmful, and Later No Harm is one of those. No
> method that maximizes utility can satisfy Later No Harm, no
> method that finds the best compromise winner can satisfy
> it.
I don't understand your terminology. Does "maximize utility" mean pick
the best winner every time, or does it just mean the method that comes
closest to doing this on average?
Fair enough, I'll need to express some
definitions, and I'm going to keep it simple, and
define a UM criterion, Utility-Maximizing. The UM
ballot allows the expression, for each candidate,
of some fraction of a full vote, i.e., each
candidate receives a vote in the range of 0-1
vote. A "sincere UM ballot" is one in which every
preference expressed is real, i.e., if the vote
for one candidate is greater than a vote for a
second candidate, then the voter actually prefers
the first candidate to the second. However, the
reverse is not necessarily true. If a voter
prefers a candidate to another, it is possible
that the voter chooses to vote the same fraction
for them. I will assume, however, that the ballot
allows the voter to express all preferences if
the voter so chooses. (So it is, at a minimum, a Borda ballot).
A "UM ballot equivalent" is a ballot from another
system translated to a UM ballot without
violating the assumptions of the UM ballot and
without creating discriminatory information not
present on the other system's ballot. Example would be:
Plurality: One candidate, 1 full vote, all other candidates 0 vote.
Borda: For N candidates, ranked, a vote of 0 for
the lowest ranked candidate, 1 for the highest,
and fractions of 1(N-1) stepwise for each in
order of preference. (Unaddressed: what if the
voter does not rank all candidates?)
Range is a UM ballot intrinsically. (This includes Approval)
Ranked methods without approval cutoff: Borda equivalent.
Ranked methods with approval cutoff: ranks
assigned are distributed equally across the range
of 1/2 vote to 1 full vote for candidates
approved, and across the range of 0 to 1/2 vote
for candidates disapproved, but not 1/2 vote.
(i.e., if there are two disapproved candidates,
and if a preference is expressed, the most
disapproved would be assigned 0 vote and the
preferred one would be assigned 1/4 vote. If
three, the votes assigned would be 0, 1/6, 2/6,
etc. (unranked candidates are assigned 0 vote,
note that this, however, is "equal ranking."
Which is frequently allowed in methods that
supposedly don't allow equal ranking.)
A voting system satisfies the UM Criterion if it
never chooses a candidate with a sum of votes on
a UM ballot equivalent to the ballot used by the
voting system, who has a lower sum of votes than
the maximum among the candidates.
Plurality satisfies the UM Criterion because it
does not allow the expression of other
preferences, and, note, it must be this way
because Range can be voted this way, if the voter
has a preferred candidate. I.e., the equivalent
of a Plurality ballot can be cast in Range, and
if all voters do this, Range will provide a Plurality result.
Either way isn't it just *one* method?
I could believe that that method doesn't satisfy LNHarm, but it would be
hard to demonstrate that that method was the big winner.
"Method" the "big winner"? For the Later No Harm
thing, it's quite enough that no ranked method
satisfying Later No Harm -- which only applies to
ranked methods or other methods allowing voting
for multiple candidates while expressing a
favorite -- cannot satisfy the Condorcet
Criterion, not to mention the UM Criterion.
> And no method that maximizes social utility, overall
> satisfaction, can satisfy the majority or condorcet
> criteria, as fundamental as they seem, when only a single
> ballot is used. They can by using a second ballot to ratify
> (or reverse) an original election that finds the utility
> maximizer.
When we analyze methods we will usually assume that voters don't change
their positions between rounds, and the same voters vote in both rounds.
Which was, certainly, a simplifying assumption
which completely neglects the reality of voting in multiple ballots.
(1) It's a different set of voters, usually.
(2) They change their minds, based either on the
first results, or on new information, or both.
By making this assumption, the analyst is tossing
aside the reasons given in Robert's Rules of
Order for holding repeated balloting instead of
election by plurality or deterministic preferential voting.
It's hard for me to imagine what approach could be used to show the
utility advantage of multiple rounds.
It's obvious, actually, but it depends on the
polling method used. Note that Range voting,
Warren Smith showed, isn't ideal because of
normalization error, assuming that voters
normalize to a full power vote, and that Range
with top two runoff actually had superior
performance. That's because, I assume, voters
renormalized to the candidate set.
And that's only the start of it. Voter turnout
depends on preference strength over the candidate
set, so turnout modifies even Range votes to
express those with higher preference strength,
and I doubt that Warren simulated this. It's
highly likely that differential turnout in runoff
voting shifts results toward what would have been
the Range winner with sincere ballots in the primary.
> Not necessarily. Suppose I have a favorite I rate at 10.
> But there is another candidate who is really almost as good,
> and, in fact, this candidate I rate at 9 is better than I've
> every experienced being elected. Am I harmed if my lower
> ranked vote for the 9 causes the election to complete for
> this candidate, whereas without my vote perhaps it was a tie
> and it went to a runoff between the 9 and the 10? And did my
> adding that other vote actually "harm" my candidate, or did
> it merely reduce my support for the candidate?
Unless you want to invent new terminology, then yes, you are "harmed"
when your 9 vote moves the win from the 10 candidate to the 9 candidate.
I don't know what the practical difference is between "harming" your
10 candidate and "reducing your support thereby making him lose."
Absolutely, this is the way "harm" is used.
However, socially, it's bogus. I have a value to
finding a compromise, and, in real election
terms, I'd be thrilled to see my 9 elected!
I didn't make him lose, I, in fact, gave him
support toward winning. Just not maximum support,
focused between him and the 9. Pure ranked
methods allow me to exert maximum vote strength
between all pairs of candidates, typically, as if
my utility difference was maximum, full strength,
between all pairs. What Range does is to require
me to limit my voting power to a *sum of vote strengths* equal to one vote.
No, I didn't make him lose, the rest of the
voters did! I voted to prefer my favorite and, in
Range, gave him a tenth of a vote over his nearest competitor.
The reason we expect that to be bad is that if next time you choose
not to rank the 9 candidate, you could let your 0 candidate win, which
isn't what we want because we (the scenario designers) know that you
actually did have a compromise choice.
Who should have the choice, voting system
designers or voters? Yes, I could choose not to
rank the 9 candidate, but get sensible! My
preference strength between that candidate and
the 10 is practically nil. (I'm sort of amazed at
voting scenarios, I've seen at FairVote, where
many voters prefer A to B, 100 to 99 rating. And
then along comes somebody who thinks very
differently and rates A 0 and B 100, and B wins
the election and supposedly the A voters are
Shocked! Shocked! How could such a massively preferred favorite lose?
But in fact, A was not "massively preferred," but
was "maximally weakly preferred," within the
Range 100 system in which those voters were
voting. If they voted that way, they were saying,
in effect, "It's really no big deal to use which
is elected, A or B, so we will leave the election to people who care more."
And that is how people really make decisions in functional societies.
I guess your response would be "maybe the 9 candidate sucked." Maybe,
but we don't know, and I tend to think that in general, compromise
choices provide better utility than flank candidates.
Sure. If we assume that left and right candidates
are on some issue scale, and that voters have
positions on that scale, and that relative
utility for two candidates has to do with
relative distance from the voter to each
candidate, then a candidate near the median
position will very likely maximize overall
utility. But, of course, it's not always that simple.
A lot of study of "strategic voting" in Range has
been mangled through the assumption of
contradictory conditions: i.e., a voter
supposedly has little difference in utility
between two candidates, but "exaggerates" by
expanding the Range distance between them. I.e,
supposedly the voter would "sincerely" rate one
candidate at 10, and another at 9, but instead votes 10 and 0.
What I wonder in a situation like this is why the
voter bothers voting at all! If the voter
believes that the only realistic possibilities
are the 10 or the 9, then *of course* the voter
will normalize to the realistic candidate set.
Tell me, which would you prefer, and how
strongly, $1000 or $900? If you knew that the
only likely choices were those two, would you, in
a vote, put 1 vote on the $1000 and 0.9 vote on the $900?
Only if there were, say, three realistic choices,
and you have zero knowledge as to which one may
prevail, would you vote 1.0 and 0.9.
But both votes are sincere, since preference has
not been reversed. Only with a new and not really
well-defined meaning for "sincere vote" was it
possible to assert that they were insincere.
(And, then, suppose that the two most likely
outcomes, by far, are the $900 and $0. Would you
vote, then, $1000 and $900. Maybe. More likely,
you'd be thrilled to get the $900 so you would vote 1.0, 1.0.)
> The goal of voting systems is to find a social compromise,
> and to fulfill that goal the favorites of many voters,
> sometimes even a majority of voters, must be "harmed," if we
> think not being elected is a harm.... Compromise is
> essential to community decision-making, and it always
> involves this kind of "harm." What a Later-No-Harm method
> does is to protect the voter from "harming" a candidate by
> taking the candidate out in back and shooting him. And then
> the method comes back to the voter and says, "Now that it
> won't harm your candidate, may he rest in peace, who else
> would you like to vote for?"
That's IRV.
You got it.
Most of the LNHarm methods don't eliminate candidates, the
particularly interesting ones being DSC and MMPO. (DSC gradually "rules
out" candidates but this isn't a prerequisite for counting lower prefs.)
Well, I'd like to see it. If I reveal some
preference for a lower ranked candidate, at all,
I don't see how this could never "harm" my
favorite under all conditions.... But I suppose
there are lots of things that exist that I don't see.
> However, sauce for the good is
> sauce for the gander. If the method hadn't taken my favorite
> out back, if my favorite remained in the race, the method
> can still come to me and say, "is there anyone else
> acceptable to you?" And while my answer might "hurt" my
> favorite, on the other hand, the answers of others might
> "help" my favorite. My answer only has the possibility of
> "hurting" if my candidate wasn't going to win without
> additional votes.
However, if my answer might harm my favorite, and I think other voters
may help my favorite, then I could conclude that I shouldn't risk harming
him.
You could. Wouldn't it depend on the severity of
the risked harm? This is why thinking in terms of
"harm" to candidates instead of to voters
misleads us. If my real utilities are 1.0 and 0.9
(and these mean low preference, quite low, I
rarely see such low preference in real elections,
at the high end), my "candidate" might be
"harmed" (and in systems where a candidate has to
seriously bust himself or herself to get elected,
it can sure seem that way), but the harm to me is
small, and my own voting is based on my own sense
of harm. I very much doubt that I would ever
regret voting 1.0, 0.9, from seeing the 0.9 be elected.
> > He could (depending on many factors, reasonably
> or
> > unreasonably) withhold lower preferences as a result,
> which means less
> > sincere voting.
>
> No. This is a very common error. One withholds lower
> preferences because the preference strength is high.
Well, I hardly think that can be said as a general rule without regard
to what election method is being discussed. Personally where I withhold
preferences in Bucklin is not going to be the same as where I withhold
preferences in IRV.
IRV is a completely bizarre system. In Bucklin,
you will do as I mentioned, and we were talking
about systems that break LNH, and especially about Bucklin.
> Truncation is not insincere, quite likely. A good voting
> system solicits and rewards sincere votes, and what we have
> done is to assume that voters aren't sincere when they say,
> "I prefer my favorite enough that I don't want to take a
> chance of electing someone else, I'm willing to take the
> risk that my vote becomes moot."
That's not an assumption, that's a definition. If you're not listing
lower preferences because you *perceive a risk* to doing so, that is what
we usually consider "not sincere."
And that is a definition that was invented in
order to define Approval as violating certain
criteria. Not sincere used to mean "reversed in
preference." I probably expressed the thinking of
the general truncating voter poorly. Put it this
way: "I prefer my favorite, and I don't give a
fig about the remaining candidates, or I'm not
going to bother to try to figure out which ones I
might prefer." Is that sincere?
There could certainly be *useful information* in where people
strategically truncate, but that doesn't mean we call it "sincere."
Sincere to means "expressing a sincere preference
between sets." Lumping together candidates in the
presence of *some* preference is not insincere.
Sometimes people talk about "fully sincere,"
meaning that every preference is disclosed, no
matter how small, but this leads to some
preposterous assumptions; it's assumed,
typically, that voters always have a preference.
In fact, we don't. Or perhaps we have a
preference but it is so small that it's very
noisy, it changes from day to day, and if you
were to ask us how much we'd spend if we could be
assured of the election of two such candidates,
we'd come up with the same amount. (Or to be
assured that they would both lose, if our
"preference" is negative for both of them.)
> > Usually sincere voting produces a better
> outcome, in
> > this case due to a greater amount of information
> provided. So ultimately
> > the good of the electorate is the consideration.
>
> "Sincere voting" is unfortunately not well defined, and so
> the statement that "sincere voting" is better is
> problematic. I agree that more information is better, but
> what kind of information? If incommensurable statistics are
> amalgamated, the result is noisy.
That's something to debate, but the only point I was making is that
LNHarm and other criteria are philosophically aimed at the good of the
electorate.
LNH isn't, for sure, because the candidate who
maximizes the good of the electorate can be excluded because of it.
All things being equal "sincere" is better than "insincere."
Maybe there is some incompatible type of voting that is better than
"sincere," but then all things aren't equal.
LNH generally involves nondisclosure to the
voting system. The information may be on the
ballot, but it isn't disclosed until the favorite
is eliminated. Now, you've said something
different that's news to me, that some methods
satisfy LNH but also disclose the "later"
preferences. I don't understand how that trick is pulled off.
> I've been working pretty intensively on Bucklin, and I
> believe that a strategically optimal Bucklin ballot, if
> Bucklin is used in a primary -- I'm leaving aside for the
> moment of Bucklin used as a deterministic runoff -- is a
> Range 4 ballot with sincere ratings based on the favorite
> being a 4 and all candidates preferred to a runoff being
> rated 2 or 3. This has to be Bucklin-ER, of course. It gives
> the voter no strategic advantage to vote this ballot
> insincerely. If they prefer the runoff to every candidate
> other than their favorite, *they prefer the runoff*, and
> they might truncate entirely. It's a sincere vote, and it is
> on a scale that treats all voters the same, assuming that it
> is equally valuable to them to avoid a runoff, as an
> absolute.
What we would do there is analyze it as a ballot with an explicit
approval cutoff.
Yes. That's what I'm doing. On a Bucklin ballot,
all votes are "approved" votes, if there is a
runoff. It means "approved compared to not
completing the election." It means "I'm willing
to cause the election to terminate with this candidate."
I don't really understand how the runoff finalists are selected. Are
you going to let a faction tie two clones in first place and have them
both go to the runoff?
Well, show me a scenario and I'll see. Here is
how I'd choose runoff candidates. The condition
is that no candidate gains a majority. Clones,
generally, would be roughly tied, because it's
likely that they'd have additional votes from the supporters of each other.
I'd look at, however, at the Bucklin winner,
i.e., the most-approved candidate. I'd look at
the ballots to see if there is a Condorcet
winner. And I'd look at them to see if there is a
Range winner, i.e,. the ballots counted as Range
ballots. That gives me up to three candidates.
Often, though, some of these kinds of winners
will be the same person. So we might have one or
two candidates. If we have three or two, those go
to the runoff. If there is only one, good chance
this is the best winner, but to be sure, because
we don't have a majority, we should pick another.
How? The scenario proposed, that has two clones
tied for first place, would be political suicide
for that faction, generally, because much of an
election is campaigning and name recognition,
dividing that between two candidates is likely to
damage both of them, that they got to first place
is pretty significant; i.e., it probably means
that one of them would have done even better if the faction had been united.
We've just defined that the Bucklin winner and
the Range winner are the same. Is there a
candidate who beats the Bucklin/Range winner? If
so, we've defined that this is not a Condorcet
winner, is there a cycle? What other candidates
might the electorate actually prefer. I very much
dislike leaving out of a runoff a candidate who,
on the face, would beat a candidate who is going
to the runoff. But I'm not going to exhaustively define this now.
Are your ideas on this at the bottom of this post?
Yeah, I did say it. The Bucklin winner is an
"Approval winner" with an approval cutoff lowered to a certain point.
> I believe that this method will discover if a majority of
> voters are ready to settle on a candidate. If they aren't,
> it will give them very good information to use in
> determining how to vote in a runoff.
But just like with TTR, the fact that there is a second round provides
incentive to *not* find a majority in the first round. That's not
necessarily bad though.
It all depends on preference strength. The
incentive, in fact, encourages more accurate
voting for the approved set. And if there is an
additional "disapproved" rank, i.e, rating 1
added to the scale I described, and if this would
help a "better disapproved candidate" to get to
the runoff, making it more likely that the runoff
could be more pleasing in outcome to me, then I
have a motive to add that rating. It's not going
to cause my favorite to lose, and it can't cause
that candidate to win the first round, it isn't
used for that. It's only used to (1) provide a
better picture of how the electorate views all
the candidates, which is helpful for future
elections, and (2) possibly make better choices
for runoff candidates, indicating one or more of
them who aren't "quite so bad."
> As a ranked ballot with
> four ranks (including the bottom), Condorcet analysis can be
> done, whether it is used for the election or not. I've
> suggested adding an additional rank, rating value 1, to be
> used to make the scale symmetrical, these are not approvals
> of the candidate, but they can be used to estimate overall
> utility.
>
> To me, it's quite important to start collecting much better
> ballot data, and this would do it, with sincere votes
> incentivized. The ratings of 1 would not harm any approved
> candidate, they merely would be a way for voters to make a
> discrimination between the unapproved candidates. They could
> be used to determine runoff candidates (and with a good
> runoff method, it's possible for there to be more than two
> runoff candidates, such as the Approval Winner, the Range
> Winner, and a Condorcet winner, if they differ (which would
> be rare)
I'm not settled on what the optimal runoff
candidate set would be. If the runoff method is
Bucklin again, there can be more than two without
harm. But this time voters will know that it's
their last chance. They can't put off lower rated
approvals again. However, helping them greatly,
they will have the results of the first election,
they will all, if they want to be, accurately
informed about how the rest of the electorate
feels about all the candidates remaining on the
ballot. They will know the risks of continuing to
bullet vote, and they will make their choice.
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