Hello,
--- En date de : Ven 19.12.08, Abd ul-Rahman Lomax <a...@lomaxdesign.com> a
écrit :
> > > Highly speculative. Bucklin probably experiences
> about the
> > > same level of bullet voting due to LNH fears as
> IRV, not
> > > much more, because the "harm" only
> happens when a
> > > majority isn't found in the first round.
> >
> > If methods typically won't require more than the
> top rank, then I guess
> > neither LNHarm nor monotonicity failures will be much
> of a problem.
>
> With LNH, the "harm" is that the voter sees a
> second preference candidate elected rather than the first
> preference.
Actually, the harm need not take that form. It could be that you add an
additional preference and cause an even worse candidate to win instead of
your favorite candidate.
> In fact, in full-vote methods (only Range is
> different), a single vote never purely flips an election
> result, rather it turns an election into a tie or a tie into
> an election.
Yes, but the concern should not be that you personally will ruin the
result, it's that you and voters of like mind and strategy will ruin the
result.
> > >In other words, Center Squeeze is a direct
> consequence of LNH compliance
> > >by IRV.
> >
> > Well, MMPO satisfies LNHarm, and is nearly a Condorcet
> method.
>
> I'd have to look at it. How does MMPO work? I worry
> about "nearly," but, sure, if the exception took
> extraordinarily rare conditions, and the results then were
> merely suboptimal, not disastrous.... I can imagine a method
> that uncovers the votes and uses them to decide other
> pairwise contests, but I'm suspicious of the claim.
The "opposition" of candidate A to candidate B is the number of voters
ranking A above B. (There are no pairwise contests as such, though the
same data is collected as though there were.)
Score each candidate as the greatest opposition they receive from another
candidate.
Elect the candidate with the lowest score.
This satisfies LNHarm because by adding another preference, the only
change you can make is that a worse candidate is defeated.
DSC is harder to explain. Basically the method is trying to identify the
largest "coalitions" of voters that prefer a given set of candidates to
the others. The coalitions are ranked and evaluated in turn. By adding
another preference, you can get lumped in with a coalition that you
hadn't been. (Namely, the coalition that prefers all the candidates that
you ranked, in some order, to all the others.) But this doesn't help
the added candidate win if a different candidate supported by this
coalition was already winning.
> > >Interesting, eh? Top three. A Condorcet winner is
> almost certainly in
> > >there!
> >
> > I think this is doubly likely if you arrange the
> incentives so that it's
> > likely that third place achieved that position better
> than randomly.
> >
> > In other words: I want to have a TTR election where
> candidates risk being
> > spoilers if they place worse than third.
>
> That would be a system where the candidate is risking
> damage to the overall benefit of the election. Did you mean
> to write it as you did? A spoiler typically will drop the
> "spoiled" candidacy one rank, not two.
That is what I meant to write, although I don't understand your second
statement.
As far as it being a "system where the candidate is risking damage to
the overall benefit of the election": We already have this with FPP,
with every candidate who places third or worse.
Basically I want a hybrid of FPP and TTR, that does better than either
at providing an actual third choice that might be able to win. That
everyone and their mother can be nominated fairly safely under TTR is
nice and democratic, but I think it's a waste of potential.
> The *theory* of oscillation or endless regression based on
> feedback between polls and voter decisions is just that, a
> theory.
What is the alternative? Do you think polls will settle on two
frontrunners almost arbitrarily?
The only alternative I can think of is that there would be no effective
polls. And I suspect that would be just as bad as having polls that don't
stabilize.
> > >From the first message:
> >
> > > "Frontrunner strategy" is a common one
> that seems
> > > to help with ranked methods as well as Range
> ones. Make sure
> > > you cast a maximally effective vote for a
> frontrunner, and,
> > > where "against" matters, against the
> worst one.
> > > Usually there are only two frontrunners, so
> it's easy.
> > > "Expectation" is actually tricky if one
> > > doesn't have knowledge of the
> electorate's general
> > > response to the present election situation. How
> do you
> > > determine "expectation." Mean utility
> of the
> > > candidates is totally naive and non-optimal.
> >
> > Mean utility is supposed to be naive, and it is
> optimal, if you are
> > "naive" about win odds.
>
> I know that this (mean voting strategy in Approval) has
> been proposed, but it's a poor model. A voter who is
> "naive" about win odds is a voter who is so out of
> touch with the real world that we must wonder about the
> depth of the voter's judgment of the candidates
> themselves!
I can't understand what you're criticizing. It is the zero-info strategy.
You seem to be attacking this strategy by attacking the voters who would
have to use it. That doesn't mean that those voters wouldn't have to use
it.
> This naive voter has no idea if the voter's own
> preferences are normal, or completely isolated from those of
> other voters. This is far, far from a typical voter, and
> imagining that most voters will follow this naive strategy
> is ... quite a stretch, don't you think?
I don't know of anyone who said that voters would follow this strategy
in a public election.
> > "Better than expectation" is mean *weighted*
> utility. You weight the
> > utilities by the expected odds that each candidate
> will win. (There is
> > an assumption in there about these odds being
> proportional to the odds
> > that your vote can break a tie.)
>
> Sure. That's the correct understanding of "mean
> utility." It means a reasonable expectation of the
> outcome. However, what's incorrect is assuming that
> voters have no idea of the probably votes of others.
Ok, but I have never done that. "Better than expectation" strategy
does not really depend on ignorance of other voters' intentions.
> Being human, each voter is a sample human, and more likely
> to represent the views of other humans than not. This is a
> far more accurate model of human behavior than the
> assumption that candidate preferences are random, which only
> would be true in a simulation that assigns the preferences
> that way. Voters are members of society, and not independent
> in the sense that their choices can't be predicted, with
> some level of accuracy, by those of a sample, even a sample
> as small as one voter.
>
> By this argument, the rational vote, zero-knowledge, is the
> bullet vote.
But when this argument is accepted, the situation isn't zero-knowledge
anymore.
> This happens to be the vote that has the best
> probability of favorably affecting the outcome (i.e., if the
> voter is the last voter). We've done it backwards. The
> default vote should be a bullet vote, and only in the
> presence of significant strategic considerations should the
> voter deviate from that.
> > "Frontrunner strategy" is just a special
> case of "better than
> > expectation," where only two candidates are
> expected to have any chance
> > of winning.
>
> Sure. There remains the issue of how to rate a middle
> candidate.
According to "better than expectation" strategy, if e.g. the two
frontrunners are expected to have 50% odds of winning each, then for
the middle candidates, you must approve those who are better than the
average utility of the two frontrunners.
> I think that the "mean strategy"
> overlooks other factors, including what might be called
> "absolute approval." I.e., if I absolutely
> disapprove of a candidate -- never mind the other options --
> in that I would not want it to be in my history that I voted
> for him or her, I won't, no matter what the math tells
> me. I'll listen to my gut instead of the math, because
> it's more likely, in fact, that the math is wrong than
> that the gut is wrong.
I don't think "mean strategy" overlooks that factor (unless you just
mean that real voters won't stick to effective strategy). I would rather
say that the numbers have been filled in incorrectly, when the result
doesn't agree with one's gut. (This is subject to the assumption that
the voter is trying to vote optimally.)
> > > But it's a complex issue. My point is that
> "better
> > > than expectation" has been taken to mean
> "average
> > > of the candidates," which is poor strategy,
> any wonder
> > > that it comes up with mediocre results?
> >
> > "Average of the candidates" is the special
> case of "better than
> > expectation," where there is no information on
> candidates' win odds.
>
> Which is a non-existent situation, unless you posit
> radically artificial conditions.
I never said that the zero-info case was an existent situation. I am
saying that the strategy of approving above the simple mean, is the
zero-info strategy, not the generally recommended strategy.
> So the "oscillation," the lack of stability, will
> only take place when the choice isn't terribly important
> to most voters.
I don't think I understand this argument.
A simple example of what I mean would be where there is a preference
cycle of A>B>C>A. Imagine that everyone likes their top two choices
better than midrange. Then, when polls predict that the frontrunners
are A and B, for instance, this causes the electorate to plan to vote
in such a way that B will actually place third. When polls pick up on
this and report that the frontrunners are actually A and C, then A can
be expected to place third. And this could go on, in theory,
indefinitely.
> > > In plurality
> > > Approval, strategy based on polls would loom
> larger. Sure,
> > > it could oscillate. But how large would the
> osciallations
> > > be?
> >
> > The only situation I'm concerned about is where,
> when the polls report
> > that A and B are the frontrunners, this causes voters
> to shift their
> > approvals so that the frontrunners change, and when
> the polls report
> > this, the voters react again, etc., etc.
>
> Of course. Except it's not going to happen. Voters will
> overstate their tendency to bullet vote in the polls.
But that isn't inherently good. That means a compromise choice without
many sincere first preferences can only win by unexpected accident.
The compromise choice would be much more likely to win if he were
identified as a frontrunner.
> Voters
> will only approve more than one when they have lower than a
> certain threshold of preference strength, and even there,
> it's questionable how much they will do it unless they
> really have no significant preference, it's hard for
> them to state a preference between two, so they approve
> both.
>
> Further, the results don't shift the way you seem to
> expect. A and B are the frontrunners, a poll shows. How do
> voters respond? One common response would be no response.
> Then there are the supporters of C. They get this news, they
> now plan to add a vote for A or B, from their prior bullet
> vote for C.
>
> There is only one class of voter who will shift their vote:
> those who already preferred a frontrunner, but who, in
> ignorance of this situation, already approved both. You have
> to understand that this is an unusual situation, in itself.
> Most voters in early polls will bullet vote, unless
> preference strength is low, and if preference strength is
> low, they aren't likely to stop approving both. But
> voters who did vote like this may raise their approval
> cutoff to reflect how they probably should have voted in the
> first place!
>
> Sure, it could oscillate. But only if most voters have low
> preference between A and B. In which case it doesn't
> matter that much who wins!
I'm not sure what you think my concern is. My concern is about
situations where which two candidates are seen as the frontrunners, is
something that doesn't stabilize.
> The incremental utility gets smaller and smaller as
> the number of voters increases (and this is relative
> utility, with the assumption that the vote affects the
> result, so this effect is compounded by the increasing
> rarity of ties and near-ties), but it never disappears. That
> optimal strategy is such when the middle candidate has an
> exact middle utility. I've not studied the other cases.
> But my sense is that as the middle utility moves toward A,
> the optimal vote moves toward double Approval. Has to be,
> I'd think, because if the utility gap goes to zero, the
> optimal vote is obviously double Approval, 100% guarantee of
> no regret over the vote.
Yes, it does, assuming the favorite and least-favorite candidates have
equal win odds. In that case your expectation is somewhere between the
midrange and whatever the middle candidate is worth.
> Another example, by the way, of how "mean
> candidate" is a bad Approval zero-knowledge strategy.
This is "mean strategy" I assume.
> It has to be probability modified, and the voter's own
> preference *must* be considered to weight the probability,
> since the voter is a member of the electorate, and if all
> other voters are unknown, we still have a net vote weighted,
> by one vote, toward our voter's position.
Yes, but in a public election, this vote is of microscopic value, which
is why no one tries to count it.
> > If candidates were at least obtaining majority
> approval, I could be
> > content with the statement. But if no one obtains a
> majority, offering as
> > consolation that the most "accepted"
> candidate won is not much more
> > comforting under Approval than under Plurality.
>
> This is an argument for requiring a majority, isn't it?
Not necessarily, because requiring a majority would alter the strategy
of the method, possibly in a bad way.
What I'm saying is that I view it as bad if large numbers of Approval
voters are failing to participate in the most important contest, or
failing to even identify such a contest.
> Sure. However, suppose there is some other threshold than
> "more than half" of the ballots approving. Set
> this threshold at X.
>
> Whatever X is, that one candidate exceeds it with a greater
> margin is "more comforting" *on average* than
> that, say, the other candidate be chosen.
I am not disputing that the candidate with the most Approval is the best
candidate to win an Approval election. Same as I wouldn't dispute that
if we run out of food we should resort to cannibalism rather than starve.
I'm saying it's bad if we do something that is prone to leading us in this
direction.
> > > It's not going to be a terrible result,
> > > if Approval falls flat on its face, it elects a
> mediocre
> > > candidate because the voters didn't get the
> strategy
> > > right.
> >
> > Well, what is a "terrible result" after all?
> It seems to me you don't
> > have to be too picky to find methods that only fail by
> electing mediocre
> > candidates.
>
> When ranked methods fail, they can fail spectacularly, and
> with sincere votes. It gets unusual, to be sure, with better
> ranked methods (it may be as high as 10% failure with IRV,
> under nonpartisan conditions, but most of those failures
> will also be of minor effect.)
I would have thought IRV would be squarely in the category that fails
by electing a mediocre candidate, and rarely by electing a terrible
one.
> I really shouldn't have written "mediocre."
> Rather, Approval can elect a "less controversial"
> candidate, which perhaps many or even most of the voters
> would judge a "more mediocre" result than the best
> candidate, were all the preferences accurately known.
Well, if voters tend to bullet vote under Approval, I guess it really
won't be much different from FPP or IRV.
> (Or, perhaps I should say, "some ranked methods."
> Borda, for starters, looks like a ranked method but is more
> accurately a ratings method with a highly restricted way of
> expressing the ratings. I'm not familiar with *how bad*
> Condorcet methods can fail. Generally, with reasonable
> distributions of candidates, the difference between a
> Condorcet winner and a Range winner are small. So I've
> had in mind a method like IRV, where the winner could be
> opposed by two-thirds of the voters, and that could be a
> maximally strong preference -- they will revolt! -- and
> that's with sincere votes. Strategic voting could,
> indeed, improve the results.)
If you listen to Warren Smith, Condorcet methods are prone to
catastrophic failure because voters have incentive (real or instinctive)
to attempt burial strategy against the worse frontrunner. When
too many voters do this, and there's no majority favorite, the result
will be the election of a candidate that nobody cared about, who was
just being used as a pawn.
This makes it odd that he has seemed to prefer Condorcet to IRV,
seeing as IRV can't have such disastrous failures.
> > > What type of voter is bad for Approval? Easy
> compromiser or
> > > tough bullet voter?
> >
> > The type of voter who is willing to cast a suboptimal
> vote due to
> > principle. It is harmful under Plurality and here is a
> situation where
> > it would be harmful under Approval.
>
> What does that mean?
>
> Here is what I get from it. The Nader voter cast a
> supposedly "suboptimal vote" under Plurality. For
> principle, i.e., the importance of voting for the best
> candidate, in one's opinion.
>
> Is that the meaning?
Yes.
> But who are we to say that this vote
> was suboptimal? Remember, the campaign rhetoric, by Nader,
> was that it didn't matter who won, Bush or Gore, they
> were both totally in the pocket of the large corporations.
> So why can't we just assume that the voter made an
> *optimal* decision? From the voter's perspective.
There are two possibilities. If the voter really didn't have a preference
between the two frontrunners, then it doesn't matter. But if they did,
then by not voting for one of them, they vote "suboptimally" because
they fail to vote in a way that maximizes their expectation. And it is
suboptimal overall, because the wrong frontrunner will be elected.
> Or does this mean the voter who supports Nader, but who
> *does* have a reasonably strong preference between Gore and
> Nader, and decides to vote that?
I don't understand what you're saying here. If the frontrunners are
Gore and Bush, then I'm calling "suboptimal" all votes that don't favor
one over the other, when the voter actually had a preference.
> Note that these situations apply to Approval. Both
> scenarios will happen with Approval just as with Plurality.
> In the first situation, i.e., Nader is believed, there is no
> incentive to add a vote for Gore or Bush.
But under Plurality it is hardly ever a concern, because the polls are
sufficiently stable that voters who wish to cast a meaningful vote have
no difficulty in doing so.
If Approval polls prove relatively unable to whittle the field down to
two frontrunners, I would expect more votes on principle and (with it)
more waste of votes.
Kevin Venzke
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