[EM] Why I think IRV isn't a serious alternative 2

[Kevin Venzke]

Hi,

--- En date de : Jeu 4.12.08, Abd ul-Rahman Lomax <abd at lomaxdesign.com> a écrit :
> > So I guess you must not just assume but *hope* that
> voters can vote
> > accurately. In that case it seems fair to criticize
> that voters don't
> > have incentive to vote accurately.
> 
> No. Voters not voting with "accuracy" still
> contribute well to the result. The quality of the results
> increases with the degree of sincerity, but the *worst case*
> is still very good. And we absolutely do not expect the
> worst case. There will be intermediate votes, and these, so
> to speak, raise all boats. Just not their own as much.

So, to try to summarize. You can argue for Range in two ways. On the
one hand, if voters really do vote similarly to how they behave under
the simulations, then Range is the ideal method according to utility.
On the other hand, if Range doesn't work out that way, no one claims
it will be any worse than Approval, which many people feel is not too
bad.

So you can argue Range vs. Approval. For me this is a tough fight for 
Range in the absence of a way to show that voters would/should play along
with it. On the other hand one can always point out that Range won't be
any worse. But on Approval's side, you can say that it's displeasing
for the method's results to disfavor those who play along with it.
If the method is going to degrade towards Approval, it would be nice if
the degradation were neutral in effect.

Other than that I guess you have to argue Approval vs. other methods.
That's difficult too.

> > > That's right. Range results shift, and they
> shift to
> > > increase regret, when voters vote
> "strategically."
> > > This is well know, but it's an error to
> consider this a
> > > reason to avoid Range. If, with realistic voting
> profiles,
> > > they shifted results to make Range worse than
> other methods,
> > > it would be one thing. But they do not, if the
> simulations
> > > were accurate.
> > 
> > Well, if the simulations were accurate, then strategic
> voter behavior
> > wouldn't even vary for different rank ballot
> methods. Everyone would
> > apply Borda strategy according to randomized polling
> data. It is not
> > very surprising that strategic Approval can outperform
> a method with
> > this kind of behavior.
> > 
> > > Nobody has challenged Warren's results.
> > 
> > What do you mean no one has challenged Warren's
> results? What would you
> > interpret to be "challenging" the results?
> 
> Showing that they were misleading. That his assumptions
> were distorted, replacing them with more reasonable
> assumptions. Or showing that the whole approach is
> defective. Unlikely. Most people who understand his work
> think the approach is sound, as far as I've seen. If
> there are exceptions, they aren't speaking up and
> revealing what they know that we don't.

I wonder if you have ever been curious to wonder what a "strategic" voter
is, for a rank ballot method.

> > It means that given a certain understanding of what an
> "accurate" vote
> > is under Range, typically an inaccurate vote is the
> strategic one.
> 
> That's right. Imagine a hundred voters, any voting
> method. If the hundredth voter can change the result in his
> favor by voting without accurate expression of preference
> strengths, under any circumstances, the method is
> "vulnerable to strategic voting."
> 
> That's a definition tailored to Range Voting. Anywhere
> else we would just say "insincerely," i.e.,
> reversing preference. 

Where does truncation fit in? Surely truncation was seen as a strategy
concern, considering how old STV is.

> An inaccurate vote with Range isn't necessarily
> insincere, at all. The voter has decided not to put more
> effort into determining relative utilities. The voter simply
> has not considered other than two frontrunners. The voter
> has simply decided that full-on Yes and No are adequate
> expressions.

Sure, but that is insincere *enough* to say that it's not what would
be expected by the simulations for a sincere voter.

> > > The simulations answer the questions of "how
> > > much" and "how often," which
> cannot be
> > > answered through the prior approach, the use of
> voting
> > > systems criteria. Approval Voting fails the
> Majority
> > > Criterion, according to the usual interpretations
> (which had
> > > to be modified to apply to Approval Voting, and,
> clearly,
> > > the modifications were designed to *cause*
> Approval voting
> > > to fail, because the students thought,
> intuitively, that it
> > > failed. That's what I mean by subjective
> analysis! See
> > > James Armytage-Green's study and application
> of the
> > > Majority Criterion to Range Voting).
> > >
> > > Okay, how often? It would be extraordinarily rare
> in real
> > > public elections, because it requires a
> significant number
> > > of voters to vote for both frontrunners, which is
> the
> > > opposite of standard Approval strategy and is,
> normally, a
> > > foolish vote if the voter does have a significant
> preference
> > > between them. And if the voter doesn't have a
> > > significant preference, well, there you go. See
> the second
> > > question!)
> > 
> > How long has it been since I noted that this is not
> correct, unless you
> > want to assume that Approval won't have more than
> two viable candidates.
> 
> Kevin, I make no such assumption. Sure, that's what I
> stated, just above, because that is, by far, the most common
> situation, even in nonpartisan elections. 

Don't you think the method being used could have an effect on this?

> It's unusual
> to have first preferences be equally divided among three
> candidates.

I didn't intend that.

> That was the French election in 2002. FairVote
> argues that because Approval doesn't satisfy Later No
> Harm, voters will be reluctant to add additional approvals.
> I'd counter that this depends on preference strengths. A
> three-way race is equivalent to zero-knowledge. What's
> the optimal Approval vote in a zero-knowledge situation.
> 
> A game theory approach would suggest that one would average
> the utilities of the three candidates, then approve those
> with utility above that average. Let's suppose that the
> situation is really symmetrical, what happens?
> 
> Full symmmetry here means that there is a Condorcet cycle,
> I think. Let's suppose one-third A>B>C, one-third
> B>C>A, one-third C>A>B. With some kind of even
> distribution of sincere utilities, voted as such, we'd
> get half of each faction approving the second preference,
> and half not. Thus each candidate would get half the votes,
> we'd still have a very close three way race, which seems
> correct. However, if voters do think Later No Harm is
> important, and some will, the votes will be distorted toward
> bullet voting. And any distortion toward bullet voting pulls
> the votes away from a majority to less than that.
> 
> And that is with a Condorcet cycle. What if there is no
> cycle, rather there is a standard political spectrum.
> 
> The left is one-third, with the A candidate in the middle
> of that, the B candidate is the middle third of the
> spectrum, and the C candidate is the other third. This is
> actually quite a reasonable distribution, though political
> reality pushes the A and C candidates toward the center. If
> we look at this distribution and predict utilities from it,
> we get that accurate Range Votes -- which, rounded off,
> become sincere Approval votes, would be we get:
> 
> (I'm going to assume, at first, that voters are
> linearly distributed. In fact, there will be a bell curve.
> I'll come back to that. This, by the way, is more of an
> intuitive analysis than any kind of rigorous one. I'd
> invite someone to look at it with more rigor, correcting my
> errors, and I expect there is more than one, i.e., besides
> true mistakes, more than one improper assumption.)
> 
> Position on political spectrum:
> A: 0.166
> B: 0.500
> C: 0.833
> 
> A voters: all vote for A
>         distance from voter to B < half distance to C,
> one-half of A voters vote also for B
> 
> B voters: all vote for B
>         voter closer to A than to C, we could assume that
> half the B voters also vote for A, and one half also vote
> for C; however, as the voter approaches the exact position
> of B, the loss from the election of the candidate on the
> other side becomes less, and at some point voting for the
> favorite outweighs the increase in utility by avoiding a
> loss to the other side. So I'd assume that the B vote
> for A is less than half. Likewise in the other direction.
> 
> C voters: all vote for C, similarly less than half vote for
> B.
> 
> So we have A vote total equals 1/3 plus less than
> one-sixth. I.e., less than 50%.
> 
> B vote total is 1/3 plus 1/6 plus 1/6, or 5/6.
> 
> C vote total is the same as A.
> 
> A multiple majority is unlikely. *But even if there is a
> multiple majority, that candidate is still the obvious best
> winner, better representing the overall electorate than the
> candidate on either side.

Which candidate, B?

With Approval it's difficult to find "obvious best winners." The
notion of a candidate "representing" voters is difficult considering
that voters, especially in Approval, are mostly just making strategic
decisions when they vote.

> However, of course, the center candidate's "core
> support" tends to be smaller, because the left and the
> right party tend to move their candidate toward the center.
> However, in that case, avoidance of adding additional
> approvals increases. While it's not nearly as clear as
> with two major candidates, even when there are three evenly
> balanced, natural strategy -- zero knowledge in this case,
> the outcome cannot be predicted, that's the definition
> of three-way -- leads to avoidance of multiple majorities.
> And a balanced election like that is itself rare. I consider
> it highly unlikely that we would see multiple majorities in
> public elections. If we did, great! Something is coming up
> with better candidates, when you have more than one with a
> majority willing to accept him or her. In tightly partisan
> races, where people place very high value on their party
> winning, and less value on avoiding a poor outcome -- they
> may even claim to not care which of the other two candidates
> wins -- what we are more likely to see is majority failure,
> *no* candidate gets a majority, and then, in this situation,
> we could have a top two runoff -- or decide it on Plurality.
> Note that what I'd support most strongly for U.S.
> implementation is Bucklin, which allows all those voters to
> first express their support for their favorite, if it
> matters that much to them. Then they can add an additional
> approval in second rank. It is quite unlikely, again, to see
> a multiple majority in the election, because many voters
> will not add second approvals.
> 
> From experience, what we are quite a bit more likely to see
> is majority failure, not multiple majorities. That's
> what actually happened. It would be interesting to know if
> any Bucklin election produced multiple majorities. All of
> the ones I've looked at -- which is really only two
> where I saw the votes, as I recall -- there was only one
> candidate who obtained a majority. FairVote has claimed that
> Bucklin was discontinued with its use for primary elections
> because it was failing to find a majority (same as
> apparently happened with IRV), so this would confirm that
> multiple majorities would be rare. Primaries are really
> nonpartisan elections in that candidates can't be
> conveniently grouped, especially not into two major parties
> with easily predictable "vote transfers" in IRV or
> possible additional approvals in Bucklin.
> 
> What I expect with Approval is that only a small number of
> voters, maybe 10%, will add approvals. Same with Bucklin,
> only a relatively small number will add additional ranked
> candidates, though probably more than with Approval, because
> of a lesser possibility of "harm to the favorite."

If we expect two frontrunners under Approval, I would be very surprised
(and extremely put off) if Approval ended up failing to produce 
majorities. This would go most of the way to convincing me that the
incentives are broken.

> > If two candidates obtain majority approval, most
> likely one of them was
> > not a frontrunner, but a compromise choice.
> 
> That's correct, if "frontrunner" refers only
> to first preference. If it refers to overall popularity,
> predicted approval votes, it's a different matter, and
> one that I did not consider above.

This is actually interesting now that I think about it.

Some six months ago I wrote a strategy simulation for a number of
methods. One situation I tested was Approval, given a one-dimensional
spectrum and about five candidates, A B C D E.

In my simulation, once it was evident that C was likely to win, one of
either B or D's supporters would stop exclusively voting for that
candidate, and would vote also for C.

So then, the frontrunners really were either B and C, or C and D. (And
C would almost always win.)

If Approval managed to behave like that, I would consider it pretty good.
I wonder if it can be tweaked to make this scenario more likely to occur.

> If more than one candidate receives a vote from a majority
> of voters, there will also be a runoff election between the
> top two.

I don't think it is viable to have a runoff election between the top 
two Approval candidates. I know you have hinted that you're not concerned
about Clone-Loser failures here.

> The real question here is whether or not it is worth
> worrying about the multiple majority, simply to comply with
> a defective criterion, the Majority Criterion. Approval
> approximates Range, reasonably well. If there are multiple
> majorities, choosing the one with the most votes is unlikely
> to damage overall satisfaction much, if it damages it at
> all. It may not be worth having a runoff, often enough, just
> to avoid that situation. I still prefer it, though.

I certainly don't think it's worth fixing, not like this. It would be
better to use MCA.

> My main point (don't you agree with it, Kevin), is that
> Majority Criterion failure in Approval is a red herring.

I wouldn't call it a "red herring" but it doesn't bother me much, because
you can't tell from the cast ballots when this criterion has been
violated.

> There has been an issue raised here that we have not
> addressed: Range strategy depends on an understanding of who
> the frontrunners are. What is a "frontrunner?" Is
> it defined by first preference, or by likely vote in the
> election? We've mostly looked at first preference, but
> actually, it's probability of success in the actual
> election that would be the basis for proper strategy.
> We'd want to look at Range polls to determine the
> latter. Better than Approval polls, even if the method is
> Approval, but you'd want both if you could get it.

In my simulations I treat poll questions as equivalent to the actual
question on the ballot. So Range voters would be asked who they would
rate where. Then the frontrunners would be those with the highest
reported scores.

> In order to do it, we need a method of *measurement* of
> election performance. Enter, stage right, Bayesian regret.
> Got any other alternative? Has any other alternative been
> seriously proposed?

I don't think so. We just called it "social utility."

> > (It works when we
> > > can see it and test it, why would it stop working
> when we
> > > can't?)
> > 
> > Because real people will be involved
> 
> That doesn't actually answer the question.

Well, if it doesn't work when we can't see and test it, the reason likely
has something to do with real people being involved.

> > Actually the fact that you are not writing just for
> me, makes it hard for
> > me to find the answers to my questions, or even
> determine whether you
> > are specifically trying to answer them, at any point
> in time.
> 
> I am trying to answer your questions. If I have not
> answered them so far, either I haven't understood them,
> or I answered them and you did not recognize it, perhaps I
> buried it in too much dicta, or I simply got diverted. It
> happens.
> 
> What questions remain? I see substantial agreement in
> certain areas. What do you think?

It is possible that we are getting closer.

My original concern is to try to reconcile the ideas that simulations
support Range and yet real voters should not be expected to mimic their
mind-read votes from the simulations.

It strikes me that ultimately you don't really need the simulations,
because you can argue in any case that Range will be at worst as good
as Approval. If you can sell Approval you can start selling Range, 
basically.

Kevin Venzke