[EM] Why I think IRV isn't a serious alternative 3

[Kevin Venzke]

Hello,

--- En date de : Lun 22.12.08, Abd ul-Rahman Lomax <abd at lomaxdesign.com> a écrit :
> At 12:56 AM 12/21/2008, Kevin Venzke wrote:
> > --- En date de : Ven 19.12.08, Abd ul-Rahman Lomax
> <abd at lomaxdesign.com> a écrit :
> 
> [starts with Venzke, then my response, then his]
> > > > 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.
> 
> Yes, that is *a* zero-knowledge strategy that misses
> something. A voter with no knowledge about other voters is a
> very strange and unusual animal. I'm saying that the
> *strategy* is a stupid one, and that real voters are much
> smarter than that. 

This is missing the point. There is no implication anywhere that a
zero-info strategy is supposed to be usable by real voters.

> Voters have knowledge of each other,
> generally. Positing that they have sufficient knowledge of
> the candidates to have sufficient preference to even vote --
> I don't vote if I don't recognize any of the
> candidates or knowledge of whom to prefer -- but they
> don't have *any* knowledge of the likely response of
> others to those candidates, is positing a practically
> impossible situation. Yet this is the
> "zero-knowledge" assumption. In this sense,
> "zero-knowledge" doesn't exist, it's an
> oxymoron.

That's fine. It makes no difference whether zero-info strategy is ever
usable in practice.

> Most voters, in fact, have a fairly accurate knowledge of
> the rough response of the overall electorate to a set of
> candidates, provided they know the candidates. Those on the
> left know that they are on the left, and that the
> "average voter" is therefore to their right. And
> vice versa. Those near the middle think of themselves as,
> again, in the middle somewhere.

Yes, this is not a zero-info situation.

> The most common Approval Vote will be a bullet vote. How
> much "knowledge" does that take?

Do you have a very concise summary of why you believe the most common
Approval vote will be a bullet vote? Are you making any assumptions
about nomination strategy, what kinds of and how many candidates will
be nominated?

> > > 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.
> 
> It's been implied that the scenario is somehow
> realistic. 

Do you want to name names? I don't know who has implied this.

> If there is no possibility that a scenario could
> occur in a real election, then considering it as a criticism
> of the method is ivory-tower thinking.

Are you talking about Saari?

> Mean utility of the candidates strategy has been proposed
> by Approval supporters, but unless the utilities are
> modified by expectations, it's a terrible strategy,
> bullet voting is better, probably.

Why do you think it's a terrible strategy? I think it is a better
strategy than bullet voting, unless you believe lots of clones have
been nominated in order to take advantage of your strategy. But that
would be a pretty bizarre fear since, if anyone ever learned of this
conspiracy, the strategy would disappear.

> > > > "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.
> 
> "Better than expectation strategy" is sound.
> "Better than mean of the candidates" isn't.
> But this is inherently a "strategy."

The latter is a special case of the former.

> > > 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.
> 
> That's right. Zero-knowledge is, in effect, an
> oxymoron, since the voter is a voter and therefore a sample
> of the electorate.

I guess you must be arguing primarily against Saari. I can't imagine why
else it would be necessary to argue that a zero-info strategy isn't
going to be relevant in a real election.

> Note that if a situation is very balanced, and with weak
> preference strengths such that votes would flip as
> described, it's probably true that one could pick any of
> the candidates randomly and Bayesian regret would not
> increase significantly over the best.
> 
> Really, Kevin, you are worrying about something purely
> theoretical, and actually unlikely, and if it did happen,
> harmless. So what if the polls oscillate? Does it tear the
> bridge apart? Or do voters decide to simply vote with some
> kind of rational sincerity, forget the polls.

I thought I was clear about what I'm concerned about. If the polls (that
is to include, the voters' collective impression on the state of all
candidates' odds) cannot determine who the frontrunners are, then many
votes may end up being ineffective, wasted.

> > > > > 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.
> 
> Half of the following is nonsense. There were aspects of
> this situation, clearly, that I need to examine more. But I
> don't have time tonight to review it, and this is a
> discussion, not polemic. Now, to what I wrote:
> 
> Perhaps. What's a "frontrunner"?  

I'm assuming there will ultimately only be two frontrunners. If this
isn't possible in some scenario then I write that scenario off as 
relatively likely to be a disaster.

> If the
> polls are based on bullet voting, and there is a risk that
> C, the voter's worst fear, will win, the voter is more
> likely to vote for B, the compromise choice. Only if A and B
> are the frontrunners will the A voters not approve B, but
> the C voter will. You vote for a second-choice candidate if
> you fear that the candidate *won't* win. If the
> candidate is a frontrunner, and you prefer someone else, who
> is also a frontrunner, you *don't* vote for that
> non-preferred candidate. But this could be a
> three-frontrunner situation, where all bets are off. (As far
> as simple frontrunner strategy).
> 
> Thus the compromise choice is *less* likely to win if
> identified as a frontrunner. People who prefer someone else
> will not vote for this candidate, seeing him as the main
> rival. Unless their own candidate doesn't have a chance,
> and they prefer this candidate to the third possibility,
> *then* they will vote for the frontrunner.

When there are only two frontrunners and the compromise is identified
as one of them, then the compromise should be unbeatable by the other
frontrunner. (Some other candidate could still theoretically win, but
I would consider this a disappointing failure of the polls to predict 
it.)

> Standard Approval strategy: vote for your favorite, the
> preferred frontrunner, and any candidate you prefer to the
> preferred frontrunner. This strategy breaks down if there
> are three frontrunners. Are there? Being in third place
> doesn't mean that one is not a frontrunner.

Under FPP being in third place means you are probably already sunk, or
will be shortly. I don't think Approval is that much different in general.

> Now, the compromise candidate isn't going to lose core
> support votes no matter what the polls. But core support
> could be quite small, though if it is very small, it
> requires, pretty much, that the absolute preference strength
> for most voters is low over the entire set of the top three.
> 
> 1/3 electorate A>B>C
> 1/6 electorate B>A>C
> 1/6 electorate B>C>A
> 1/3 electorate C>B>A
> 
> Classic center squeeze, on the edge (i.e., take one vote
> away from B, B, everyone's second choice, is history
> with IRV. Even though in a faceoff with B, either of A or C
> would lose by a vote of 2:1.
> 
> Poll result shows B in third place. Now, *How far* in third
> place? Small. Won't affect the next poll, I'd say.
> Also won't affect chances of winning. If everybody
> bullet votes, we have a three-way tie, a tossup. But not
> everyone will bullet vote, and B will win, with Approval,
> though this could vary depending on preference strengths not
> expressed above. Still, the B voters are less likely to add
> approvals for A or C, whereas the A or C voters are more
> likely to add approvals for B, since they see each
> other's candidates as much worse. (B voters may be
> closer to A or C, but see them as both *roughly* equally
> undesirable.)
> 
> (Imagine linear issue space, spanning -1 to +1, A is at
> -5/6, B at 0, and C at +5/6.)
> 
> What happens if the voters think B is trailing?
> 
> It depends on who is leading. If voters think B has no
> chance, it's moot. They won't vote for B, except for
> the B voters, since the other voters have a favorite, who
> is, by the definitions of the problem, a frontrunner. Vote
> for your favorite frontrunner, plus anyone you prefer to
> your favorite.
> 
> But there is a rather clear exception to this strategy. If
> the *worst* frontunner is reasonably likely to win --
> perhaps he's leading, even -- then you'd want to
> know who has the best chance of beating him. You'd want
> to know who could accomplish that, should your own candidate
> fail. You'd want to figure out who a compromise
> candidate might be. I.e., you'd want better information
> than you would get in a plurality poll. I'd want to have
> Range data, the more detailed the better. With Range data,
> one would get a sense of preference strengths. The MSNBC
> polls, which were Range 2, default vote 1 for candidates not
> rated, would be much better than pure approval polls, though
> pure approval would be better than plurality.
> 
> Higher res Range would be even better.
> 
> 1/3 of the electorate votes for B, for sure. B only needs a
> little more, 1/6 of the electorate, to win. Where do these
> votes come from?
> 
> If the polls are reasonably accurate, the A voters know
> that C has a 1/3 chance of winning, roughly. The A voters
> have quite a good reason to fear that C will indeed win.
> They strongly prefer B to C. Some of them will add an
> approval for B. Some of them have, in fact, only a weak
> preference for A over B. That's about 1/12 of the
> electorate, say. (This is the B-ward quarter of the A
> voters). The same is true on the other side, with the C
> voters. There is the 50% of the vote needed to get a
> majority, but this situation may result in only a plurality.
> B will get 1/3 of the vote, minimum. Additional approvals
> from B voters will tend to balance, and there won't be
> many of them. On the other hand, additional approvals from A
> and C voters, and there will be more of them, will all go to
> B.
> 
> Bucklin, not really much of a problem. I vote for my
> favorite, then B in second place if B isn't my favorite.
> Some voters wouldn't do this, but I'd think this
> would be confined to the outer 1/3 of the electorate at most
> (1/6 on the A side, away from B, the same on the C side).
> 
> B would win in the second round with 2/3 of the vote. The B
> voters may truncate, not add any additional preferences, but
> if they do, they split on the candidate they add. It's a
> wash. We have 1/3 of the voters, the supporters of A and C,
> to the extremes, truncating. So we see roughly 1/3 of the
> 1st preference vote in the second rank votes. That's
> roughly what I've seen in municipal Bucklin elections.
> 
> Further, consider what happens if it is Bucklin and a
> majority is required. I understand center squeeze. I want to
> make sure that the compromise candidate, my second choice,
> gets into the runoff, at least. Exactly how I will vote will
> depend on my position, on the preference strengths, but the
> motive becomes fairly high to add a second preference vote
> and not merely bullet vote. My second preference vote
> won't cause my favorite to be eliminated, and if the
> runoff allows write-ins, I could still consider that vote
> there, I'll want to know the first round election
> results before I decide. If the compromise candidate is
> eliminated in the primary, then what happens depends, again,
> on preference strengths and the overall numbers. Strong
> preference for a majority of voters: a write-in campaign,
> with those voters marking, in second rank, their second
> choice. If B is a true Condorcet winner, with significant
> preference, B could actually win, and Bucklin in the runoff
> prevents the spoiler effect.
> 
> Running a write-in campaign, the organizers and voters must
> understand the risk. The runoff isn't going to require a
> majority, that protection is gone, so I'd think they
> would suggest voters vote for the write-in, in first or
> second rank, period, plus their favorite; if they prefer
> their favorite, then first rank. But the additional vote
> will be there, this time. B might win with 2/3 of the vote.
> (The best of A or C might get 50%, if that, depends on how
> many of the B supporters add 2nd rank votes for the nearest
> of A or C. A double majority is unlikely, but possible in
> this situation. Barely. B will win, as a write-in *if the
> preference strength is sufficient. It might not be.
> 
> Imagine that the position of A in that -1 to +1 spectrum is
> -0.1, B is 0, and A is +0.1. B's core support has shrunk
> to a span of 0.1 (5% of the voters). -- Yes, yes, I'm
> assuming a linear distribution. So sue me. It's just for
> illustration. The absolute difference in position between A
> and C has shrunk from 5/3 to 1/5. Prediction: no write-in
> campaign, and low turnout in the runoff. The B voters,
> almost entirely, won't show up, but also many of the A
> and C voters. The result will actually depend far more on
> the *campaign* between A and C. And no strategic
> complications.

Unfortunately if you don't agree with everything you've written here,
I'm not so inclined to comment on it, as it is fairly complicated and
long.

> > [...]]
> > > > 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.
> 
> Actually, there are very strong reasons for requiring a
> majority, hang the strategy issues. Lack of a majority means
> that the electorate hasn't made a collective decision,

But when you say that there will be a remedy, if a majority is not
reached, then there is less incentive to try to attain a majority (or
most votes, etc.) in the first place.

The electorate does not reach, or fail to reach, a collective decision,
in a vacuum, without respect to the political institutions in place.

Compare the fragmentation under first-round TTR with a single-round
Plurality election. There are more candidates and lower vote totals in
the former. The electorate "hasn't made a collective decision" but this
is entirely because the method hasn't yet provided the incentive to come
to a decision.

> What a majority requirement does in a primary is encourage
> bullet voting. Bullet voting is fully sincere! A bullet
> vote, in an Approval method, indicates that the voter
> prefers the candidate over all other candidates. 

This is a good case of your earlier statement that strategic voting
is not necessarily a bad thing.

> > 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.
> 
> If they care, they will participate. So what's the
> problem? 

The potential problems are
1. They cannot tell what the most important contest is
2. They take your advice and tend to bullet vote no matter what the
polls say.

> > > 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.
> 
> Isn't the metaphor a tad extreme? Just how likely is it
> that the most-approved candidate was actually not preferred
> by a majority. It's possible, but actually not likely at
> all. 

I'm hoping it isn't very likely. But you are saying that voters won't
necessarily care about polls, that they will vote their gut, that they
will tend to bullet vote.

> And how much damage is done in this case? It's
> hardly likely to be a bad outcome, but the lower that X is,
> the more the likelihood increases. 

The thing to compare it to is Plurality. Plurality hardly ever has
problems like this. So if Approval is going to be more prone, for whatever
reason, there also need to be good arguments to say why Approval is
still better than Plurality.

> > > 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.
> 
> I'm calling Approval "Open Voting," because
> the voting really isn't about "approval,"
> it's about "consent," or a "decision to
> support," a different animal. Most voters will bullet
> vote, probably roughly 90% or more.

You must assume there are very few candidates, and that the frontrunners
are actually the most common favorites.

> Where Open Voting makes
> a difference is with those who support minor candidates. 

I am almost speechless that this is your claim, and that you don't
seem to want to argue that Approval would operate better than 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.
> 
> Right. That strategy could quite possibly be common.
> It's easy to think that way.
> 
> > This makes it odd that he has seemed to prefer
> Condorcet to IRV,
> > seeing as IRV can't have such disastrous failures.
> 
> It certainly can. With sincere votes. That's the
> problem, Kevin.
> 
> Center Squeeze.

I don't think you're grasping the severity of the alleged problem with
Condorcet, if you're comparing it to center squeeze under IRV. Under
IRV you can hardly win without getting many sincere preferences. 
(There's no incentive to give you insincere preferences.) Under Condorcet,
in a scenario where burial strategy is rampant, you can be elected
receiving only "pawn" votes and not a single sincere preference.

> Supposedly
> one advantage of IRV is that it encourages voters to vote
> sincerely. I think it probably does that, though it
> probably, also, doesn't do it to any great extent beyond
> that which happens with Bucklin. The problem is what it does
> with those sincere votes. It doesn't count most of them,
> for starters, usually. We don't really know -- precisely
> because the votes aren't counted or reported. 

Well, if there are still two expected frontrunners, and the voters have
the sense to rank down at least that far, then IRV will never reach
the lower preferences that LNHarm protects, unless IRV is in the process
of going into the ditch because a frontrunner got eliminated.

> > > 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.
> 
> However, with the consent of that voter, who, by voting
> that way, has indicated that gaining the additional utility
> of a better winner is relatively unimportant.

If the voter has deliberately done this then I consider that to be the
first case I mentioned.

Anyway, I really don't care what kind of awful results voters appear to
be consenting to, if this produces worse results overall.

> Now, of course, the problem here is that Plurality
> doesn't allow the expression of additional preferences.
> The voter has a Hobson's choice. However, that's
> terribly easy to fix. Just Count All the Votes. Open Voting.
> Approval. No cost.

There may be a cost. As this whole discussion has suggested, the incentives
and electoral dynamics under Approval may be different from those under
Plurality, and it isn't completely obvious that Approval always comes
out on top.

> > > 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.
> 
> Suboptimal from whose point of view? The voter decides not
> to vote in the "real election." The voter could
> equally well decide to stay home. For whatever reason, the
> value to the voter of the Nader vote exceeded the value of
> the Gore vote. Or Bush vote, we too easily assume that all
> these voters would vote for Gore. I suspect that with IRV,
> maybe half, maybe more, of them would have voted for Gore.
> The rest would have truncated.
> 
> Another way of putting this is that the voter doesn't
> like either Gore or Bush. The voter may have a preference,
> but the strength is low. If it were a runoff between Gore
> and Bush, the voter might well stay home. Now, if the
> voter's preference strength is low, what is the value of
> a Gore > Bush vote? It actually doesn't change the
> overall social utility much. It overstates the voter's
> true preference strength.
> 
> You may not think this voter's vote to be optimal, and
> I certainly don't either. But the voter apparently
> thought differently.

Here is the question: Are there methods that make voters more inclined
to vote suboptimally? I am concerned that there may be, especially as you
speak of intuitive voting behavior under Approval, which may have no
connection to strategically wise voting behavior, or behavior that is
adequately informed by polls. It could be that some methods aren't
conducive to producing useful polls, as well.

> > 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.
> 
> Compared to what? The proper comparison of Open Voting is
> with standard vote-for-one Plurality, and then possibly with
> IRV, as an example. 

I was comparing to FPP. FPP has no difficulty getting down to two 
frontrunners.

> It's got lower Bayesian regret than
> IRV, apparently, even with all it's problem. 

Even if so, this finding doesn't use your ideas of how Approval polls 
will work and how often people will bullet vote.

> Sure, if
> all voters bullet vote, it's simply Plurality. 

It could be well worse than Plurality, depending on the situation with 
the polls.

Kevin Venzke