[EM] Simple illustration of center-squeeze effect in runoff voting

[Abd ul-Rahman Lomax]

At 06:47 AM 1/23/2009, Kristofer Munsterhjelm wrote:

>I'll say again: if there are more than two viable parties, the this 
>could happen. If there will be only two viable parties, why use Approval?

You've missed something crucial: Approval is being proposed for 
public partisan elections where there are only two viable parties. 
When there are more than two, Plurality breaks down very badly. 
Approval fixes the spoiler effect. Where a majority is required, it 
also would improve primary results, and used in a runoff it would, in 
unusual situations, provide a simple solution to the write-in 
problem. But Bucklin probably does both of these better.

Approval is proposed, by me, because of its terminal simplicity. 
Essentially, an old error is eliminated, the assumption that voters 
won't or shouldn't equal rank.


>As a concrete example, consider the 2002 French Presidential 
>election. You support Bayrou - are you going to approve of Jospin 
>alone, or of both Jospin and Chirac? You probably don't know that 
>the Le Pen supporters are as powerful as they are, so you approve 
>only of Jospin. Then the runoff picks Le Pen and Chirac. If there 
>had been no runoff, Chirac would have won outright, which is better 
>than Le Pen, but not what you wanted.

Absolutely, understood very well. Bucklin would do better. For 
reasons that escape many voting systems experts, Range would do 
better. Condorcet would do better, but with a cost. Hybrid 
Range/Bucklin/Condorcet would be best, but every complexity makes 
implementation less likely.

At one point it was fairly widely discussed, and just about everyone 
who wasn't stuck with IRV agreed that Approval was an improvement. 
The only objections we see are based on "Voters won't like it," but 
Bucklin, which is a kind of approval voting, but ranked, was very 
popular with voters. Sure, many of them bullet voted, but this is a 
rational and effective vote for most voters; the extra votes are only 
required, really, for a few. Bucklin answers the objection of many to 
Approval: with Approval, they can't express their preference for one 
candidate *and* approve others. That's simple to fix! Just use a 
ranked ballot, as Bucklin did, then bring in lower ranks only when a 
majority isn't found in the first rank.

And hybrids can get much better; but we need to keep one thing in 
mind. Plurality usually works. Plurality usually elects the Condorcet 
winner. Etc. Advanced voting systems may only affect one election out 
of ten or so. (Depends greatly on many factors; in some situations, 
typically with many candidates, plurality breaks down badly, *unless* 
it's plurality with a majority requirement, *and* runoffs don't 
involve candidate eliminations. That's actually standard Robert's 
Rules election practice. Some candidates withdraw and voters shift 
their votes according to the previous results. *They don't want to 
keep voting forever!* Eventually a compromise is found. (And, 
naturally, this is typically done when the voters are present at a 
meeting together.)




>Of course, you may say that if the method was approval, others would 
>have voted in styles different from bullet-voting, but I'm trying to 
>show a problem; and if it's true what you say, that most people will 
>bullet vote, then the scenario is all the more plausible.
>
>>With a majority requirement, Approval gets much better. Then we'd 
>>want to look at runoff conditions. Approval should *ameliorate* -- 
>>not entirely eliminate -- Center Squeeze. Approval theorists have 
>>largely failed to anticipate, I think, the degree of bullet voting 
>>that will occur. In Bucklin, which is Approval with some degree of 
>>Later No Harm protection (not absolute by any means), bullet voting 
>>was seen with most voters. But most voters, by definition, support 
>>frontrunners! I prefer Bucklin for public elections because it 
>>remains simple to canvass, resembles Approval in some good ways, 
>>and still allows voters to express an exclusive first preference. 
>>I'd allow multiple voting in all ranks, so a three-rank Bucklin 
>>ballot could be quite expressive. (Traditional Bucklin, as in 
>>Duluth, Minnesota, only allowed multiple votes in the third rank.)
>
>An aside: you like Bucklin. Have you considered MDDA? Like 
>ER-Bucklin, it also passes the favorite betrayal condition (meaning, 
>you don't have to vote someone below favorite if that person *is* 
>your favorite). MDDA also meets SFC, which means that if there's a 
>coordinated majority, that majority needs not to falsify any 
>preference. It acceps truncated ranked ballots (like Bucklin).
>
>MDDA works like this: Ranked ballots, all ranked are approved. 
>Before the Approval phase, check for each candidate if there's some 
>other candidate that is ranked above that candidate on a majority of 
>the ballots. If so, disqualify the candidate ranked below. Do this 
>for all candidates for which this is true, unless that would 
>eliminate all candidates. The Approval winner of the remaining candidates wins.
>
>Also, regarding bullet voting: given my French example above, I 
>should rationally argue that bullet-voting is prevalent, but I'll do 
>otherwise. Both the Burlington and the SF data shows that 
>bullet-voting is not as common as you say.
>
>The raw ballot images for SF say that some people bullet-voted by 
>ranking the same candidate first, second, and third - that works 
>like bullet-voting because if that candidate is X, and X is 
>disqualified, X is removed from all positions of the ballot, hence 
>he's no longer in the running. Similarly, if X wins, X is then 
>removed from the ballots, which means all positions of the virtual 
>bullet ballot have been invalidated.
>
>Now you may say that SF voters aren't clever enough on the whole to 
>bullet-vote this way. That leaves Burlington; and I suppose you 
>could say that Burlington is unrepresentative - unlike most areas of 
>the nation. Thus, we would need more data -- but at least we *can* 
>check if bullet-voting is prevalent, at least unless what you said 
>is specific to Approval, in which case we can't (unless we can get 
>UN voting data or similar).
>
>>Polling errors are mostly moot. Most voters don't vote based on 
>>polls, they vote based on their own impressions of their community. 
>>Voting systems theorists obsess about "strategy." Voters don't, 
>>generally. If sophisticated strategy is used, it's organized by 
>>people who supposedly know what they are doing, and it's 
>>questionable how much it's followed. Some will follow voter 
>>information cards. Some won't.
>
>Those impressions could be even less accurate than polls, 
>particularly in large countries. If you're in a liberal area, maybe 
>you think more people are liberal than is really the case. If it's a 
>close race, inaccuracies will just make the situation worse.
>
>Regarding organized strategy, it's unclear to what extent this will 
>happen. The most similar situation is that of vote management in 
>STV. Some countries (or local jurisdictions, in the case of local 
>elections) have used vote management, while it's unheard of in other 
>places (like Australia, for instance). The brief use of STV in New 
>York had quite a bit of vote management involved, where the large 
>parties (Democrats and Republicans) tried to use consistent strategy 
>to win disproportionate numbers of seats.
>
>>>Voters shouldn't have to do this.
>>We should make it easy for voters? Why? Is it a simple task to 
>>negotiate the winner? And that's what voters are doing. It gets 
>>really compressed into a single ballot, but most deliberative 
>>bodies don't work that way, and a majority is required to make a 
>>decision. Approval works really well in this environment, I've seen it.
>
>The task is for the method to pick the winner which pleases most the 
>greatest. The input is preferences (with or without preference 
>strength) and the output is the winner or a social ordering.
>
>If we were to negotiate, well, then just stick everybody in an 
>assembly and *have* that negotiation. But that doesn't scale. Why 
>doesn't it scale? Because the system takes too long to settle into a 
>stable state.
>
>If you try to attach negotiation onto a voting method, then that 
>method may also fail to settle. It's clearly infeasible to have an 
>assembly of a million people - so even if the voting method reduced 
>this a hundredfold, you would have a problem running it in a country 
>with 100 million voters. An Approval-style method with multiple 
>rounds could cycle, for instance.
>
>But to directly answer your question: why should we make it easy for 
>voters? Because voting is hardly worth it even now. There's no 
>reason to make it harder (in the sense of the voter having to think 
>thoroughly in order to craft his effective vote). You may say that 
>this hits against ranked ballots as well, but in a good ranked 
>system, you just have to give your preferences, if you have any. No 
>method is strategy-proof, but some are less susceptible than others.
>
>>Basically, know what you want, it's very clear, bullet vote. Could 
>>happily accept more than one candidate, vote for the ones you would 
>>happily accept. Unclear on which it is? Lean toward the bullet 
>>vote, if there is majority failure, you can modify your later vote. 
>>But whenever you have trouble deciding which of two candidates to 
>>vote for, vote for both!
>>What's hard about that? What's hard is when a majority is not required.
>
>It's hard in exactly the situations where your vote would count the 
>most. See the examples above. I'll grant that a runoff does help, though.
>
>>>  Since we know Plurality is bad, and IRV is bad as well (in one 
>>> sense, it has to be, so it elects the "right" first candidate in 
>>> a multiwinner election), that leaves Condorcet - or something exotic like MDDA.
>>I don't think I understand this statement. Range is the ideal 
>>single-winner election method that doesn't allow a runoff with 
>>majority failure. And it's simple to canvass. Of course, the 
>>simplest Range method is Approval.
>>There is a meaning to Condorcet failure, but not having preference 
>>strength information is a severe problem; and any method which 
>>considers preference strength for other than resolving Condorcet 
>>cycles is clearly flawed and can make preposterous choices. Yes, 
>>the Condorcet winner can be a preposterous choice, and would *lose* 
>>in a runoff. The only reason we think otherwise is that we imagine 
>>fixed preferences and a fixed electorate that votes according to 
>>these fixed preferences in the runoff, without considering the 
>>results of the first ballot. In real deliberative bodies, people 
>>respect preference strength and will yield first preference when 
>>the strength of it is weak. What goes around comes around.
>
>You say that "any method which considers preference strength for 
>other than resolving Condorcet cycles is clearly flawed and can make 
>preposterous choices". But Range considers preference strength for 
>other  [reasons] than resolving Condorcet cycles, and what you said 
>implies that the ranking-based CW should win when there is one.
>
>If the Condorcet winner is a "preposterous choice" and could lose in 
>a runoff, well, have a runoff; but if we're considering single-round 
>methods, let's compare how they work /as/ single-round methods. Is 
>the distortion from three-way (or more) races more likely than the 
>distortion from pizza-election cases? I think the former is more 
>likely than the latter, because in a society where people value 
>peace, they would personally value candidates that are good for many 
>but really bad for some lower than a compromise; and in a society 
>where people don't, those "many" would show up in a hypothetical 
>runoff or (in the single-round instance) vote max score for the 
>"good for many really bad for some" candidates anyway.