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

[Kristofer Munsterhjelm]

Abd ul-Rahman Lomax wrote:
> At 05:41 AM 1/21/2009, Kristofer Munsterhjelm wrote:
> 
>> My usual argument against Approval (in favor of something more 
>> complex) is this: Say there are three viable parties (if there will be 
>> only two, why have Approval in the first place?). You support A > B > 
>> C. If A is in the lead, you can approve of A alone. If A's a minor 
>> party, then you should approve of both A and B. But if the parties are 
>> close, then it may not be clear who you should approve - if A's 
>> slightly too low (and the important contest is A vs C), then voting 
>> only A will split the vote and may cause C to be elected instead of B. 
>> If A's not that low (and the important contest is A vs B), then voting 
>> both A and B will cancel your vote for A with your vote for B. It 
>> becomes more difficult the closer the parties are in support, and 
>> polling errors could cause further problems.
> 
> Approval works within a multiple election environment, classically it 
> wasn't used with anything other than a true majority requirement, and it 
> was probably expected that initial votes would be bullet votes. Approval 
> as a deterministic method that must find a winner with a single ballot 
> is simply a more sophisticated, improved form of Plurality, as is IRV, 
> but Approval is far simpler.
> 
> The scenario described is unusual in partisan elections, but I certainly 
> wouldn't propose Approval as an ideal election method. It is merely the 
> largest improvement that can be accomplished with such a minimal shift 
> from Plurality: just start to count all the votes. Dump the 
> no-overvoting rules.

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?

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.

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.