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

[Abd ul-Rahman Lomax]

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.

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.)

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.

Optimal strategy in Range, for example, is only slightly better than 
a "sincere vote," i.e., one where preference strengths are accurately 
expressed. Actually, in the simplified situations I examined, 
"approval style voting" in Range was *the same* in expectation as 
"range style voting," with an intermediate candidate voted at an 
intermediate rating. However, *the variation* was greater: the 
"sincere vote" was more stable or conservative; the bullet vote was 
more effective in getting the best of what the voter wanted, but more 
at risk of getting the worst instead (by failing to vote for the compromise).

My suspicion, unproven, is that an accurate vote in Range is 
*generally* the best strategy, zero-knowledge. At the other extreme, 
where the voter knows the frontrunners accurately (and, totally 
extreme, the voter knows all the other votes and knows if the voter's 
vote could affect the outcome, and, if so, the voter votes to 
accomplish the best possible result), a bullet vote is just as 
effective as anything else.

>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.

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.

>  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.