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

[Kristofer Munsterhjelm]

Dave Ketchum wrote:
> On Fri, 23 Jan 2009 12:47:53 +0100 Kristofer Munsterhjelm wrote:
>> 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?
> 
> Count of parties is not useful.  Usually there are only two leading 
> candidates and election method matters little.
> 
> Trouble is, occasionally there are more leading candidates, as in the 
> example below, and, THEN, methods matter.
> 
> Whether this was truly center-squeeze or not, the idea applies - two 
> candidates off to the side, each with a bunch of dedicated followers, 
> and a bunch of candidates sharing the center votes.

So it's important to the extent that third parties actually are voted 
on. For instance, there's no point in using Condorcet in Malta, unless 
one thinks this would make third parties more brave and thus try to 
break the two-party system there (assume for the sake of the argument 
that Malta wasn't completely parliamentary). However, there *would* be a 
point in using Condorcet in the U.S., as the 2000 election shows, except 
if the third parties would never become anything more than that, in 
which case we've lost and Duverger's law is just a reflection of reality.

If third parties become more than minor parties, and have the chance of 
being competitive, then the problems above can occur. They do in IRV, 
and to a lesser extent in Approval. But this is where it's most 
important that the methods don't err, because if they do so, they may 
confine the third parties to minor party status!

>> 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.
> 
> As with Approval, Condorcet voters have choices:
>      Dedicated followers of the two on the side likely bullet vote.
>      Center voters properly vote for a bunch of center candidates - 
> hoping one such will win.
> ...

The point with that example is that in Condorcet, this problem doesn't 
exist. If you're a Bayrou supporter, you can vote Bayrou > Jospin > 
Chirac > Le Pen, usually without having to worry that your later votes 
will defeat your former ones. Since Condorcet fails LNHarm, this *may* 
in some situations happen, but in that case, Jospin or Chirac (probably 
Jospin) was the reasonable compromise anyway.

Condorcet voters can vote the entire rank because voting A > B > C 
contributes to both A versus B and B versus C. On the other hand, 
Approval voters voting {A, B} | C don't contribute anything to the A 
versus B contest, and similarly, if they vote A | {B, C}, they don't 
contribute anything to the B versus C contest, so they have to guess or 
otherwise find out which contest is the most important.