[Election-Methods] Is this Condorcet method reasonable?

Steve Eppley SEppley at alumni.caltech.edu
Wed Dec 12 08:10:11 PST 2007


Juho Laatu wrote:
> On Dec 11, 2007, at 0:02 , Steve Eppley wrote:
>> If candidates may not withdraw after the voting, some of them may be
>> forced to withdraw before the voting (also known as "deciding not to
>> run, out of fear of being a spoiler that worsens the outcome") or some
>> voters may be induced to vote insincerely.
> Fortunately the results of the election are typically not known 
> beforehand. Therefore the reasons and information behind a withdrawal 
> before the election are typically quite different from what they would 
> be after the election. 

As I wrote in my previous email (above) what I meant by "withdrawing 
before the election" is deciding not to run.  Even without precise 
knowledge, fear of spoiling will motivate candidates not to run.  In 
partisan elections, the decision not to run will typically be made not 
by the individual but by his/her party.  If the voting method is 
spoiler-prone, the party will be afraid to nominate a potential 
spoiler.  Even in non-partisan elections, fear of being a spoiler (given 
a spoiler-prone voting method) will deter potential candidates from running.

> I also note that e.g. in the US presidential elections there have been 
> few spoilers and many candidates that could have become spoilers but I 
> think there are not many that would have given up the race already 
> before the election.

That is not what I have observed.  Ask yourself why do the parties each 
nominate only one person per office?  The reason is to avoid spoiling 
and losing.  Many people have competed to be the nominee of one of the 
two big parties, and nearly all who failed to be nominated chose not to 
compete in the general election.

>>   I've observed considerable
>> voter negativity regarding not having a good enough candidate to vote
>> for on election day, in systems where spoiling prevents candidates from
>> running, and having to "hold one's nose" while casting a vote for a
>> less-preferred candidate.  I expect there would be considerable voter
>> negativity regarding the need to vote strategically in systems that do
>> not permit withdrawal.
> After an election with withdrawals there can be two winners - one that 
> would have won based on the ballots and one that won as a result of 
> the withdrawals. Maybe the voters that supported the first "winner" 
> are also disappointed with the method. That may be true especially if 
> the first winner did not "win" as a result of strategic voting. Or if 
> most of his supporters think so.

Yes, but all voting methods are subject to disappointment by supporters 
of a loser, particularly if there exists another voting method that 
would have elected their preferred candidate.  So, why single out 
withdrawal methods for this criticism?  Furthermore, why believe that 
disappointment with a withdrawal method will be greater than 
disappointment with methods where voters must calculate and organize 
strategies every time there's a high-stakes election?

It appears to me that critics of withdrawal are forgetting that the 
incentive for candidates trying to win will be to compete to be the best 
compromise.  Their positions on the issues will be similar.  Assuming 
this is so, and assuming the underlying voting method chooses from the 
top cycle, how great could the voters' disappointment be?  Here's a 
spatial diagram to illustrate my point:

  L                 C1                  R
                  C2  C3

Assume C1, C2 and C3 cycle.  Since they are spatially near each other, 
the disappointment of the voters who prefer the pre-withdrawal winner 
should not be intense.

Assuming the C candidates are similar on the issues, I would NOT expect 
the voters' ranking of the C candidates in such elections to resemble 
the classic example of majority cycling:

     ?%      ?%      ?%
     C1      C2      C3
     C2      C3      C1
     C3      C1      C2

I would expect the voters to be far more split: a significant number of 
voters who rank C1 first would rank C2 second and a significant number 
of voters who rank C1 first would rank C3 second, etc.  I would also 
expect the voters' preference intensities regarding the C candidates to 
be relatively small compared to the intensities involving L and/or R.  I 
would expect the candidates' and parties' preference intensities 
regarding the C candidates to be small too.

Assume C1 > C2 > C3 > C1 (where '>' means "is ranked by a majority 
over") and that C1 wins if no one withdraws.  It has been suggested that 
C3 may pay C2 to withdraw.  If so, why care?  Elections are crude 
instruments for making social choices.  Furthermore, C1 has the moral 
high ground and could offer to pay C2 not to withdraw or could offer to 
pay C3 to not pay C2.

Note the similarity between withdrawal and parliamentary coalition 
formation.   When parties form a coalition to select the executive 
cabinet officers (in particular, the prime minister) they are not bound 
by the votes of the recent election.  Who knows what deals they will 
make?  At least with withdrawal, all a candidate can do is step out of 
the way of their supporters' next choice.

> Juho

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