[Election-Methods] Is this Condorcet method reasonable?

Juho juho4880 at yahoo.co.uk
Wed Dec 12 10:28:28 PST 2007

On Dec 12, 2007, at 18:10 , Steve Eppley wrote:
> As I wrote in my previous email (above) what I meant by "withdrawing
> before the election" is deciding not to run.

Ok, there are two cases, one where the candidate has already been  
identified as a candidate and another one where not.

> 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.

I'd classify this as a special case where the idea is to eliminate  
the impact of losing to candidates of one's own party. In this case  
there are methods that can be used to eliminate the risks without  
using withdrawal. One approach is e.g. to use minmax and simply  
decide that party internal losses will not be counted. (I'm however  
not sure that any defensive actions are needed.)

>> 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?

Ok, within a party limiting the number of candidates is possible (and  
stepping up as a competitor to one's own party after losing the pre- 
elections is maybe not an option to most people).

The risk of being a (party internal) spoiler is smaller in Condorcet  
based methods than what it is in plurality.

>> 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?

The problem with withdrawal is that the candidates and politicians  
themselves are given the option to "change" the result "after the  
public election" based on their own opinions. In some sense the  
ability of one or few persons to decide the winner beaks against the  
default rules of democracy. (Also the increased risk of corruption is  
one additional concern.)

>   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?

I don't want to defend strategies. They are bad in all scenarios. On  
the other hand I'm not convinced that withdrawal would significantly  
reduce strategic voting (including concerns of strategic withdrawal).  
One can also claim that in normal large scale public Condorcet  
elections (and when assuming that the voters have the tendency to  
make their own decisions instead of expecting voting orders from the  
party) the impact of strategic voting can well be insignificant.

> 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.

Ok, the cycle is likely to be weak then.

> 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?

You didn't expect any strategic or otherwise insincere voting to be  
present. If so, maybe C1 should win.

>   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.

I accept the ideas of representative democracy (representative will  
decide instead of citizens deciding directly) and allowing the  
representatives the luxury to work in the way they wish until the  
next elections. It is more problematic to me to allow the candidates  
to decide who will be elected.

Some more discussion on the example above:

The example could be extended a bit by assuming that the C1  
supporters voted strategically and this way were able to make C1 win.  
In Condorcet elections this could mean that the sincere preference of  
the strategists was C1>C3>C2 but they voted C1>C2>C3 and successfully  
buried C3, and that C3 would have been the winner with sincere votes.  
Now C2 would have some moral reasons to withdraw and change the  
winner from C1 to C3. C2 and majority of his/her supporters could  
also prefer C3 to C1.

There are however problems like deciding who will withdraw. Also  
others may have voted strategically, or at least often people are  
tempted to explain their losses that way. This could lead to closed  
negotiations between C1, C2 and C3 right after the election. The  
voters would need to wait for some time for C1, C2 and C3 or their  
parties to decide who will be allowed to win. This setting doesn't  
sound very positive to me.

If two of the three cyclic candidates are from the same party (C2,  
C3), then that party could decide that one of the two candidates  
should withdraw (C2) (and voters would maybe accept that). One  
problem is that C3 lost to C2 but now wins. On the other hand C3 won  
C1, so he is a good winner from that point of view. But as already  
said, I'd prefer this dilemma to be solved in the basic method  
without withdrawal. (Well, maybe allowing a party member to withdraw  
to make another party member win would be an option that would be  
less problematic than a free withdrawal option. I prefer  
deterministic voter decisions though.)

I'm still missing an example where the withdrawal option would bring  
clear improvements (on problems that are likely to appear in  
elections) and would not introduce many problems itself. One big  
problem is also the quite possible perception of the voters that the  
candidates/politicians ignored the opinion of the citizens and  
decided otherwise. In the case of withdrawal multiple explanations to  
the withdrawals are likely to exist (=no clear well justified  
explanation of defending against strategic voting).


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