[EM] Condocet with many candidates - two round elections considered

[Juho]

On Jun 16, 2010, at 4:34 PM, Peter Zbornik wrote:

> Dear all, dear Markus Schulze,
>
> after having presented Condorcet elections to some people in the  
> Czech green party, the following question came up.
> Condorcet elections might work with three candidates, but what about  
> if there are twenty of them, will the system work and elect the best  
> candidate?

Condorcet methods work quite as well with more than three candidates.  
Some problems even get smaller when the number of candidates increases  
(maybe majority of them???).

>
> Q1: What would you answer for Condorcet elections in general and  
> Schulze-method elections in particular?

Different Condorcet methods are very similar in real life elections.  
The first thing that might cause different results when compared to  
some other methods is that the Schulze method uses winning votes to  
determine the strength of pairwise preferences. Other characteristic  
features of the Schulze method are that in case of a top level cycle  
it uses uses beatpaths and always elects from the Smith set. The  
difference to other common Condorcet methods is quite marginal here.

In general the answers from practical elections point of view are very  
similar to all Condorcet methods. Different Condorcet methods meet  
different criteria and give different results in some specific  
examples. These properties can be used to promote one method or  
another, or oppose them, but as already said, from practical elections  
point of view the differences are very small.

> Q2: Specifically, would you recommend a two-round construct, i.e.  
> the three best candidates (or x best?) meet in the second round.

No, Condorcet methods can handle all this in one round. I can  
understand that if people are used to having two rounds then it would  
be nice to first see who the leaders are and what other voters were  
thinking, and only then make the final decisions. One could handle  
this as well by arranging first a test election (or one or more polls)  
and then the final round that would include all the candidates. If  
there are very many candidates then it might be practical if some of  
them would not participate in the final round (to ease the task of  
voting), but I don't see any other reasons for arranging the final  
round with few candidates only.

(Multiple rounds make strategic voting slightly easier but I don't  
expect strategic voting to be a problem if the number of voters is  
higher than say 10.)

> Q3: Would such a two-round system help to deal with the case of the  
> "dark horse" winning with long beat-paths and people being  
> dissatisfied with the election?

I don't think so. Condorcet methods allow also candidates that do not  
have high number of first preferences to win. I.e. also good  
compromise candidates from smaller groupings do have a chance if the  
supporters of the largest groupings generally like that candidate and  
rank her second after their own candidate. Other kind of "dark horses"  
are probably not a problem. They could be a problem only if the voters  
start doing something irrational in wide scale, like ranking some bad  
candidates above all the serious candidates. Strategic voting could be  
one more way to try to introduce "black horses", but I don't believe  
that to be a problem, and second round would not help.

> Q4: If yes, how many candidates should be in the second round and  
> how should they be selected (Schulze ranking?)?

(I said "no" but...) Any proportional ranking based approach would be  
fair in the sense that it would pick candidates from all segments of  
the party. But that would work also against the target of electing a  
candidate that all like. And in that process one could also eliminate  
some candidate that would be the winner at the second round (assuming  
that opinions would change a bit and the first ranked (Schulze  
ranking) candidate would not win). Therefore it would be more natural  
to pick candidates that got good (single-winner) Condorcet results at  
the first round. This approach could look a bit biased sine the  
centrist / "liked by all" candidates would be over-represented. So, if  
there are not too many candidates, maybe better to keep all of them  
also at the final round. Keeping them all may also give more complete/ 
accurate information on how liked each one of them is.

>
> One such mis-election with dissatisfied voters would be enough to  
> discredit Condorcet elections in our party and two-round elections  
> might give an additional sense of security for some voters in the  
> face of a novel and fairly complex election system. In the Czech  
> republic we currently use two-round elections.
> However, if two round Condorcet elections bring no additional value,  
> then there is no need to complicate an elegant election system.

Yes, I can understand that people that are used to a two-round method  
may feel like being surprised if the method elects someone already at  
the first round, especially if they did not anticipate who the winner  
would be. And as I already said, maybe polls or preliminary elections  
would be a better approach than trying to eliminate some of the  
candidates before the final round. It is also possible to allow some  
candidates to withdraw before the final round (but I wouldn't  
encourage them of put pressure on them since it is better to let the  
voters decide).

BR, Juho


>
> Thanks for your advice.
>
> Best regards
> Peter Zborník
>
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