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

[Kevin Venzke]

Hi Peter,

--- En date de : Mer 16.6.10, Peter Zbornik <pzbornik at gmail.com> a écrit :
>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?

In my opinion, in theory, Schulze performs exactly as well with many as
with few candidates.

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

I would not say Condorcet in general is excellent at this, but Condorcet
fans tend to prefer methods that don't break when you have many candidates.

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

The only reason I would recommend something like this is if you expect
that voters may not be familiar with the strongest candidates. If voters
do not obtain *new* knowledge between rounds, and their preferences don't
change, then the pairwise contests among them are going to be exactly
the same, and the Schulze result would most likely be the same.

>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?

If the "dark horse" can win in this way (more likely: he wins because
everyone gives him a mid-range preference and he defeats everyone) he will
most likely still win when you eliminate all but a few candidates. So
again, a second round only makes a difference if the voters are supposed
to get new information and change their preferences.

The ordinary two-round method is different from this because when you
eliminate candidates, the "best" candidate could very easily change, since
it's all based (in theory) on who is everyone's favorite candidate.

Kevin Venzke