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

[robert bristow-johnson]

On Jun 16, 2010, at 9:34 AM, Peter Zbornik wrote:

> 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?

one serious problem that *any* ranked-order system has is if there are  
more candidates than ranking levels on the ballot.  it means that  
after you rank your top, say, five candidates, you have no ability to  
weigh in on the rest of the candidates and it might be one of those  
candidates who ends up battling against another of the unranked  
candidates.  all unranked candidates are essentially tied for last  
place and you are prevented from ranking Satan or Beelzebub or Hitler  
lower than a dozen other candidates that you might not care so much  
about.

i think that ballot access rules, that limit the number of candidates  
to around the number of ranking levels, is the answer.

>
> Q1: What would you answer for Condorcet elections in general and  
> Schulze-method elections in particular?
> Q2: Specifically, would you recommend a two-round construct, i.e.  
> the three best candidates (or x best?) meet in the second round.
> 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 am less concerned about the DH problem than many here are.  if  
Liberals rank the DH above the Conservative candidate, it means they  
like the DH better.  if Conservatives rank the DH above the Liberal,  
it means they like the DH better than the Liberal.  if the DH ends up  
winning with very few first choice votes, then the DH may very well be  
the most acceptable compromise candidate over either or any of the  
polarized candidates that have more first choice support.

remember, assuming a Condorcet winner exists, electing *anyone* other  
than the Condorcet winner means that you are electing someone when a  
majority of voters have agreed that some other specific candidate is  
better and have explicitly marked their ballots as so.  you can call  
that specific candidate that the majority of voters preferred a "Dark  
Horse", but that's just a label.  the fact is that candidate is still  
preferred by a majority of voters over any other specific candidate.   
if you are taking the stated preferences of the voters at face value,  
how can you decide on anyone else and call that election reflective of  
the will of the voters?

now, if *no* Condorcet winner exists, then that's a different story.   
perhaps (instead of Schulze) electing the Smith set candidate with the  
most first-choice votes might prevent the Dark Horse from winning, but  
i think that the Schulze winner is a better choice (if they happen to  
be different).

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

i dunno about a party election, but in a general election one of the  
main problems is that only a fraction (around 50%) of the original  
voters show up for the second-round runoff.  that's one of the main  
reasons for settling the election on a single Election Day.

--

r b-j                  rbj at audioimagination.com

"Imagination is more important than knowledge."