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                                                      CHAPTER 4


                                 THE IDEA OF THE CONDORCET CANDIDATE


The idea of the Condorcet candidate is an important element in modern day voting theory which it is useful to know to understand this area and the position taken on voting systems in this book.  The first item below is the text of an exchange I had with a political science student in Russia on this matter.  The second item is a piece I wrote as part of an exchange with a proponent of promoting Condorcet election in our voting system.


                                An Explanation to a Student in Russia


                                         May 26, 2004


Konstantin, I want to try to explain the idea of the Condorcet candidate as I understand it.  I may have some things wrong and may get back to you after doing some more checking.


When you have an election for a single candidate for an office but have more than two candidates running, you may have a problem.  If you do as we do in the US in many elections, the candidate with the most votes wins, but such a candidate may not be the one that most voters would prefer.  So in such elections it may be possible for votes to be so split that an extremest candidate with a small but determined voting group actually wins.  Runoff elections are an attempt to get around this problem.  In France, for instance they take the two top candidates and decide between them.  But as the last presidential election there showed, this may also result in an unsatisfactory outcome as well as in the case where La Pen got to the runoff and Chirac won by default.



Condorcet, a French mathematician, was one of the first to point out such problems in voting processes.  He suggested that in multi- candidate elections that the person who would win in each possible one-to-one election should be the one chosen, hence the so-called Condorcet candidate.  That is, the main idea is that in a multi- candidate race (three or more candidates for an office) each race is conceptually broken down into separate pairwise races between each possible pairing of candidates--the candidate who beats each of the other candidates in their one-to-one races is the Condorcet candidate.


If there were five candidates for an office, candidates a, b, c, d and e, you have the following pairwise one-to-one elections.


           ab  bc  cd de

           ac  bd  ce

           ad  be



If a would beat all of the other candidates, he would clearly be the Condorcet candidate and you would need only four elections to determine that.  But if a would lose vis-a-vis all the other candidates and b and c would also lose vis-a-vis the remaining candidates, you would have to have ten elections to get the Condorcet candidate.  So determining who he/she is would take from four to ten elections.  Based on this, if you had ten candidates, finding the Condorcet candidate would take from 9 to 45 elections.


I think you can see the practical difficulty here.  I came across a web page on this in which it was suggested that one could use a system of weighting candidates to simulate such elections, but I am skeptical and need to do more reading to understand it. 


                                    Condorcet Elections--A Dissent


                                            July 16, 2007


Dave Ketchum, Thank you so much for all the effort you put into giving me information on the Condorcet method from the wikipedia.

It really was helpful to understand where you are coming from.


The method is very much what I told you I understood by it.  The method uses rankings to calculate how each voter would vote in all the pairwise elections that would have to take place to determine the Condorcet candidate.  That involves determining from the rankings how each voter would vote in each of these elections and then summing up the results for all voters.  While the matrices in the article look simple, the process of calculating all of this clearly is not easy which surely is the reason, as commented at the end of the wikipedia piece, that the process is currently used nowhere in the world.  In the US, for example, it would be a nightmare to try to introduce such a system where the voting infrastructure consists of a mix of paper ballots, mechanical voting machines and computerized systems.  Even in the case of computerized voting, using the system would require a considerably complex program with all the hazards that might entail--one botched election and you would totally discredit such a system.


Approval voting has the advantage that it does not suffer these difficulties.  It involves no additional complexities and can be adopted on current voting systems.  In addition, it has other advantages, not least of which is the fact that it has a strong tendency to choose the condorcet winner.  When it does not, it gives in my judgment a good alternative, it chooses the candidate which most voters find acceptable.


ON AV and the wasted vote syndrome.  It is incorrect to say that AV does not kill it.  Under AV every voter has an incentive if there is one candidate whom they both approve of and favor to give that candidate a vote.  It has been well established, as sort of a parallel to Arrow's theorem, in the technical literature that there is no voting system in which it does not pay for a voter to vote strategically--hence the wasted vote syndrome in plurality voting.

But the merit of AV is that it allows voters to vote both sincerely and strategically and hence better express their preferences in the voting process.  And since, as opposed to IRV, it only involves more counting you do not get into some of the bizarre problems with IRV which you clearly recognize.


I would maintain that of the feasible possibilities now available in terms of voting systems the best bet really is AV.  As I pointed out in my piece on approval voting, that system of voting 1) Does result in an outcome that effectively reflects voters' preference, 2) Is transparent to voters in terms of understanding the results, and 3) Is easy to administer.


We need to open up our political process to responsible third parties and we need to do it now.  AV can do that without the problems of IRV and that is why I have been urging third parties to support a campaign to petition Congress to introduce AV in federal elections.


Regards.                                      John Howard Wilhelm


P.S. I really enjoyed our exchange and wish to thank you for it.