[EM] first-wave Condorcet versions for public election

[Juho Laatu]

Dear All,

 

One more formulation of the IRV or Condorcet question could be: Why is Condorcet less popular than IRV?



 

One reason for this is that experts that support Condorcet have not yet agreed which completion method is the best. Another reason is that explaining the differences of alternative Condorcet completion methods leads to quite detailed technical discussions. These two together mean that it is difficult to make simple and concrete proposals that would be backed up by "strong academic support".



 

IRV has also the additional benefit that the vote counting process looks pretty much like an exciting real life fight where some candidates at some point have to give up and donate their votes to the other candidates. To many people this kind of dramatic nature of the vote counting process may be more interesting than e.g. the relatively complex technical terms that are used on this mailing list to compare different Condorcet alternatives.



 

The following mechanism is my favourite single winner mechanism for two reasons: 1) technical merits (it is simple and it makes a good pick), 2) it is easy to explain and understand. I think this is about the level of simplicity that would be required to make Condorcet methods more understandable and acceptable to other than the hard core experts.



 

Least Additional Votes:

"Elect the candidate that wins all others. If there is no such candidate, elect the one that needs least additional votes to win all others."



 

Not a word about cycles and cycle breaking, not even about pairwise comparison matrixes. This is not really a new method but maybe a new way to describe the rules.



 

Any support to this kind of thinking and the voting method in question in this group?



 

- - -



 

I'll write also few other observations here to give some background to why I like this particular voting method (and this style of defining the voting method).



 

James Green-Armytage wrote:

> However, I would not feel especially good about a method that isn't Smith-efficient, even to start out with.



 

I both agree and disagree with this. I don't feel good about methods that elect an alternative that is not in the Smith set. But on the other hand I similarly do not like methods that create preference loops even in situations where all voter preferences are all non-cyclic. I have however learned that laws of nature and mathematics are such that preference loops occur in group opinions and I can't do anything about it. Condorcet methods are thus still maybe the best single winner methods although they have to cope with this loop problem somehow. For similar reasons I question the value of the Smith set. Sometimes the poor option of electing someone outside the Smith set may still be the best option.



 

I'll use one concrete example.

101: a>b>x>c

101: b>c>x>a

101: c>a>x>b

100: x

Let's say that we have here four parties of about equal size, and each party has one candidate. Candidate x is a Condorcet loser but, using terminology of the voting method I described above, candidate x would need only two additional votes to become a Condorcet winner. Candidates a, b and c would each need 102 additional votes to become Condorcet winners.



 

Most people on this list agree that Condorcet winner should always win. Although candidate x is a Condorcet loser, it is very close to being a Condorcet winner (two votes missing). The structure of the graph describing the results must thus in some sense be very flat. If one draws a graph that describes the results of the election, Smith set is typically drawn on top and candidate x below it. This leads to thinking that that "candidate x is clearly below the Smith set and should therefore not be elected". I however claim that the visual structure of such a graph impacts our thinking too strongly here. Graph based visualizations are in general not a very useful tool when discussing voting related matters that involve cyclic preferences.



 

I guess often also the wish to make election results a linear preference order is present. This happens although we (in theory) already know that group preferences can not be presented as a linear preference order (although individual preferences maybe can). For this reason I don't feel quite comfortable with Condorcet completion rules that try to re-establish this linear structure of individual preferences also in the final results (since that simply is not natural for group preferences).



 

I like to see the Least Additional Votes method description in the light of "real life impact" (instead of trying to "re-establish a linear preference order" or using other order based measures to justify the method). In the voting example above the election could have been held in order to elect a captain for a pirate ship whose crew consists of pirates that are citizens of four very different countries (maybe about 10 from each country instead of the 100 in the example to be more practical :-) ). Electing pirate x as the captain would be a rather good option since in case of a mutiny planned by a, b or c they would maybe not dare to try it since they would not be able to persuade sufficient majority of the crew to participate in the mutiny (51+% majority with some uncertainty of the plans of few individuals and/or their fighting skills is too risky). Mutiny against captain a, b or c would be easier. Same rules apply of course also in politics. "Least additional votes" may t
 hus
 sometimes have a real meaning and impact in the real world (=getting two additional pirates in the ship to eliminate the risk of mutiny in this case). (There may be also other "real life" criteria than this "mutiny criterion" but I won't go further in that direction now.)



 

In the election methods mailing list I have in the recent months observed lots of discussion on criteria that are related to making the voting methods as strategy free as possible. Sometimes I have even gotten the impression that when electing the winner from the candidates in the top loop (Smith set) it could be anyone in the top loop, as long as the numerous strategy criteria are fulfilled. I guess this has not really been the case, but my point is that one should give high priority to selecting the candidate that we think is best, and maybe a bit less priority to all the strategical considerations. This is based on the assumption that strategical voting is not that easy in real life, at least not in elections where the number of voters is large. Many of the strategical voting cases are problematic only in situations where the voting behaviour of the voters is known. In real life this is seldom the case. (And cycles are also rare.) With this I want to say that sometimes sim
 plicity
 and/or "real life need" based rules may be more sensible than detailed strategy based criteria.



 

All the comments above were written in order to explain why the Least Additional Votes method is so good (possibly in the "fight against IRV" :-), for the non-experts, as well as just in general). James Green-Armytage presented a number of number of good tools and arguments that could be used when trying to achieve consensus within the community on the best single winner method. I didn't consider the Smith set as critical as he did, and as a result I'm leaning in a somewhat different direction when trying to locate the best Condorcet method. Any comments appreciated.



 

Best Regards,

Juho Laatu

(long time follower but not so active participant of the election methods list :-)

 

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