[EM] "margins" Condorcet methods have a critical strategy problem

[Juho Laatu]

Hi,
 
This is a response to James Green-Armytage's mail
http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015125.html
 
You asked me to read the mail after I had defended the margin based methods. Now I did - or actually I had read the mail ealier but only now find some good time to reply.

I think strategies in voting methods are quite different in large public elections and in small elections. To keep the answer simple and because public elections are the default case (and because this is easier :-) ) I'll cover the large public election case only.
 
In general I think one should always evaluate the seriousness of each strategy problem before deciding to defend against it by modifying the voting method. I drafted a quick list of possible classifications in http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/015172.html.
 
But now to the mail itself.
 
I think this vulnerability is one of the worst I have seen. I however do not want to jump to the conclusion that margin based methods are all bad. I'll try to analyse where and how likely the problems are.
 
First I try to list some reasons why this strategy would not be used in real life:
- bad reputation to the party that (publicly) proposes it voters to use the strategy
- impossibility to co-ordinate party votes without the plot leaking out
- lack of understanding of the voters (it is difficult enough to give a sincere vote)
- common knowledge that this strategy exists, which means that all parties could try the same trick
- or same percentage of voters from each party would do the trick
- risk of electing C
- unwillingness of voters to participate in this kind of plotting
- it may be that there are more cases where strategical voting attempts bring harm than it brings benefits => people think that it is better to be sincere
- government and parties may do propaganda to emphasize that sincere voting brings best results (in Condorcet methods) and strategies typically harm the voter
- exact number of votes of each party is not known (gallups may give some info)
- rankings of those voters are known even less
 
In summary, the risks of recommending this strategy may well lead to not recommending its use. If there is a threat that members of different parties want to apply the strategy themselves, it may be better for the parties to recommend not to use this (nor any other) strategy. Otherwise the results couls be a mess and the party could lose the election instead of winning it. Parties that defend sincere and honest voting might also get more support from the voters.
 
 
Some more detailed notes follow.
 
In example 2 the B voters voted strategically B>C>A.
 
Let's assume that a margins based method was used as the voting method because it was considered to be the sincere method (one that brings the intended results with sincere votes).
 
What if the voter preferences were sincere and B>C>A was the true opinion of the B voters. In this case it would not be a good idea to modify the voting method (e.g. to use winning votes) since then it would give wrong results with these sincere votes. And it is impossible to tell how many of the B>C>A voters were sincere and how many did that for strategic reasons.
 
What I mean is that every deviation from the sincere method makes the voting method worse so that it no more gives correct results with sincere votes. If the voting method is changed, then we may have to recommend all voters to vote strategically. But of course that is not a nice idea. All such steps may lead us away from the target of electing the best candidate. This is the reason for my interest to try to live with the sincere method as long as I can.
 
 
In the last example (numbered as 3) I noted one interesting thing. If both A and B supporters would truncate their votes, then it doesn't change the situation much is also voters of C do the same thing. And if all truncate their votes, then we are close to recommending a plurality based method to be used. (A vores vote A, B voters vote B, and C voters vote C)
 
I guess the good part of Condorcet is allows people to give their full rankings. Therefore strategies that involve such heavy truncation may reduce ranking based methods to something less.
 
 
Summary:
I hope that in large public elections most of the stratecic voting cases would be too problematic, general opinion would be in favour of voting sincerely and there would be no efficient strategies that would force everyone to voting stretegically. I was not yet convinced that this strategy, although a very threatening one, would be probable in large public elections. If that would be the truth and margins would be the chosen sincere method, then margins could be still used despite of this vulnerability. Making changes to the sincere voting method may bring other kind of problems. Of course this is a problem situation that just must be balanced right.
 
Best Regards,
Juho

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