On Mar 30, 2005, at 02:53, Gervase Lam wrote:
Should I thus read your comment so that you see MinMax (margins) as a sincere method (the best one, or just one good sincere method) whose weaknesses with strategic voting can best be patched by using Raynaud (Margins)?
Roughly speaking yes, but not exactly. If you think Margins is an important way to measure closeness to being a Condorcet Winner, then Raynaud(Margins) might be the next best thing. I cannot think of any other reasonable Margins method.
Of course, if you are willing to move away from Margins, there are other
more simple pairwise methods around that are reasonably 'strategic
resistant'.
I think margins is one natural sincere voting method. For practical purposes I accept also methods that do not make sense as sincere methods. They may be needed in order to fight against strategic voting.
In general think it would be very informative to always mention which sincere method each proposed practical voting method is based on. Or if there is no such complete sincere method in the background, then one should at least mention what (sincere) criteria have been taken as the basis. It seems that often the default value is simply to assume that the (ranking based) methods are Condorcet compatible. Many take also Smith set as granted I guess (I don't). For my taste using only these basic criteria is a bit lean. The main goal of a voting method is anyway to elect the best possible candidate, and defending against strategies is just something that may be needed in order not to let the voting method fail because of the strategic votes.
Examples may help to clarify what I mean. (SVM = SIncere Voting Method, PVM = Practical Voting Method, SC = Sincere Criteria)
SVM: MinMax (margins), PVM: Raynaud (margins) - the case that we discussed
SVM: MinMax (margins), PVM: MinMax (wv)
- winning votes used to defend against strategies
- I think both margins and winning votes based PVMs (as well as any others) are ok as long as there are god reasons to use them
- someone might claim that also winning votes based methods could be used as SVMs (?)
SVM: MinMax (margins), PVM: MinMax (margins)
- it would be nice if the SVM could be used also as the PVM
- I think this case could be feasible in many situations; it all depends on if strategy threats are considered marginal or serious
SC: Condorcet, PVM: MinMax (wv)
- when Condorcet is used as the SC any defensive means are ok as long as they don't violate Condorcet
- if there is a top cycle, any candidate could be elected
SC: Condorcet + Smith set, PVM: ...
- now the winner (in case of a top cycle) could be anyone within the Smith set
SVM: Condorcet + Approval for cycle resolution, PVM: Condorcet + Approval for cycle resolution
- this case just demonstrates that there could be also other SVMs than MinMax (margins)
- The "sincere target" is thus to elect the most approved candidate if there is no Condorcet winner
Selecting a PVM is of course a problem of finding a balance between SVMs and methods that are good in eliminating strategies (= balance between threat of not electing the best candidate because of deviation from the target SVM and threat of not electing the best candidate because of strategic voting). In cases where strategy problems are considered big we end up selecting some strategy eliminating focused PVM. In cases where strategy problems are less threatening we end up selecting a PVM that is close to the SVM.
Typically examples of strategic voting are handled as abstract examples that demonstrate that strategic manipulation of the end result is possible. In order to evaluate their real weight I would like to see an estimate on what the probability of each strategic voting case is in real life. One could for example look at some real life presidential election in some real country and then estimate how easy it would be to implement the strategy, how detailed information of the voters' preferences is needed, how many voters (and from which parties) would follow the strategy etc. In my opinion at least large scale public elections are not very easy to manipulate (in ranking based elections).
If someone is interested, I would be happy to see examples e.g. on how the "SVM: MinMax (margins), PVM: MinMax (margins)" case (this one should be an easy target) can be fooled in large public elections (with no more exact information than some opinion polls on how voters are going to vote).
As a response to your comment, I'm "willing to move away from Margins" in the PVM area if there are good reasons to do so (= to defend against strategies). Also other than margin based methods can be taken as the starting point (SVM) if they are properly justified. I picked the MinMax (margins) up because I think it is too often seen as a no good method although I think it is a good candidate for a SVM and possibly a well working PVM too.
I have tried to open a discussion on these topics by putting a mark on the opposite end of the playing field than where most players seem to be. I mean that it seems to be a typical thinking pattern to take Condorcet and Smith set as the only SC and then use all the remaining freedom and energy to find the most strategy resistant method (i.e. without caring which one of the remaining candidates would be most suitable for the job). The "MinMax (margins) as a PVM that is also the wanted SVM" approach represents the other end of the playing field.
Best Regards, Juho
P.S. One more comment. I have criticized also the interest to force the group opinions into linear opinions (i.e. transitive, like we expect the individual voters' preferences to be). This linearization of group opinions may give a false feeling of finding a sincere "big brother" opinion. This thinking is problematic since we know that group opinions are not linear but may be cyclic. Better justification is thus needed if some group opinion linearization methods are claimed to be SVMs. Or maybe they are just PVMs. I don't know if anyone has claimed or wants to claim them to be SVMs.
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