[EM] strategy-free Condorcet method after all!

[fsimmons at pcc.edu]

Very ingenious!Perhaps the method could be adapted some way to choose a clone class, then  a sub clone class within the winning clone class, etc.----- Original Message -----From: Jobst Heitzig Date: Saturday, November 14, 2009 4:32 amSubject: strategy-free Condorcet method after all!To: EM Cc: Forest W Simmons > Dear folks,> > it seems there is a stragegy-free Condorcet method after all -- say> good-bye to burying, strategic truncation and their relatives!> > More precisely, I believe that at least in case of complete > information(all voters knowing some details about the true > preferences of all other> voters) and when all voters will follow dominating strategies, > then the> following astonishingly simple method will always make unanimous > sincerevoting the unique dominating strategy, and it will always > elect a true> beats-all winner (=Condorcet winner):> > > Method: Reverse Llull> =====================> > 1. Sort the options into some arbitrary ordering X1,...,Xn (e.g.> alphabetically or randomly), publish this ordering, and put i=n.> > 2. If already i=1, then X1 is the winner. Otherwise, ask all voters> whether they prefer Xi or the option they expect to be the > winner of> applying this method to the remaining options X1,...,X(i-1).> > 3. If more voters prefer Xi, Xi is the winner. Otherwise, > decrease i by> 1 and repeat steps 2 and 3.> > > Why should this be strategy-free?> > If n=2, the question in step 2 is whether X1 or X2 is preferred > and the> method is traditional majority choice in which sincere voting is known> to be the dominant strategy in case of 2 options.> > For n>2, we prove strategy-freeness inductively, assuming it has been> proved for n-1 options already: Since we assume that each voter > followsdominant strategies and knows enough about the other voter's> preferences, and since each voters knows that sincere voting is the> unique dominant strategy for all cases of at most n-1 options, > she will> know in step 2 which option Xj would win if the method was > applied to> X1,...,X(i-1), and she will also know that her vote at this step does> not influence which option Xj is but only whether Xi or Xj will win.> That is, in step 2 all voters face a simple majority choice > between two> known options Xi and Xj, so again voting sincerely in this step > is the> unique dominant strategy. By induction, the whole method is > strategy-free.> > > The method is in some sense the reverse of Llull's famous > earliest known> "Condorcet' method from the 13th century (cited recently on this > list):In the classical Llull method, voters would first make a > majoritydecision between X1 and X2, then a majority choice > between the winner of> the first choice and X3, and so on working thru the whole list of> options, always keeping the last winner and comparing it with > the next> option in the list. The overall winner is the winner of the last > comparison.> So, the only difference between classical Llull and Reverse > Llull is the> order in which these pairwise comparisons are done. If we assume all> voters vote sincerely in classical Llull, both method would be> equivalent. But with strategic voters, the difference is > important: In> classical Llull, a voter's voting behaviour in one step can influence> the results of the later steps (because it can influence which > candidate"stays in the ring"), whereas in Reverse Llull it cannot.> > > In practice, the method can be sped-up by using approval-style ballots> on which each voter marks after step 1 every option Xi which she > prefersto the expected winner of the subset X1,...,X(i-1).> > As for additional properties, Reverse Llull is Pareto-efficient,> Smith-efficient (i.e. elects a member of the Smith set), and > monotonic,but not clone-proof.> > I wonder if we can also find a clone-proof version of this... > Any ideas?> > > Yours, Jobst> 
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