Dear Raph, you wrote: > I was thinking of a 'stable marriage problem' like solution.
Good idea! If it works, the main difficulty will be to make the whole process monotonic, I guess... Yours, Jobst > > Each voter rates all the candidates. > > Each voter will assign his winning probability to his highest choice > (probably split equally if he ties 2 candidates for first). > > If 2 voters 'marry', then the candidate with the highest score sum is > the compromise candidate. > > Solve the stable marriage problem. It might be necessary to randomly > split the ballots into 2 'genders' to guarantee that a stable solution > exists. > > Using the above example: > > G1: A1(100) A(70) A2(0) > G2: A1(0) A(70) A2(100) > G3: B(100) > G4: C(100) > > (unnamed options are rated zero) > > If a member of G1 'marries', then the compromises are > G1: A1 (+0) > G2: A (+40), i.e. 100->70 (-30) and 0->70 (+70) > G3: A1 and B tie (+0) .. effectively not a 'marriage' > G4: A1 and C tie (+0) .. effectively not a 'marriage' > > Thus rankings are > G1: G2>G1=G3=G4 > > Similarly > G2: G1>G2=G3=G4 > G3: all equal > G4: all equal > > Thus the 25 G1s will 'marry' the 25 G2s and compromise on A. > > The result being > > A: 50% > B: 25% > C: 25% > > Also, what about an iterative method. If the candidate with the > lowest probability has less than 1/3 probability, eliminate him and > re-run the calculations (and probably rescale the ratings). This is > kind of similar to the requirement that a candidate has 1/3 approval > before being considered. > > As an added complication, in the above, it might be worth doing a > second pass. Once all the marriages are stable, you could have > 'suitors' propose to 'engaged' voters and make an offer with a > different compromise candidate. > > For example, if two voters has ratings, > > A1(100) A2(90) A3(75) A4(55) A5(0) > A1(0) A2(55) A3(75) A4(90) A5(100) > > The possible compromises are A2, A3 and A4. However, A2 favours the > first voter and A4 favours the 2nd voter. It might be the case that > after being refused, a 'suitor' could sweeten the deal by offering a > better option. > ---- Election-Methods mailing list - see http://electorama.com/em for list info