[EM] MOP-F2 / compromising
juho.laatu at gmail.com
Thu Jul 11 01:30:22 PDT 2019
This mail will be short. :-)
Condorcet methods are vulnerable to compromising strategy when there is a top loop. It is not easy to defend against that strategy. This threat may however look more serious on paper than it is in real life, since in real life voters are typically not aware that the group opinion will be circular.
MOP-F2 offers voters an easy and natural way to indicate willingness to compromise, without modifying their rankings. Instead of voting A>B>C, the voter can vote A>B>>C, and thereby indicate that A and B are his favourite candidates, and electing B would not be a bad thing. Without going to the details, I just note that this way of handling the compromising incentive seems to provide quite natural means to pick the winner among the looped candidates in a sincere manner, and without falsified rankings in the ballots.
> 1) Votes are ranked votes with one cutoff. Candidates above the cutoff are called protected candidates. The default position of the cutoff is at the beginning of the vote (i.e. no protected candidates).
> 2) Count the margins (for each pair of candidates). This is based on the rankings only.
> 3) Modify the margins using function f, where
> - f(m,p) = m + sign(m) * (1-p/N) * 2 * N
> - m is the original pairwise margin
> - p is the number of votes that identified both candidates as protected candidates
> - N is the number of votes
> - sign(x) is +1 if x>0, -1 if x<0, and 0 if x=0
> 4) Use the Minmax algorithm to find the winner (i.e. the candidate whose worst defeat (based on the modified margins) is smallest).
> * Note that function f will modify only the strength of the defeats. The direction of the defeats will not change.
> * Note that function f can be simplified to (a shorter but maybe less intuitive) form f(m,p) = m + sign(m) * 2 * (N-p)
> * Note that function f stretches the range of defeat strength values from [-N, N] to [-3*N, 3*N]
> * In the name of the method MOP refers to "Modified Overall Preferences", F refers to word Favourites, and 2 refers to the "stretch factor" 2
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