Let D1 be the candidate whose maximum pairwise opposition is minimum, in other words the MMPO winner. We could say that D1 is a good defensive candidate because she minimizes the number of votes scored against her by any other candidate. Similarly, let O1 be the candidate whose minimum score against another candidate is maximum. Then O1 is relatively good at offense. Another candidate relatively good at defense is D2, the candidate against whom the great offensive scorer O1 scores the fewest points. Another candidate relatively good at offense is O2, the candidate that scores the most points against D1. Continuing in this vein, for each natural number n greater than one ... let D_(n+1) be the candidate against whom candidate O_n scores the fewest points, and let O_(n+1) be the candidate that scores the most votes against D_n . Let S be the set of candidates that come up infinitely many times in this process. Use random ballot to pick the winner from the set S. In particular, in the case when both sequences are eventually constant, then there are two candidates D' and O' such that D' is the candidate against whom O' scores the fewest votes, and O' is the candidate that scores the most votes against D' . In this case, the winner is decided between D' and O' by random ballot. There are many possible variations on this idea. I'm a long way from knowing which variation would work best. Gotta Run, Forest
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