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Old June 23rd, 2009, 12:14 PM
Squirrelloid Squirrelloid is offline
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Default Re: Noobs vs. Vets III: Revolution, MA, CBM, Pretender Design/Upload

Not really interested in playing a huge MP game yet, but I did want to comment on how you assign nations.

The most fair way to do it would be to have each player submit a ranked list from 1:n where n is the number of nations available. You then minimize the sum of squared rankings for nations awarded across all players. This is actually a remarkably simple thing to do - one way to accomplish this is if you think of it as a player : nation matrix where the elements are the jth players rank of nation k, you're looking for an ordering of the columns (nations) to minimize the sum of the diagonal (row k gets assigned column k). There are n! possible orderings, so you don't want to actually brute force it for 24 players, but there are clever things you can do. (For example, an heuristic search would get you an approximate best answer, a principle coordinate analysis would tell you who's rankings are similar to each other and let you break the problem into sub-problems in most cases, and I'm sure someone better at math than I am can figure out something truly clever to do to arrive at the actual solution).
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