Talk:Space of possible elections: Difference between revisions
→Speeding up computation
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::: Regarding number of ballots with normalization, I think it can be calculated in the following manner. For c candidates and r possible scores, we can think of it as looking for every possible pair of candidates who are to be min/maxed, multiply this by 2 (since either the first candidate in the pair is min'ed and the second max'ed, or vice versa), and then for the remaining candidates not in the selected pair, they can be scored in any permutation of ways, so they are r^(c-2). So this altogether is: 2 * (c choose 2) * r^(c-2). [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 23:32, 25 July 2020 (UTC)
::::That seems accurate if the normalize is done by the voter. If the normalization is done automatically it would be different, as you'd get rational numbers for the votes. In that case one must consider all possible intervals between the min/max voters and all combinations of scores within the interval. Then we must also be careful to remove degenerate cases. For 0-5 ratings (6 levels) we get 3, 61, 579, 4381, 30243 for c=2,3,4,5,6..., for 0-9 (10 levels) 3, 169, 2883, 38041... Closed form seems a bit trickier than I thought, but doable. [[User:lucasvb|lucasvb]] ([[User_talk:lucasvb|talk]]} 00:06, 26 July 2020 (UTC)
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