Talk:Space of possible elections: Difference between revisions

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:: Yes, this is a good point, although the applicability (whether the ballots are equivalent) really depends on the system in question. I'd expect many systems to produce additional constraints in the number of elections. It is also not difficult to estimate the number of ballots with normalization, I might add that in later. [[User:lucasvb|lucasvb]] ([[User_talk:lucasvb|talk]]} 21:29, 24 July 2020 (UTC)

::: 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: (c choose 2) * r^(c-2). [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 23:32, 25 July 2020 (UTC)

::: 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)