Talk:Space of possible elections

Speeding up computation

This is a pretty broad section, but I'll mention specifically how you can reduce the number of valid ballots to consider. We discussed earlier that scored ballots can be boiled down to their margins i.e. A:5 B:3 C:3 is equivalent to A:2 B:0 C:0. So that could greatly reduce the number of cardinal ballots to consider (unless you're dealing with write-in candidates). Something to note is that if you assume normalization, then this trick no longer works i.e. you can't raise or lower the scores of all candidates by the same amount because at least one candidate is at the max score, and at least one other at the min score. The exception is if all candidates are scored the same, since A:5 B:5 C:5 and A:4 B:4 C:4 are both, in some sense, normalized yet equivalent.

Later on I might add some content or links to this Talk page describing how to figure out the number of possible [[rated pairwise preference ballot]s there are, though it depends on what kind of transitivity rules you impose on the system. BetterVotingAdvocacy (talk) 21:15, 24 July 2020 (UTC)