Is there a good data structure to represent Ordinal Data? I frequently see pairwise count matrices used [1], but they don't seem to completely capture all of the information. For example, the number of times a choice was first, second, third, or last such as would be necessary for the Borda method [2].
Well, Condorcet and Borda do fundamentally different things with people's preferences.
There's no real way to simplify it beyond "here's a set containing the rank order of every voter" if you don't know in advance what election method will be used. In fact, you might argue that the rank order is insufficient, and you also need to know whether the voter would approve of each option in an approval vote, or 0-10 rankings for range voting, or whatever.
Condorcet cares most of all about people's preferences between pairs of options, so that's why you'd summarize it as a matrix made out of those pairwise preferences. Borda cares most of all how many times something is "first place", "second place", and so on, and cares nothing about the pairwise rankings; Borda advocates claim that pairwise rankings will just confuse the issue.
(Opinion: I happen to believe that Borda is garbage for anything where politics is involved. It might be okay for the kind of contests where it's in use, like the baseball MVP or Eurovision, except those are probably secretly political too.)
Comments
Is there a good data structure to represent Ordinal Data? I frequently see pairwise count matrices used [1], but they don't seem to completely capture all of the information. For example, the number of times a choice was first, second, third, or last such as would be necessary for the Borda method [2].
[1] http://en.wikipedia.org/wiki/Condorcet_method#Pairwise_count... [2] http://en.wikipedia.org/wiki/Borda_count#Voting_and_counting
Well, Condorcet and Borda do fundamentally different things with people's preferences.
There's no real way to simplify it beyond "here's a set containing the rank order of every voter" if you don't know in advance what election method will be used. In fact, you might argue that the rank order is insufficient, and you also need to know whether the voter would approve of each option in an approval vote, or 0-10 rankings for range voting, or whatever.
Condorcet cares most of all about people's preferences between pairs of options, so that's why you'd summarize it as a matrix made out of those pairwise preferences. Borda cares most of all how many times something is "first place", "second place", and so on, and cares nothing about the pairwise rankings; Borda advocates claim that pairwise rankings will just confuse the issue.
(Opinion: I happen to believe that Borda is garbage for anything where politics is involved. It might be okay for the kind of contests where it's in use, like the baseball MVP or Eurovision, except those are probably secretly political too.)