[EM] Theorems to optimize Kemeny Young?

[culitif at tuta.io]

Hey all,

I took a crack at Kemeny Young and started off by doing it in the most brute force way possible: It generates all possible permutations of the list of candidates (all possible paths) and then assigns a score to each of them, keeping the one with the highest score. Obviously this is highly impractical and ends up being O(n!) where n is the number of candidates. I was wondering what theorems exist that could help me optimize this. I'm guessing that since its a Condorcet method, if there's a strong Condorcet winner, I should just return that winner right? Also if there's a subset of weak Condorcet winners then some permutation of those winners should lead the highest-scoring path right? Are there any other safe assumptions to make?

Side note, do y'all have any recommendations for social choice theory books? Preferably something that discusses things like Kemeny Young and questions like the ones I have above.

Best,
Culi.
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