Consider the Schulze, Kemeny-Young, Ranked Pairs and Borda count voting methods. (The last is obviously the odd one out in this list!)

Suppose that there are only two voters. Each voter gives a ranking over $m$ different options, possibly with ties.

Are any of these four methods equivalent in this case? [Here equivalence means producing an identical ranking of all $m$ options, not just an identical winner.]

Are more methods equivalent when we do not allow ties in the individual rankings?

These methods are not equivalent when there are more than two voters, but with only two voters there can be no Condorcet cycles, so intuitively one would expect things to be simpler.



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