[EM] pairwise comparisons

[Curt]

Hi, 

I’ve been chewing on some questions as part of exploring my views of ranked voting, and thought I would share here. For those of you who prefer not to think more philosophically about this, please excuse the missive. :-) But for the rest of you, I’m interested in your thoughts.

Imagine a set of ten candidates, and one voter. The voter is asked to determine their views of these candidates. But instead of just being asked to rank them in order, the voter is asked to judge them pairwise.

For ten candidates, this means 15 questions. Each question being a comparison of A and B, with the voter picking their favorite of the two.

First question, is it possible for a voter to generate a cycle? We know it is technically possible, trivially demonstrated. But is it possible that a voter, using some internal set of principles, would also generate a cycle? I would argue yes.

If the voter does generate a cycle via these pairwise comparisons, what does this mean? Does it mean the voter is confused? Does it mean the voter is inconsistent? Does it mean that this cycle or cycles are an accurate depiction of the voter’s actual views?

Say that we then ask the voter to create an actual ranked ballot out of these ten candidates, and the voter manages to do so. What happened in that process of the voter deciding the rankings? Was it a clarifying experience? Did the voter’s preferences change? Did the voter compromise? Did the voter lie?

And finally, say that a collection of these voters submit their ranked ballots (not just their pairwise comparisons), and the votes are tabulated, and the result is a three-candidate Smith Set, where each candidate defeats all other candidates outside the Smith Set.

What does that Smith Set mean? Is the electorate confused? Is the electorate inconsistent? Or is the Smith Set an accurate depiction of the electorate’s actual views?

Thanks,
Curt