Saturday, October 05, 2024

Condorcet's Paradox- What can we do about it?

My curiosity prompted me to open the recruiting-related files in the folder when I was interning at a firm this summer. My conclusion after briefly looking at the documents was that it was not easy to choose among a group of well-educated and experienced candidates. Though I do not remember the exact details of the comments on candidates, I did remember seeing some cycling, controversial opinions. Something like, person A prefers Candidate X over Y, and Y over Z (X > Y > Z, person B prefers Candidate Y over Z, and Z over X (Y > Z > X), and person C prefers Candidate Z over X, and X over Y (Z > X > Y). I didn't understand why it took months for them to find the candidate that everyone likes and now it seems this has something to do with Condorcet's paradox.

I also see another slightly different document, that asks the people to rate the candidates from 1-10. So does simply adding a rating scale solve the Condorcet's paradox? Borda Count helps explain it. It is a rank-based voting system where each decision-maker ranks the options, and points are assigned based on their rankings. The candidate with the highest total score wins. For example, if person A ranks X > Y > Z, X gets 3 points, Y gets 2, and Z gets. This process is repeated for each manager, and the points are summed.

Even though Borda Count is not applicable to voting for obvious reasons, it is at least something that we can do to mitigate the effects of Condorcet's paradox.

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