Tideman’s Bottom-N Runoff

cfrank

This probably already exists but I like the idea. It’s a rank order system based on Tideman’s bottom-2 runoff that proceeds recursively.

Informal description: Eliminates Condorcet losers in steps, each time from the largest possible pool of candidates (which pool of a given size to examine must be addressed).

Let N be the number of candidates.
From the N candidates with the fewest first-place rankings (or lowest scores, etc.), determine if a Condorcet loser exists.
If no Condorcet loser exists, reduce N by 1 and repeat from step 1.
If a Condorcet loser exists, eliminate them from the election, let N be the number of remaining candidates, and repeat from step 1 until a single candidate remains.

Just like Tideman's Bottom-2 Runoff, this system is Condorcet compliant and also satisfies the Condorcet loser criterion. I believe this is due to Smith compliance. Variants can use alternative criteria (as opposed to the number of first-place votes) to determine which subset of candidates to examine. For example, a more general/robust method might only consider Condorcet losers among non-Bucklin winners.

I’m actually not certain whether this system turns out to be equivalent to the bottom-2 runoff. I believe it is generally different, but I haven’t constructed a distinguishing example yet. (1/19/2023)

The only reason for considering such a system is to enhance the robustness of the bottom-2 runoff against Condorcet-cycle induced non-monotonicity.