[EM] A family of easy-to-explain Condorcet methods

[Daniel Carrera]

Hi everyone,

I'm new to this list. I recently posted this on Reddit r/EndFPTP but I
would like to get your thoughts as well. Like many people here, I love
Condorcet methods but worry that they're hard to explain. I recently
learned about BTR-STV from rb-j's thread a few years ago and it made me
realize that there is a whole family of really easy-to-explain Condorcet
methods. They all work like this:

Step 1: Sort candidates according to your favourite rule.
Step 2: Pick the bottom two candidates. Remove the pairwise loser.
Step 3: Repeat until only 1 candidate is left.

Every method in this category is Smith-efficient, so it automatically meets
many important rules like Condorcet loser, Mutual Majority, and
ISDA. Whether the method meets any other criteria presumably depends on the
sorting rule you picked (Step 1). For example, BTR-STV uses the STV sorting
rule including the implication that you sort again every time you remove a
candidate. An even simpler method is:

Step 1: Sort candidate by number of first-place votes.
Step 2: ...
Step 3: ...

I just can't imagine anything simpler, and here we have a Smith-efficient
method that I suspect almost anyone will find sufficiently intuitive. I
think it's simpler than STV because it doesn't have the "transfer votes"
rule. On Reddit someone suggested a change to Step 2:

Step 2: Pick the bottom candidate and compare him pairwise against every
other candidate. If he loses any of those races, kick him out.


In any case, I was hoping that someone here could comment. Maybe you can
help me figure out what other criteria this method meets or fails. For
example, I figured that it is not independent of clones. I have no idea how
to figure out whether it meets the monotonicity criterion. I think that
monotonicity is extremely important and I think I might see it as a deal
breaker if it's not present. Perhaps someone can come up with a variation
that is still simple but meets important criteria.

Also, does anyone know which criteria are met by BTR-STV? I know that it's
Smith-efficient but fails independence of clones. But that's all I know.

Thanks for the help.

Cheers,
Daniel.
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