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

[Daniel Carrera]

Dear Markus,

On Tue, Jun 29, 2021 at 7:16 AM Markus Schulze <markus.schulze8 at gmail.com>
wrote:

> Dear Daniel,
>
>  > 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.
>
> This proposal doesn't automatically meet ISDA.
>

Hmm... yes, I see that. My bad. I think that if you change Step 2 so that
the bottom candidate is compared against every other candidate *AND* you
pick a sorting rule that puts the Smith set on top, then I think that would
meet IDSA. For example:

Step 1: Rank candidates by number of pairwise wins (Copeland sorting). Use
first-place votes to break ties.
Step 2: Pick the bottom candidate and compare him against every other
candidate. If he loses any match, kick him out.
Step 3: Repeat until you find a Condorcet winner or only 1 candidate is
left.

I think *this* version would meet ISDA. Am I right?

Someone on Reddit has made the case to try to make the system resistant to
DH3. The only way I can think of to avoid DH3 is to sort by first-place
votes, but then I suspect that that wouldn't meet ISDA.

Cheers,
Daniel
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