[EM] Simple Acceptable Ranked Choice Voting

Kevin Venzke stepjak at yahoo.fr
Sun Jan 15 05:41:50 PST 2023

```Hi Forest,

> Perhaps we need to use the entire finish order of the seed method to get an appropriate
> uncovered winner:
>
> Unc(Finish Order)
>
> Initialize the variable X as the candidate highest in Finish Order.
>
> Then ...
>
> While X is covered, replace it with the highest Finish Order candidate that covers it. EndWhile.
>
> Elect the updated X.
>
> I would like to suggest as the seed method the following version of MaxMinPairwise Support:
>  [...]

Unfortunately I don't find this to be monotone with "MMPS." The issue is that a winning
candidate B may wish for a candidate they defeat, A, to have a certain number of votes
against B, so that A is the initial chain head that B then defeats. So when B gains some
votes at the expense of A, a different candidate D becomes initial chain head and wins:

0.328: D>B
0.253: A>C
0.204: A>B  <-- changes to B>A
0.140: C>D>B>A
0.074: B

I calculate in the "before" scenario the MMPS order is ADBC, B alone covers A, no one covers
B. Then in the "after" scenario the order is DBAC, and no one covers D.

> If I'm not mistaken, the following variant of the FBC is satisfied by this version of
> MaxMinPairwise Support (before the uncovering modification):
>
> If the winner W of this method is ranked top on ballot B, and the winner changes when F is
> moved to equal top with W on ballot B, then the new winner must be F.

Yes, MMPS does seem to satisfy the weak FBC. But the *strong* FBC compliance (i.e. what I
normally just refer to as "compromise incentive") is worse than Bucklin or C//A. So I guess
if the legislature enacts MMPS it should make sure not to forget to allow equal ranking.

I am thinking you got lucky with the first draft of MGAscent being monotone. (To be honest
it makes me question my own result there. Why should the max gross score version work and
nothing else? Not sure.)

Kevin
votingmethods.net
```