[EM] Favorite Betrayal and Condorcet, and LNHarm

[Kevin Venzke]

Hi Forest,

Le samedi 23 avril 2022, 12:37:18 UTC−5, Forest Simmons <forest.simmons21 at gmail.com> a écrit :
> Suppose a method has a runoff between the MMPO winner X and the and DMC winner Y.
> 
> If the runoff is by a separate trip to the polls, then the runoff votes will all be sincere.
> 
> Now suppose instead, that the runoff is instant, but by a separate set of ballots submitted
> simultaneously with the other ballots (the ones that determined X and Y) ... and that this
> second (or third) set was expressly limited for use in the runoff (for the case of distinct
> X and Y).
> 
> If the rational voters both understood and trusted this process, wouldn't the runoff set be
> sincere?

Yes, a separate runoff ballot ought to be sincere.

> Would the method as a whole be considered UD compliant?

(Moving this question up.) To the extent that the answer is no, we may have trouble answering
the other questions.

But there is at least a UD-compliant method that these rules can resolve: Just say everything is
done using a single ballot.

> An if not, should that disqualify the method from adoption?

No, for me UD doesn't have anything to do with the actual merits of the method. It's more to do
with whether we will have a good, consistent way of assessing the merits.

> Wouldn't the method as a whole be considered to satisfy the Plurality Criterion ... even if
> the MMPO winner X beat Y on the runoff ballots, and Y had more first place votes than X had above
> bottom votes on the original ballots ... the strategic ballots that got X and Y into the finals?

If there were only one ballot then no, clearly not. You could have MMPO winner X pairwise beats
DMC winner Y while a third candidate Z disqualifies X. That could happen if X and Y are from the
same major party. Z voters might be almost half the electorate and are not able to side with
anyone in the runoff because there's only one ballot.

If there are multiple ballots, I'd still say no, because the problem is only "solved" if the Z
voters are *required* to pick between X/Y on the runoff ballot. I don't think that's a legitimate
way to satisfy Plurality.

> Would the method as a whole be considered to satisfy the FBC?

Surely not. For one thing you're using DMC, which (as a method itself) fails it, and then you
end in a plain runoff, which I don't think any FBC method can do. Both the MMPO and DMC sides
will be corrupted by the incentive to set up a desirable final pairing.

> Would the method as a whole satisfy the Condorcet Criterion even though it is possible that
> neither X nor Y was the sincere CW even when there was one?

Well, when we talk about UD criteria we don't have a concept of "sincere CW," only voted CW.

If there's only one ballot then yes, it satisfies Condorcet, because a Condorcet winner will
always be returned from the DMC side and it will always either beat or *be* the MMPO winner.

If we say that different ballots could show a different CW, or no CW, then I don't think the
question is answerable.

> Is this instant runoff method (unlike IRV) efficiently precinct summable? (Yes!)

Kevin