[EM] STAR challenge

[Kristofer Munsterhjelm]

On 07.06.2022 05:49, Forest Simmons wrote:
> VSE (voter satisfaction efficiency) simulations seem to bear out that
> STAR is a significant improvement over plain old Score voting, but not
> quite as good as Score restricted to the Smith Set.
> 
> So it appears that simple STAR is the low hanging fruit worth some trial
> and error tweaking experiments to convert it into the best public proposal.

I'd say there are two ideas of generalizing STAR, call them cardinal and
ordinal. The cardinal one should preserve the property that in an LCR
election where the centrist is highly rated, he wins, but where he's
ranked poorly, he loses. (Making this cloneproof without just degrading
to plain Range is hard!)

The ordinal one, on the other hand, should find the CW whenever he
exists, and probably also elect from some nice set (Smith, Landau or
Banks). STAR itself doesn't do this.

> Some brainstorming is definitely in order. Ted Stern has been working on
> this.
> 
> Some possible directions:
> 
> 1. Simplify the description of Score restricted to Smith to be on a par
> with the simplest description of STAR
> 
> 2. Find a better runoff opponent for the score winner.
> 
> 3. Compare STAR with Score Sorted Margins and Sequential Pairwise
> Elimination based on a Score agenda.
> 
> Here's one idea:
> 
> For each ballot B, and  each candidate X, let B(X) be ballot B's score
> for candidate X. Let S(X) be the sum over B of B(X). Then the score
> winner is the candidate X that maximizes S(X). Elect the winner of the
> runoff between the score winner and the candidate X that on the greatest
> number of ballots B, maximizes the product B(X)S(X).

I haven't thought about it in detail, but I think Range's de jure IIA
compliance implies that Benham-Range and BTR-Range are both Smith. They
might even be equivalent to Smith,Range. So if you want to look for a
simpler way of explaining Smith,Range, those may be it.

My thinking is like this, for Benham-Range:

Benham-Range eliminates the current Range loser until there's a CW.
Since Range passes IIA, eliminating without normalization doesn't change
the order of the other candidates. Hence all but one Smith set member
will be eliminated, after which the highest scoring Smith set member
becomes the CW and wins. So Benham-Range is just Smith,Range and may be
easier to explain.

Benham-BTR I'm much less sure about because it protects the loser who
pairwise defeats the other. This is more like STAR. It might be that a
prospective loser is protected all the way up the Smith set, and then
beats the highest rated Smith set member pairwise -- unless such a
scenario is impossible.

For runoffs, I think you could argue in two ways. Either the runoff is
about telling two quite good candidates apart, or it's about giving each
faction of the electorate "their" candidate to vote for. The former
suggests (if it's a manual runoff) just picking the two Smith set
members with the highest rating; the latter, something more like "the
candidate rated highest by voters who rated the first candidate low".

If I had to choose, I'd probably go for the former, though it could
affect the turnout in the general: if both candidates are good, a lot of
voters may simply decide not to vote in the general.

Automating the former, STAR would probably do a good job because it's
unusual for a candidate to be the CW yet not in the top two by highest
rating. At least it gets the bang for the buck award, even if it's not
perfect :-)

-km