[EM] Sequential (proportional) approval voting and VRA considerations

[Kristofer Munsterhjelm]

On 17/01/2020 18.38, Jack Santucci wrote:
> Hi,
> 
> This seems like a good venue to raise the following concern.
> 
> In working through SPAV
> (https://twitter.com/jacksantucci/status/1217959180834951175?s=20), I
> have arrived at the following conclusion.
> 
> It literally and mechanically dilutes the voting strength of a cohesive
> minority, if some of that minority "approves" of a winning candidate in
> the majority. The key term there is "vote dilution."
> 
> And do not mistake me for a preference voting shill. As you'll see in
> the tweet, STV has properties that feel similar. But they are not the
> same as what I see in SPAV. Unless I am seeing things that don't exist.
> 
> I suspect that the response (if I am right) will be to re-engineer SPAV,
> in order to rescue the broader concept of "approval voting." Have at it
> if you want. But the implications for minorities in polarized settings
> (see http://mattbarreto.com/papers/polarized_voting_wa.pdf) have to be
> priority #1.

You've discovered Hylland free riding :-)

The natural/obvious way to design a multiwinner method is:

1. Elect someone.
2. Diminish the weight of the votes responsible for getting him elected,
so a majority won't capture every seat like in block voting.
3. Go to 1.

The problem is that if you know that X will be elected even without your
vote, you'll weaken your vote by also voting for X. So your incentive is
to not vote for X. But if enough people think like that, then there's
nobody left to vote for X, and he loses.

Schulze's solution to this is very Condorcetian (and also quite
complex). I've been trying to handle the problem in a simpler way, and
that Bucklin method I mentioned in another post reduces the incentive to
engage in Hylland free riding, but doesn't eliminate it entirely.

I suspect a Condorcetian approach will force itself through, even if in
stages (e.g. when you're to elect the kth candidate, you'll evaluate all
pairs of remaining candidates and find the CW, instead of evaluating all
remaining candidates and finding the highest scorer).

The reason I suspect so is because a method can't distinguish between
someone who didn't vote for X because he doesn't support X, and someone
who did it for free riding purposes. So when a candidate Y is to be
elected, he has to defend his claim for the next seat against W in such
a way that whether someone voted for X is irrelevant to whether Y or W
comes out ahead. And it doesn't seem possible to do so in a way that
doesn't depend on both who Y is and who W is.

But without further research, that's just a hunch, and I've been wrong
before.

Note also that STV passes Droop proportionality, so if more than
1/(seats+1) of the voters rank some group of candidates ahead of
everybody else, then at least one of the winners must come from that
group. That should help with polarized voting. The analogous concept for
PAV/SPAV is Warren's "racist voting" concept where, if everybody
approves only of a certain group, and nobody approves of more than one
group, then the number of candidates from each group will reflect the
fraction who approved of each.