[EM] Endorsement for STAR voting

[Kristofer Munsterhjelm]

On 2024-03-19 22:06, Closed Limelike Curves wrote:
> I think Kris is mostly correct when he says this:
> 
>> Over time, this incentive to entry could reduce STAR to Range.
> 
> but I see this as intentional. Score and approval are great systems on 
> their own.

In the mail I responded to, Rob said:

>>> I don't feel comfortable with the strategy burden imposed on
>>> voters by plain "score voting" (a.k.a. "range voting").  Most of
>>> us agree that  the best strategy for "score/range" is a "min/max"
>>> strategy....basically, turn the election into an approval
>>> election.  It doesn't seem fair to have a system that requires
>>> voters who want to maximize the utility of their ballot to know
>>> enough about the system to  know the "min/max" strategy.

So if you agree that STAR will reduce to Range, that's fine, because my 
point then stands: if Rob's not comfortable with the strategic burden of 
Range, and STAR reduces to Range, then that's a problem for STAR.

> They elect Condorcet winners in the presence of strategy, but 
> score does /better/ than Condorcet if voters are honest. They satisfy 
> sincere favorite, IIA, and rarely incentivize order reversal. It's hard 
> to design something better that won't hurt the average voter's brain.

IIA is a means to an end, and that end is that the outcome shouldn't 
change if candidates who don't win enter or leave. For Range, although 
it passes IIA, we still don't get that end unless the voters' ratings 
are calibrated to a scale or scales that don't depend on the candidates 
who are present.

How would you suggest that such a calibration be done?

If it can't be done, then Range's IIA compliance, while nice in a 
box-ticking way, doesn't really do what it implies it does.

There's a flipside to Range passing all these criteria as well. Since 
Range has opportunities for strategy in a large proportion of elections 
(see JGA's papers), yet passes a bunch of strategy-related criteria like 
pariticipation, weak FBC, etc., that implies that a very large amount of 
its strategic potential is concentrated into the question "where do I 
put the Approval cutoff" or "how do I set the max and min candidate 
ratings". And that's something that even honest voters will have to 
contend with, since there are multiple honest ballots.

> I expect that as soon as STAR is a thing, parties will start nominating 
> candidates in pairs. This is good; it gives voters more choices. STAR is 
> a two-step procedure, where first you hold a score vote to pick the 
> frontrunners (because the first round is score), and then you hold 
> what's effectively an approval vote to pick the single best candidate.

It's not so good if you want STAR to be substantively different from 
Range, though. And with max-min being the optimal strategy in Range, the 
second round would become redundant.

The whole rationale for STAR, as I've understood from its creators, is 
to mitigate problems with other methods like Range's max-min strategy. 
To quote from the STAR voting paper[1]:

> STAR Voting was invented in 2014 with the objective of better
> delivering on the underlying goals of voting reform advocates, while
> addressing serious issues with Plurality Voting and limitations with
> leading reform proposals like Top Two Runoff, Score Voting, and Instant
> Runoff Voting (IRV).
It's difficult to "address limitations with ... Score Voting" if the 
method is made to reduce to Range itself. So to the degree that is what 
it's for, its clone incentive compromises its logic.

> It's fun to imagine more complex voting systems, but I've come to 
> recognize an iron law of voting systems: *every 
> sufficiently well-designed voting system converges to score*. We have an 
> impossible trilemma:
> 1. If your voting system doesn't respond to strategic exaggeration, it's 
> not responsive to voters. (If you rank a candidate 1st, they damn well 
> /should/ do better than if you put them in the middle!)
> 2. If it responds to exaggeration but penalizes compression (ranking 
> several candidates first makes them less likely to win, compared to 
> ranking them all), it's Duvergerian (favorite-betrayal incentive).
> 3. If it responds to exaggeration but doesn't penalize compression, it's 
> approval voting (at least if you have strategic voters).
> 
> Of these, it seems like voting theorists have converged on #3 being the 
> least-bad option, although some systems try to compromise.

You should probably say "cardinal voting theorists have". To pick a few 
names, neither Woodall nor Schulze has converged on cardinal voting.

Your observation also ignores, or looks like it ignores the effect of 
imperfect information. Suppose that you know that you're going to be a 
pivotal voter, and your preferences are A>B>C. You're dropped either 
into a universe where A is one full vote short of being the CW 
(currently being pairwise tied with B), or into one where B is one full 
vote short of being the CW (currently tied with C). The method used to 
call the election passes Condorcet, and any ties are broken at random.

If it's the former universe, then your A>B>C vote will make A the CW. If 
it's the latter, then it will make B the CW. It's true that in the 
former universe, you would want the method to not penalize A if you 
compress your A>B>C vote into A>B=C; and in the latter, that it not 
penalize B if you compress your A>B>C vote into A=B>C.

However, with imperfect information, you don't know which universe 
you're in, so you would want to be able to express your preference both 
for A>B and B>C at the same time. Approval doesn't do that. And so 
imperfect informaton keeps methods from converging to Approval.

In this veil of ignorance setting, if the method were Approval, you'd 
have to gamble and hope you got it right. Since the candidates are a 
full vote short, partial rating in Range will have no effect.

Of course, since Condorcet methods are manipulable, this isn't free. You 
get funny business in the cycle regime in return for being able to both 
maximally support A against B and B against C in the transitive regime. 
Methods that fully pass Condorcet fail FBC (though it's possible to pass 
Condorcet in the no-truncation case while passing FBC).

I think that shows that the matter isn't as clear cut as the argument 
would have it. If invariance to compression destroys this ability to 
make an effective vote under imperfect information, that invariance has 
a cost, and thus it's not a dominating property in the Pareto sense. 
There's no inevitable convergence.

In short, good ranked methods let you direct your voting power 
contingent on the state of the election. The cost is that when there's 
no obvious way to do so, it can go wrong. Rated methods lack the former 
and thus can also do away with the latter.

Strategies like "determine if you should do A=B>C or A>B=C by looking at 
the polls" are then workarounds where the voter gets contingent voting 
power by estimating the state of the election himself. Manual DSV.

> The only way I can see us moving past this trilemma is if we have some 
> outside-the-box mechanism. We can't /just/ look at vanilla voting 
> systems that pick the best candidate from a pool. We need to look at 
> mechanisms that make support costly /across /races or decisions. Voters 
> need to be on the hook if they try to just top-rate all their favorites, 
> but that incentive has to come from paying a cost somewhere /other/ than 
> inside the race. If you try to make it costly to support multiple 
> candidates at once (like cumulative voting does), you just get 
> favorite-betrayal and plurality again.
> 
> Improvements on approval voting will probably come from some direction 
> like working out how to make the VCG mechanism more resistant to 
> coalitions and letting voters rate candidates across multiple races. 
> Most decent voting systems are already up against the brick wall of 
> top-shelf methods labeled Score/Approval/STAR/RP/Tideman 
> alternative—notice that all of these except STAR were proposed more than 
> 30 years ago, all give similar results in practice, and we /still/ 
> haven't figured out a way to beat them!

You might be interested in James Green-Armytage's Dodgson-Hare method 
which goes outside the box by allowing candidates to withdraw from the 
count.[2]

Alternatively, if you really want to go outside the box, drop elections 
entirely and do sortition. Do away with the problem. The assembly would 
still have to vote on issues, but the participants in an assembly can 
discuss among themselves, which would contribute to stability.

There's also Heitzig's randomized consensus methods[3]. These try to 
solve the "tyranny of the majority" by using randomness, incentivizing 
the voters to find a consensus option. IMHO, they have some problems 
with repeated games, and can't be used for big one-shot decisions like 
"who should be President this term" due to variance of the outcome; but 
they could still be of interest.

Although I don't know enough about the subject to be sure, I suspect 
that group strategyproof auction mechanisms would at least be 
inefficient.[4] They might not even be possible.

Voting with money would in any case be a bad idea due to income effects, 
and even in a generalized sense (if you use "time until you can next 
vote" as a proxy for money, say), it could lead to initially successful 
voters using their accumulated gains to tilt the playing field. That 
voting itself isn't rational may also be a problem: if voters are 
incentivized by something else than the chance of being a pivotal voter, 
then compensating would-be pivotal voters with near infinitesimal 
amounts may not make much of a difference.

-km

[1] WOLK, Sara; QUINN, Jameson; OGREN, Marcus. STAR Voting, equality of 
voice, and voter satisfaction: considerations for voting method reform. 
Constitutional Political Economy, 2023, 34.3: 310-334. 
https://link.springer.com/content/pdf/10.1007/s10602-022-09389-3.pdf

[2] GREEN-ARMYTAGE, James. A Dodgson-Hare Synthesis. Constitutional 
Political Economy, 2023, 34.3: 458-470. 
https://link.springer.com/article/10.1007/s10602-023-09392-2

[3] https://www.pik-potsdam.de/members/heitzig/maxparc

[4] I'm mostly going on a hunch by analogy to budget neutral 
individually strategy-proof mechanisms and one-sided strategy-proof 
stable matching mechanisms, none of which are Pareto efficient.