[EM] Endorsement for STAR voting

[Closed Limelike Curves]

Sorry, I think I gave the wrong impression by mentioning score. Score does
happen to be my favorite system, but a better way to word my comment is
that at some point, if we're comparing score vs. STAR vs. anything Tideman
built, we're talking about methods that can pick the best candidate maybe
95% of the time. It's not about score itself; the point is we're running up
against the limits of what clever mechanism design can really do.

On payment systems: I'm looking at generalized-sense payments. I don't
expect any of these mechanisms to be Pareto-efficient, but the question is
whether we can improve on the status quo of "no trade at all" in a way
that's not *catastrophically* vulnerable to group strategy, at least.

Here's an example of what I'm talking about: take every race or election on
the ballot. Have people specify their marginal utility of casting an
additional vote, e.g. "I'm willing to give away 1 presidential vote in
exchange for 3 congressional votes." We can use linear programming to find
the market-clearing price for trading votes across races, subject to the
constraint that the total number of votes in each race must equal the total
number of voters, and each voter must have at least 0 votes in each race.
Elect winner by highest score, where each ballot is weighted by the number
of votes they ended up with.

This is a large market with many buyers/sellers of an indistinguishable
good (votes), so the trading prices on votes should end up Pareto
efficient+honest (by the usual welfare-economic theorems about perfect
competition). If I had to take a guess, this is probably a more substantial
improvement in social welfare than the difference between score and ranked
pairs (even though I haven't touched the way we choose winners within each
race).

On Sun, Mar 24, 2024 at 12:03 PM Kristofer Munsterhjelm <
km_elmet at t-online.de> wrote:

> 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.
>
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