[EM] Score DSV

Sun Aug 30 08:39:43 PDT 2009

Jameson,

You asked: "The part about other partisans not caring about utility seems strange to me. Why not?"

I don't want to engage in a debate on this on this list about the value of utility as a criterion, but can answer your question...Political scientists and many other social scientists (who approach election theory from a different angle than economists or social choice theorists) generally dismiss utility or Bayesian regret as a meaningful election assessment tool for several reasons. The quickest to understand is simply that there could be a candidate who is preferred over all other candidates by a large majority, yet another minority-favored candidate could be the utility maximizer (average utility), simply because the minority of voters really hate the majority winner and strongly like the other, while the majority think the winner is better, but not great. Because the principle of Bayesian regret is in direct conflict with the principle of majority rule, many people reject it. Individuals can differ on the value of majority rule vs. utility, but it is a reason often cited.

There are of course many other considerations that cause many scientists to reject utility as a meaningful measuring system, such as the proven natural non-linear logarithmic scoring tendency of the human brain, the unreliability of scoring compared to ranking and either or comparisons (which is why eye doctors use Condorcet logic and ask whether lens 1 or 2 is better repeatedly, rather than asking you to score all the lens options), etc.

Terry Bouricius

----- Original Message ----- 
  From: Jameson Quinn 
  To: Kevin Venzke 
  Cc: election-methods at electorama.com 
  Sent: Sunday, August 30, 2009 12:30 AM
  Subject: Re: [EM] Score DSV

  2009/8/29 Kevin Venzke <stepjak at yahoo.fr>

    Hello,

    --- En date de : Sam 29.8.09, Jameson Quinn <jameson.quinn at gmail.com> a écrit :

    >> I don't see why you would guess that Score DSV
    >> would have better Bayesian Regret than Range. It looks like you tried
    >> to make a method that helps a voter get the best result for himself,
    >> which isn't the same as
    >> getting the best result overall.
    >
    > I tried to make a method where honesty was strategic. That
    > means allowing voters to usefully distinguish
    > A>B>>C from A>>B>C or A=B>>C for any
    > A, B, and C. This method does that, which removes any need
    > for strategy at all in many cases, and gives defensive
    > strategizers a chance to punish it in many more.

    Yes. Making honesty the best strategy is a common goal. But for BR it is
    a bad thing with sincere votes.

    >> Warren defines BR in such a way that Range is unbeatable
    >> given sincere votes.
    > Absolutely, which is why I stated my BR challenge in terms
    > of rational voters where at least half have an attainable
    > strategy threshold.
    >  
    >> If he measured your method, admitting strategic votes, he
    >> would make
    >> strategy assumptions that would make it look terrible.
    >
    > Yep, which is why I (implicitly) offered to do the
    > programming.

    Warren makes his sim available. I'm not sure if it can easily do this
    method, but probably.

    > My strategy assumption is that voters will use
    > strategy iff it has an expected value greater than some
    > threshold. This is a very easy bar to meet in the case of
    > Score voting (approval-style strategy is a painless win) and
    > much harder in the case of good Condorcet methods (where
    > "good method", in my definition, means that they
    > reduce the cases in which strategy works, and increase the
    > cases in which it backfires, to the point where almost any
    > voter with less-than-perfect information has a negative
    > expected value for strategy, and even under perfect
    > information only a tiny fraction of voters can benefit from
    > strategy). Therefore, *rational* strategic voters will be
    > more strategic under Score than under a good Condorcet
    > method, giving the Condorcet method a possible margin for
    > victory. Score DSV, because it takes the actual utilities
    > into account sometimes, should have the widest victory, if
    > the differences are significant.

    Issues:
    1. If you don't use Warren's methodology and assumptions, it's not clear
    that your results will be convincing to a Range crowd. (And other crowds
    don't care as much.)

  The part about Range partisans being wedded to Warren's assumptions I understand, though I don't necessarily agree. The part about other partisans not caring about utility seems stranger to me. Why not?

  Anyway, I'm proposing having each virtual voting group evaluate whether strategy will help them, given different levels of true information. I think this is feasible computationally, and I don't see how anybody in any camp could argue that finding utility in this case is not relevant.

    2. When Range voters vote approval-style and Condorcet voters use
    reasonably sane strategies, Range/Approval is known to be worse, as the
    number of viable candidates increases. So it won't be that novel to show
    that your method is better than Range here.

  Where are you getting this?

    3. Given the nature of the differences between Approval and Condorcet,
    it seems that Score DSV's consideration of ratings is more likely to
    hurt it than help it here.

  With honest votes, or considering strategy? I can't see why you'd say this. Score DSV is more like Range than your average condorcet system.

    > I realize this is all hot air until I actually program
    > this. Yet it is at least falsifiable hot air.
    >
    >> Your wiki page seems to be lacking some
    >> proofs.
    >
    > As in, all of them? :)
    >
    > Guilty as charged. Which proofs would you like to see
    > first? I make about 25 provable/disprovable claims on the
    > page, that's a lot of work and it would help if I knew
    > which ones y'all wanted me to start with. (I already got
    > Marcus to disprove one of my claims for me by posting here,
    > so my evil plot worked... thanks, Dr. Schulze :)

    Well, here are some comments going over the page quickly.

    "If there's a Condorcet winner, all voters' ideal strategy will be to
    vote approval-style, and the Condorcet winner will win, thus this method
    satisfies the Condorcet criterion."

    I wrote out a whole long thing here but eventually realized that you
    aren't ruling out non-Smith candidates from winning. And that is why you
    are talking about strategy above.

    Fortunately or unfortunately depending on your perspective, you have to
    evaluate Condorcet compliance based on cast votes. If a voted CW doesn't
    necessarily win, then Score DSV isn't a Condorcet method.

  Ouch. That passage is obviously unclear. I meant "strategy" in the sense of "declared strategy". I was not considering any strategy at all from the actual voters on the ballots they would input to Score DSV, but virtual "declared" strategy on the output (imaginary) renormalized ballots, which are intended to be equivalent to (the probabilistic average of) their strategic Range ballots if their input ballots are honest and if they knew the true Smith set but nothing else. In other words: if there is a condorcet winner, the correct Range strategy for those who know that winner (and nothing else) is to vote approval-style for that person and all better candidates, thus Score DSV chooses the CW. It is a Condorcet method, even though it does not satisfy the Smith criterion (if there is no CW, it could potentially elect the condorcet loser, if that candidate had a high renormalized utility).

    The fact that voters have a defensive counterstrategy isn't remarkable
    or reassuring in itself; we would want to know what it is and whether it
    is intuitive to use it. When we talk about the larger group being a
    majority, I'm not sure we can design a Condorcet method where there isn't
    a defensive counterstrategy.

    It would be nice to see reasoning as to why Score DSV would outperform
    Condorcet methods wrt favorite betrayal incentive.

    By the way, it's controversial to say that favorite betrayal is a typical
    strategy in Condorcet methods. Compared to other rank methods Condorcet
    is generally good at this, and Schulze(wv) was nearly perfect when I
    tested it.

  I was not aware of this.

    I don't remember (and won't examine presently) the precise wording of
    SFC (strategy-free criterion), but Score DSV doesn't seem to satisfy
    the votes-only shortcut interpretation, because it can elect B with
    these rankings:
    49 b (a and c rated zero)
    24 a>b
    27 c>a

    The criticism is that the A>B voters can give away victory to B, when
    assuming no order reversal, A might be the "sincere CW" but B definitely
    is not.

  This case has a CW, so Score DSV would choose that winner. There is no condorcet cycle. You need at least 4 of the b voters to vote b>c for your example to work. Then your example is no longer covered by the SFC, which states: "If a Condorcet candidate exists, and if a majority prefers this candidate to another candidate, then the other candidate should not win if that majority votes sincerely and no other voter falsifies any preferences. 
  In a ranked method, it is nearly equivalent to say: If more than half of the voters rank x above y, and there is no candidate z whom more than half of the voters rank above x, then y must not be elected." 

    It doesn't satisfy the votes-only interpretation of SDSC, because it
    can elect B with these rankings:
    49 b
    24 a
    27 c>a

  Again, no, only if you change 28 total b and a voters to b>c and a>b, respectively, which puts you out of the purview of SDSC.

    This is related to favorite betrayal.

    Again, it could be that it technically satisfies SDSC but I'd have to
    reread it.

    The "defensive participation" criterion I would like clarification on.
    I don't see how it doesn't imply Participation. It sounds like you are
    saying that if X wins, I can cast any vote I want, and nobody I rate
    below X will become the winner.

  That's not what I was saying - but I've further looked at Schulze's criticism and, more generally, the class of situations where the Smith set is larger than 3, and I realize that what I was saying for both of these criteria does not, in fact, hold.

  So it's still a very good system in my opinion, but I can now see little reason to favor it over other approval-condorcet hybrids which allow ties (such as Llull voting), aside from the greater expressivity of the ballot.

  Jameson

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