[EM] Score DSV

[Jameson Quinn]

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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