[EM] Score DSV

[Kevin Venzke]

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.)
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.
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.

> 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.

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 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.

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

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.

Kevin Venzke