[EM] Measuring the risk of strict ranking
Kevin Venzke
stepjak at yahoo.fr
Tue Jun 28 08:00:40 PDT 2005
Mike,
--- MIKE OSSIPOFF <nkklrp at hotmail.com> a écrit :
> You continued:
>>
>> In other words, it must *never* be optimal strategy (i.e., be best for
>> {a,b})
>> to vote A=B. The problem with this is that most likely the optimal strategy
>> will
>> be to vote the more viable candidate over the less viable one.
>>
>> If you insist on this latter property and FBC at the same time, then the
>> probability that the winner comes from {a,b} must be totally independent of
>> whether you vote A=B, A>B, or B>A.
>>
>> The latter property is satisfied by "MinGS" ("elect the candidate whose
>> fewest
>> votes for him in some contest is the greatest") and Woodall's DSC method
>> (which
>> is not a pairwise count method).
>
> I reply:
>
> Just at first glance, that sounds pretty good, guaranteeding that the chance
> of the winner coming from {Dean, Nader} is completely independent of how you
> order those two. Your ordering of them depends only on which you choose over
> the other. Isn't that a further reduction in the lesser-of-2-evils problem?
>
> I haven't looked at MinGS or DSC, and maybe they have some big disadvantage,
> but it's my policy that even the most unlikely solution deserves a look.
Sorry, it would have helped if I had given the "latter property" a name.
MinGS and DSC both fail FBC pretty obviously. I'm not currently aware of a
method which satisfies FBC and the latter property; I think such a method
might have to be equivalent to plain approval.
>What an embarrassment. Yes, that's a ridiculous result, when increasing the
>A & B voters without bound makes them both lose. Does that clinch it for
>MDDA over MMPO?
I think it does. (Actually, MMPO's SDSC failure already bothered me quite a
bit.)
>Which method, MMPO or MDDA, makes it less likely that those LO2E
>progressives will regret ranking Dean in 2nd place, instead of in 1st place
>with Nader?
>
>MDDA.
I've written a simulation which aims to measure this. I'll have to make the
results prettier (and scaled) before I post them, but your conclusion is the
same as my simulation's.
Here's an excerpt... With four candidates, five factions, 50000 trials, and
"A->B" means "win moves from A to B when a strict A>B ranking is introduced
by one faction who had tied A and B at the top." Candidate "C" refers to
any other candidate.
B->C B->A C->A C->B
ranked Approval: 0 0 0 0
Schulze(wv): 336 5079 7 0
Schulze(m): 460 5075 251 0
MMPO: 545 5303 0 0
MDDA: 392 4056 0 0
tC//A: 1205 4513 0 0
C//A: 858 4458 363 0
ERBucklin(whole): 787 3023 625 556
For the FBC-satisfying methods, only "B to C" and "B to A" win moves occur.
Schulze, ERBucklin, and C//A also have "C to A," and ERBucklin also had
"C to B," which is not just favorite betrayal incentive, but nonmonotonic
incentive.
Two things strike me about this data:
1. Schulze(wv) showed extremely little favorite betrayal incentive.
2. tC//A seems surprisingly poor, despite the intuitive argument that, "even
if you sink your compromise, you can still vote for him fully in the approval
stage."
Kevin Venzke
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