[EM] Measuring the risk of strict ranking

[Kevin Venzke]

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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