# [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).
>
>
> 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
>
>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.

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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