[EM] Kevin--The 3-slot method, FBC, MMPO

Kevin Venzke stepjak at yahoo.fr
Sat May 21 22:46:50 PDT 2005


--- MIKE OSSIPOFF <nkklrp at hotmail.com> a écrit :
> Is the limitation to three rank positions necessary to the FBC compliance? 
> There are drawbacks to only having 3 rank positions. I'm not saying that the 
> gain isn't worth it.

No, although the method I defined requires some measure of approval.

What I'm going for is a method that won't intimidate voters, and which
behaves reasonably without much need for strategy. I think voters will respond
better to "put all the candidates into three groups" than to "rank the
candidates; equal-rank if you want."

I'm very pessimistic about having a ranking as well as a cutoff that needs
to be placed. I'm also pessimistic about interpreting all ranked candidates
as approved, since voters could unwittingly vote too far down.

> Limiting it to 3 rank positions prevents compliance with SFC, SDSC, and 
> Condorcet's Criterion.

I agree.

> But the method you described meets the usual votes-only CC. But Plurality 
> meets that too, and it's pretty much agreed that Plurality isn't intended to 
> meet CC, and that, therefore, plain votes-only CC isn't what is intended for 
> CC.
> Other votes-only CCs? Sure, maybe the method you defined could meet those. 
> One of them says explicitly that it doesn't apply to nonrank methods. The 
> other explicitly says that nonrank methods fail. So then, whether or not 
> your method passes those CC versions depends entirely on whether we classify 
> your method as a rank method. :-) What can we say about a criterion that a 
> method may or may not pass, depending on how we classify that method? :-)
> That tells us that there's something wrong with that critrerion.

Remember that my scheme does not involve labeling a method as being "ranked" 
or "non-rank." A method that doesn't admit all preference orders may or
may not be able to satisfy a given criterion.

I agree that a three-slot method couldn't satisfy Condorcet, Minimal Defense,
or (say) Later-no-harm, as I interpret those criteria.

> Anyway, back to that 3-slot method:
> As I said, if the 3 rank positions confer FBC compliance, that could be 
> worth the loss of SFC, SDSC, and Condorcet's Criterion.
> If one is ambitious about what to propose, I'd rather have the more 
> ambitious SFC, GSFC, and SDSC. But maybe it's too ambitious to hope that 
> voters would make use of those criterion compliances. 

I think it's possible. I'm worried that when asked to rank candidates,
voters will lazily leave out some options, or worse: Decide to rely on
popular candidates' voting advice.

I agree that Approval minimizes these problems better than this
Condorcet//Approval variant.

> But it's a near toss-up. Because, without SFC or SDSC, it loses much of its 
> advantage over CR and Approval. And CR and Approval's FBC compliance is 
> transparently obvious, not something difficult to prove, and probably more 
> difficult to convince the public of.

True. On the other hand, it is always complained that Approval doesn't allow
the voter to specify a favorite. Also, perhaps the use of three slots would
deflate the "one man one vote" misunderstanding that Approval runs into.

> SDSC would be good to have, because, with Approval or CR, we have no way of 
> knowing if progressives will ever have the courage to not vote for the 
> Democrat, even when Nader (or someone like him) outpolls the Republican. 
> Progressives aren't known for their adventurousness, you know. So SDSC would 
> be a good thing to have.

Although you can't satisfy SDSC with three slots, you certainly come closer
than with two slots. In general it should be safe to rank the progressive
above the Democrat: If you create a Prog>Demo>Repub>Prog cycle, then your
Prog>Demo vote is removed and we try it again. It's not likely that Repub
will end up winning by approval in this case.

> But the methods that meet SDSC don't meet FBC. And if those methods will 
> have progressives ranking Democrats over progressives, then we gain nothing 
> by having SDSC, when its benefit isn't used. So which is the one to have?

Another thing I want to note is that the three-slot method is not really
vulnerable to offensive order-reversal: If you thwart a (voted) CW by burying 
him under a weak candidate, you have to then vote for your preferred candidate 
and the weak candidate equally.

I've also been thinking: I think the problem with WV methods in failing
FBC is that they fail a criterion which might go something like this:

"Increasing v[a,b] in the pairwise matrix must not increase the probability
that the winner is either A or B."

Assuming I'm onto something there, it might be the case that MMPO aka
Simpson-Kramer satisfies FBC. Increasing v[a,b] under MMPO can't make any
candidate lose except for B. I think I might be able to prove compliance 
(one way or the other) for the 3-candidate case.

An attempt at a votes-only weakening of FBC:
"Let S represent the set of candidate(s) ranked in equal-first on a set 
of identical ballots. Let X represent a candidate ranked below first on 
those ballots. Then, raising X to equal-first on those ballots must not
decrease the probability that the winner is either X or in S."

This doesn't cover all the bases: It could be that ranking X in first
causes your last choice to win when otherwise your second-to-last choice
would have won. But in my mind, the main guarantee FBC makes is that
you can list any number of candidates as favorites without thereby
contributing to one of them losing.

Kevin Venzke


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