[EM] MCA, 3RC, Pair Approval, Manipulability

[Forest Simmons]

On Sun, 1 Jun 2003, [iso-8859-1] Kevin Venzke wrote:

> Forest,
>
>  --- Forest Simmons <fsimmons at pcc.edu> a écrit :
> > > Question: What advantage does MCA have over three-rank Condorcet?
> > >
> >
> > Good Question!
> >
> > I think it's easier to explain to the lay voter: "If nobody's favorite
> > gets more than fifty percent of the votes, then the most acceptable
> > candidate wins."
> >
> > We need to compare the two methods on more examples to clarify the other
> > advantages and disadvantages.
>
> I thought a bit about my question after posting it, and these reasons
> occur to me:
> 1. MCA is so close to Approval that it's almost a two-rank method.  Thus if
> it's agreed that two-rank Condorcet (Approval) is better than three-rank
> Condorcet, then MCA should be better for those same reasons, whatever they are.
> 2. It's easier to explain, as you said.
> 2. Three-rank Condorcet requires a cycle-breaker of some kind.  That raises
> the question of which it should be, and makes it even harder to explain.

Excellent points.

>
> Advantages of 3RC over MCA:
> 1. I'm worried that less savvy voters will fill out an MCA ballot like
> it was a 3RC ballot.  In other words, that they will put unduly lousy
> candidates in the second rank.

I'm more worried that the naive voters will be too picky for their first
rank in cases where they should put a compromise in with favorite.

> 2. The expectation from ordering two candidates is the same no matter which
> two ranks you place them in.  In MCA, A>B>_, A>_>B, and _>A>B all have
> different values.
> 3. Strategy is simpler, because MCA has two ways to win, and more odds to
> estimate.
>
> Regarding manipulability by false information, I would say we should
> suspect right off the bat that 3RC will outperform MCA, because MCA
> strategy requires more information (as from polls).
>
>
> > The Strong FBC method holds up well on this example because the B and C
> > supporters have no incentive to approve any pair other than {B,C} and the
> > A supporters have no incentive to approve any pair other than {A,B}. The
> > finalist pair then turns out to be {A,B} and A wins.
>
> Is this so?  I would think that:
> A voters approve (A,B) as you say, because although A is destined to lose
> based on the poll, B is better than C;
> B voters approve (A,B) and (B,C) because they can win both (they think they
> are the CW, so they're fine as long as they get in the winning pair);
> C voters approve (A,C) expecting to win, and/or (B,C) to ensure a decent
> result.
>
> (It also occurs to me that some A voters might want to approve (B,C), in
> order to avoid (A,C) winning, resulting in a C victory.  Possible?  The
> strategy A uses in the first place is "defend the CW"...)
>
> Expected results:
> (A,B): 6000
> (A,C): 0-4000
> (B,C): 2500-6500
> Either (A,B) or (B,C) wins, B wins in either case
>
> Actual results:
> (A,B): 7000
> (A,C): 0-3000
> (B,C): 1000-4000
> So (A,B) wins, and A beats B, as hoped.
>
> (But if enough A supporters actually approved (B,C), B could still take
> it.  In that case, this method is not so good, but at least it would
> be clear from the results that the A supporters were duped.)
>

I stand corrected, it is quite possible that {B,C} could be the finalist
pair in this method if the A supporters vote cautiously enough to approve
a pair of low utility, last choice candidates [remember A>>B>C]. That
would be kind of like Nader supporters saying, "We would like the contest
to be between Nader and Gore or else between Gore and Bush."  It goes
against the grain, but it is rational.


I have to agree with Alex that MCA would most likely give the win to A.
In fact since, according to the polls A is last choice for sixty percent
of the voters (with no chance of fifty percent approval, let alone fifty
percent favorite), neither the B nor the C supporters would feel any need
to up rank their compromise candidate to favored status. An infinitesimal
urge to express preference of favorite over compromise would be sufficient
if they believed these polls.


Forest