[EM] Majority Criterion poor standard for elections

[Abd ul-Rahman Lomax]

At 03:51 PM 10/25/2006, Juho wrote:
>On Oct 25, 2006, at 7:07 , Abd ul-Rahman Lomax wrote:
> > And methods which ignore strength of preference cannot maximize
> > social utility.
> > And if strength of preference is considered, there goes the
> > Majority Criterion....
>
>I at least made a try few mails back on the list with "Ranked
>Preferences".

Tried what? To satisfy the Majority Criterion while allowing 
preference strength to influence the outcome? I don't think it is 
possible. However, I found the description of "Ranked Preferences" to 
be incomprehensible. It's *complicated*. I suspect that there might 
be a way of expressing it which is much simpler, or maybe not. If 
not, forget about it. If I can't figure it out with a few minutes of 
focused attention, the public will *never* go for it.

>  I don't claim that all the criteria are fulfilled but
>some basic cases work. Votes 55: A>B>>C, 45: B>>A>C elect A (the
>majority favourite) although the B supporters strongly disliked her.

Let's express this in Range terms to see what it might mean.

I'll assume that there are three candidates total, A, B, and C. What 
has been expressed above could simply be represented by assuming that 
there are four ranks. A preference gap of two ranks is expressed by 
">>". So the range ratings (Range 0-3) are:

55: A:3 B:2 C:0
45: A:1 B:3 C:0

Hey, why did C even bother to run? Perhaps to cause the election of 
B.... Range can do that, it is not immune to the influence of 
"irrelevant" candidate entries, if they distort the matrix. However, 
the remedy for this is in the hands of the voters: it is to bottom 
rate more than one candidate. A voter might bottom rate a whole range 
of candidates. If this is recommended practice (not just 
bullet-voting), then Range would not be vulnerable to strategic 
presentation of really bad candidates.... They would not raise the 
rating of moderately bad candidates....

Anyway, this election, as stated, comes out to be (totals)

A: 3 * 55 + 45 = 210
B: 2 * 55 + 3 * 45 = 245

B wins. B wins even more handily if the >> represents a greater gap.

>Strong votes however have power in other circumstances since votes
>40: A>>C>B, 40: B>>C>A, 20: C don't elect the Condorcet winner C
>since A and B supporters strongly dislike her. Social utility is
>maybe not yet maximized but maybe improved??

Unclear. Badly polarized vote patterns often create weird results.

I'd suggest coming up with a clearer explanation, with calculation 
examples of the proposed method.

In any case, the Majority Criterion is doomed for any method which 
*considers* preference strength, no method that allows preference 
strength to affect the results can satisfy the Majority Criterion. 
Yet it is quite clear that it is necessary to consider preference 
strength to get optimal election results, or else casual or trivial 
preferences carry the same weight as strong preferences (in some of 
the examples we have given, these "preferences" are actually "needs.")