[EM] Proposed method of cycle resolution

[Diana Galletly]

I know there are already far too many methods out there, but here's
another (two) that I'm vaguely partial to.  I'm sure there are good
reasons why neither of them is any good, but since I can't see them
(and neither can my work colleagues) I thought I'd toss them out to
this list for the eagle-eyed to pick over.

Method 1: RMS voter satisfaction
Basically everything proceeds as with any other Condorcet method
unless/until a cycle occurs.  If there is a cycle, the Smith set is
determined.  Then for a member, X, of the Smith set calculate
the "RMS voter satisfaction" as follows:

Compared with each other member Y of the set, determine what proportion of
voters prefer X to Y.  Sum the squares of these proportions, divide by
the number of comparisons, take the square root.  The candidate with the
highest value of this wins.

Method 2: RMS voter dissatisfaction
As for method 1 up to the point of determining the Smith set.  Then for
a memebr, X, of the Smith set calculate the "RMS voter dissatisfaction"
as follows:

Compared with each other member Y of the set, determine what proportion of
voters prefer Y to X.  Sum the squares of these proportions, divide by
the number of comparisons, take the square root.  The candidate with the
lowest value of this wins.

(The basic rationale behind these mtheods is that, whilst I don't want just to
take the difference between the number of people voting A>B and the number
voting B>A, and nor do I just want to consider the percentage of people voting
whichever is more preferred, I do want to give slightly more weight to higher
percentages.  But I also want to be able to differentiate between "58% of
people preferring A to B and 40% of people preferring B to A" and
"58% of people preferring A to B and 10% of people preferring B to A".)

I think I am keener on the dissatisfaction measure, as I think that minimising
dissatisfaction is probably the best/easiest thing to do, and that attempting
to maximise satisfaction is more likely to lead to anomalous/undesired
results.

Diana.