[EM] Steph: You still haven't heard my question.

[MIKE OSSIPOFF]

Steph wrote:

I do not hate Middle, I just dislike under and over representation
when it comes from the system...

In a sense every voting system's result comes from "the system".
But when, with Approval, the voters keep to the voter median,
that also comes from expressed wishes of a majority of the voters.

Steph continued:

As for a complete mathematical and thorough definition of
reciprocal fairness, try this.

Suppose two sets, S1 the set of voters and S2 the set of candidates.
Suppose an electoral method that produces scores for each candidate.
If you can split S1 in |S2| subsets each of a cardinality equal to the score
obtained
by the corresponding candidate, you can link these two sets using a 
bijective
mapping. Each voter contributes to one and only one candidate.
If an electoral method produces scores that verify this property,
it respects reciprocal fairness.

Is this well defined enough for you?

I reply:

Maybe, but defining your criteria isn't nearly enough. Did you notice
that I kept asking you if you could justify your criterion in terms
of something more fundamental? Is it that you didn't notice that,
or is it that you can't justify the criterion?

The point that I wanted to make yesterday was this:

Either you justify your criterion in terms of other standards, and
ultimately in terms of standard that others accept as fundmental,
or you just hope that people will accept your criterion itself as
a fundamental standard. The latter isn't at all likely, and so I repeat:
Can you or can you not justify your criterion in terms of something
that others accept as fundamental?

By the way: Of course for a public proposal, a criterion that can only
be written in mathematical language is quite useless. For something
more usable, then, you'd have to write it in English (or French, Esperanto, 
etc.). If you write it in French, I'd have to find a translator, but I'd be 
willing to do that. Your previoius reference to your criterion didn't tell 
nearly enough about it to be a definition.

But never mind
that. The question is whether or not you can justify your criterion
in terms of some standard that an appreciable number of people accept
as fundamental.

Mike Ossipoff






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