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

Stephane Rouillon stephane.rouillon at sympatico.ca
Fri Jan 17 08:56:04 PST 2003

```Mike --

I will try to be more specific and link my criteria to a more fundamental
issue.

Voter median is a very insteresting concept. I suppose you consider this
the candidate that could recover the highest number of vote by removing
all candidates to its right or its left if you could align all candidates along
a unidimensional ranked line. Some would argue it is a circle and the
extremities depend on every voter lower preferences... In fact this previous
definition
has several holes because it is very hard to formalize. Do you
have a formal definition? Be my guest...
If you ask for thoroughness you have to be prepared to fulfil it too.

Or we can simply admit it is the equivalent of the approval winner if
we do not bother being method dependent. It is what you seem
to say below. Am I right?

MIKE OSSIPOFF wrote :

> 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.

Let's suppose we can come up with a median voter definition.
Would you agree that adding candidates to some extremity should not
alter the result? Or the method would be cloning or crowding dependent?

> 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?
>
>
> 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?

Using methods that verify my criteria, adding a new candidate should only affect
the two
neighbour subsets because this new candidate would represent better the idea of
these
voters in the available ranges of ranking. Using other methos like approval no.
Because the new comer could have the exact balanced position that maximises
the acceptance of its two neighbour groups (and even groups further with
approval).
On the other side of the rainbow, other voters will change their mind reacting
to
this new possibility. It highers the possibility of the first side finding their
optimal agreement,
so the second side HAS to play it safer and will conceide by accepting a more
"median" or centrist
candidate.Use Alex or Bart strategy with utilities, the maths confirm.

>
> 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

The result is: methods that do not respect the "reciprocal fairness" criteria
are extremist-candidate-dependent.
It is understandable that when you put a new median candidate, it could become
the winner.
But adding a very left candidate should not affect the right candidates results.

But if adding a new candidate C makes the winner move from A to B, I think it is
a fundamental bias.
"Reciprocal fairness" is mandatory. It is not sufficient to ensure a fair
election.
The same problem can arise from vote splitting.
To put it in words you like. Putting a Nader candidate should not afect the
Gore-Bush result.
With plurality it does because of vot splitting.
With approval it would, because anti-Nader people (We, especially you, can think
they are wrong,
but it does not stop them from existing and voting) would add G.W. Bush on their
ballot.
You can argue that in this specific case the polls should have shown everybody
that
candidates,
the run will be tighter and these problem will rise more often.