[EM] IIA Theory

[Craig Carey]

At 12:26 06.10.99 , you wrote:
>To paraphrase Eric Cartman, 'Ay! I know that I stuffed up in my
>definitions but that's low! (and wrong!) (more further down)
Thanks David. The could be gold under the IIA sandstone yet.

       AN ANALYSIS OF THE CATCHPOLE IIA RULES  (PART II)


Mr Catchpole was seeking to say that the 'IIA' rule has this
 meaning.

         The election is invariant to the adding or
         removing of a candidate, provided that both
         before and after, there are no preferences
         anywhere for that candidate.

Lets have that loser that is not voted for, be candidate R.

For the moment, just consider a case where there may only
 be a preference for R if it is on a single paper.

The usual preferential voting elections can be represented
 as win and lose regions inside of simplexes.

Vertices would be made the correspond to the number of votes
 for that vertice's voting paper.


When Mr Catchpole, say, adds candidate R to an election, then
 the hyperdimensial simplex flat that contains the win-lose
 regions is extended out to the new vertex for R.
The ratio of votes for each type of paper is not permitted
 to alter in any way if that way moves the point representing
 the ratio of votes, into the measurable bulk of the new
 simplex.

Here is a question for Mr Catchpole:

 If a solution is put in a triangle and then a 4th quite
 new candidate is added and allocated a vertex above the
 triangle, then:
 What is the significance of the Catchpole-IIA rule?.
 What is a method that your rule eliminates.

Rather than imposing a Catchpole IIA rule, wouldn't it be
 better to allow anything not voted for to be a candidate.
 For example uncountable sets of sets could take along
 side anything else that got 0 votes.
 (The Catchpole-IIA theory has got one vote hasn't it?).

Can the IIA theory be transmuted by anybody into something
 valuable?. I'd like a reference to the person or
 mathematician who named/published the "IIA" rule. Was it
 quoted accurately?.

...
>
>rather than "win-lose slates". However [A] is patently true for any
 theory grounded on inconstistent and incomplete axioms

_____________________________________________________________
Mr G. A. Craig Carey
E-mail: research at ijs.co.nz
Auckland, Nth Island, New Zealand
Pages: Snooz Metasearch: http://www.ijs.co.nz/info/snooz.htm
       Public Proxies, MEDLINE Search, Multithreaded Add-URL
_____________________________________________________________