[EM] IIA Theory

[David Catchpole]

I expressed a "criterion" or "modification" in the message which applies
generally. The use of W' is this- consider system W and schema V. Take all
proper subsets of candidate lists for V. Is there an electoral system W'
such that W' of V is independent of the removal of irrelevant alternatives
to W of any proper subset? If so, then W must be such an electoral system.
This criterion operates always and in the case of single member systems is
satisfied by Condorcet completion systems.

The criterion written in my earlier message, in your formalism, would
probably be easier to get a precise meaning from than my waffling above.

It's a little (?) easier to elicit the implication that Condorcet
completion systems satisfy this criterion than to work out (P1) using the
case-by-case process you described much earlier.

On Sat, 9 Oct 1999, Craig Carey wrote:

> How are you going to modify it. To make it not apply in those regions
>  where it fails IFPP, for example, would lead to a complex formula.
> 
> To partially apply an unmodified IIA rule, can be the same a strictly
>  applying a improved version.
> 
> However, I presume it would be wanted to the have vote alteration
>  effects constraints rule(s) simple. Such rules ought not cover tens of
>  pages of paper at any time, as the number of candidates tends towards
>  being infinite.
> 
> It seems to me that the rejection of IIA indicates that preferential
>  voting theory is not in any true and broad sense, a part of
>  'social decision theory' (or whatever that realm of ideas is called).
> 
> [IIA might now be uninteresting (like pairwise comparing)

Grrr....