IIA Theory

[Bart Ingles]

DEMOREP1 at aol.com wrote: 
[...]
> I mention again that (A) an election is held for a time period using the
> votes as cast once (i.e. not multiple replays of an election with added or
> dropped choices or voters) [...]

I have been thinking (ouch) about the assumptions made regarding the
nomination process by proponents of various systems:

(A) Proponents of systems which break the field of candidates into pairs
(or larger subsets) for comparison, i.e. ranked systems, seem to try to
avoid any assumptions whatever about the overall field, instead relying
on criteria such as IIA to make sure the method is not overly
self-contradictory.  Any comparisons between candidates or groups of
candidates are considered relative.

(B) Proponents of systems that require the entire field of candidates to
be evaluated as a unit (e.g. approval voting or rated methods) seem to
implicitly assume that the field of candidates is reasonably
representative of the entire universe of possible candidates (as
determined by the makeup of the electorate).

If voter ratings were based on the universe of potential candidates,
then those ratings could be considered absolute.  A good nomination
process should closely approximate that universe, so the resulting voter
utilities for that field could then be considered an approximation of
absolute ratings.

If removing a candidate from that field changes the outcome, that may
just mean that the reduced field of candidates is no longer
representative.  It does not by itself necessarily invalidate a voting
system which doesn't use partial-field comparisons.

Bart