[EM] Re: IIAC [was Arrow's Theorem.]

[Forest Simmons]

I appreciate what you are saying, but I'm not sure that your version of
the IIAC is the most commonly accepted one either.

There are versions that have to do with deleting losers from the ballot.
The deleted candidates don't have to lose to the winner on every ballot in
most versions.

There are versions that have to do with adding candidates to the ballot.
In your version that candidate has to be uniformly dominated by the
previous winner, but that is stronger than the usual requirement, which is
merely that if the newcomer changes the outcome, then the newcomer must be
the new winner.

Your definition cannot be applied directly to traditional lone mark
plurality ballots because the only way to make the newcomer lower than the
winner on such a ballot is to mark the winner and leave the newcomer
unmarked. This cannot be done without wiping out all of the other
candidates and leaving only the original winner marked on all of the
plurality ballots.

True, your version can be reasonably applied to the underlying preference
orders upon which the lone mark ballots were based, but this is one
more level of abstraction, for which I can see no justification,
since the more common candidate removal version doesn't require it.

Forest


On Wed, 16 Jul 2003 Kislanko at aol.com wrote:

> In a message dated 7/16/03 2:50:29 PM Central Daylight Time, fsimmons at pcc.edu
> writes:
>
> > I'm not sure if there is a universally accepted version of the IIAC, but I
> > prefer the version that doesn't require the voters to go back to the polls
> > if a losing candidate withdraws between the time the ballots are collected
> > and the time they are counted.
>
> This is where the language needs to be made more precise. An attribute of an
> election method is not dependent on another vote - that's a different
> election, and may not even necessarily use the same method as the first. (Indeed, this
> is typical for the elections that require a majority winner, regardless of
> the vote-counting method that picks the "top two", the method for the "run-off"
> is majority vote between two candidates.)
>
> The IIA criterion doesn't call for another vote, it just asks if the
> vote-counting method would result in a different winner were another
> candidate be ranked lower on all ballots than the winner by the

Here's the Pareto dominance condition that makes your version different
from previously discussed candidate addition versions.

> vote-counting method being considered. Some methods fail this test,
> because the way the votes are counted include contributions for
> non-winners that can be increased depending upon where in the ranked
> ballots the alternative is listed. If that doesn't change the original
> winner, or only changes it to the inserted candidate, the method
> passes IIA.
>
> If the voters change their relative rankings for the other candidates because
> of the addition, it is a different election, not an attribute of the
> vote-counting method.  In that case the addition is a RELEVANT alternative, not an
> irrelevant alternative.
>
> People seem to slip back and forth between arguments about algorithm
> behaviour and voters' behaviour. But an argument about an algorithm should stick to
> observations about the algorithm.  "If voters voted differently" can justify
> anything.
>
>
> Paul Kislanko
> http://www.kislanko.com
>