[EM] Arrow's Theorem.

[Rob Speer]

On Mon, Jul 14, 2003 at 03:13:36PM -0400, Kislanko at aol.com wrote:
> In a message dated 7/14/03 2:05:14 PM Central Daylight Time, rspeer at MIT.EDU 
> writes:
> 
> > believe that Approval satisfies non-dictatorship (duh), Pareto
> > optimality (if you get 100% of the vote, then of course you win), and
> > IIA (adding a new candidate doesn't change the approval totals for
> > existing candidates).
> > 
> 
> No, Approval does not satisfy non-dicatorship.

Are you sure you're saying what you mean to say? Approval takes the
votes of more than one person into account; therefore, it satisfies
non-dictatorship.

> Pareto optimality isn't proved 
> by the 100 percent case.

The second assertion you've made without any backing. Please, convince
me.

> IIA does in fact change the approval totals - if the 
> IIA candidate is more desirable than my last-approved candidate I might not 
> approve my lowerst-ranked candidate after a better alternative is made 
> available.

IIA doesn't take into account changing other votes.

When IIA is considered for preferential methods, it is assumed that a
vote like A>B>C>D becomes something like A>B>E>C>D when candidate E
enters. It is not considered that A>B>C>D could become B>A>E>C>D, even
if a voter might have a strategic reason to change their vote that way.
Changing an approval vote of A=B > C=D to A=E > B=C=D is the same thing.

I really want Approval to fail a condition of Arrow's Theorem somewhere.
It seems a shame that the only method satisfying all of the conditions
would be such a basic method. But so far, nobody has given me an actual
example of how Approval violates any of the conditions,
without changing definitions.

-- 
Rob Speer