[EM] Approval meets IIA ?

[Chris Benham]

  Marcus,
You wrote (Mon.Mar.1,04):

"Arrow proved that there is no single-winner election method with
the following four properties:

   1) It is a rank method (= a ranked-preference method).
   2) It satisfies Pareto.
   3) It is non-dictatorial.
   4) It satisfies IIA.

All four properties are needed to get an incompatibility.
For example, RandomDictatorship is a paretian rank method that
satisfies IIA, RandomCandidate is a non-dictatorial rank method
that satisfies IIA, Approval Voting is a paretian non-dictatorial
method that satisfies IIA, my beatpath method is a paretian
non-dictatorial rank method."

To my mind, Approval does NOT satisfy Independence of Irrelevant Alternatives (IIA), or even
the much weaker Independence of Clones.
For my demonstration, I am assuming that the voters know nothing but their own sincere ratings
of all the candidates on the ballot, and that in that situation they all use the best "strategy"
of approving all the candidates they rate above average, and no others.

Initial two candidate election (with ratings out of ten).
01: A(9)>>B(1)
99: B(8)>>A(7)

B wins 99 to 1. Now we add a third candidate X, which all the voters rank adjacently to A, and who
therfore meets the Blake Cretney definition of a clone of A. 

Same voters and initial 2 candidates, but with a third candidate added.
01:A(9)>>X(2)>B(1)
99:B(8)>A(7)>>X(1)

A wins 100 to 99. So adding a clone of A, which ALL the voters ranked last, changed A from a 
1/100 loser to the winner.

One of my fundamental standards is that a method should perform reasonably when all the voters
vote sincerely (taking no account of how any other voters might vote). 
A method should be able to cope with insincerity, but to perform reasonably it definitely shouldn't
DEPEND on insincerity.

Chris Benham