[EM] Arrow's Theorem - The Return (again)

[Alex Small]

Eric Gorr said:
> Arrow seems to be perfectly content with allowing equal rankings.
>
> Approval voting merely requires the user to divide the options into  two
> different groups, but doing do does not violate Arrow's Axioms or
> definitions regarding voter choice.
>
> Again, from his book:
>
>    "However, it may be as well to give sketches of the proofs, both to
> show
>     that Axiom I and II really imply all that we wish to imply about the
> nature of orderings of alternatives and to illustrate the type of
> reasoning to be used subsequently." (page 14)

No, no, no, no, no!

Arrow assumes that, whether voters happen to have strict preferences or
whether they instead rank some candidates equal, voters are free to report
ANY transitive ranking of candidates (which might include equal rankings).
 Based on this information, i.e. every voter giving his COMPLETE
preference order, the election method then chooses a winner.

Approval does NOT allow voters to express their complete preferences. 
Sure, if a person happens to have a lot of equal rankings so that the
candidates fall into two groups, then Approval lets that PARTICULAR voter
express his full preferences.  BUT, if the person sorts the candidates
into 3 or more categories, Approval does not let them express their
complete preferences.

Once again, Arrow basically proves that no method can satisfy all of the
following criteria simultaneously when there are 3 or more candidates:

1)  Non-dictatorship (plenty of methods, and any seriously proposed
method, will satisfy this)

2)  Pareto (plenty of methods, and any seriously proposed method, will
satisfy this)

3)  IIAC

4)  The use of RANKED ballots, which allow ANY voter to indicate his
entire preference, WHATEVER it might happen to be.


APPROVAL DOES NOT SATISFY THIS CRITERION!  If my preference is A>B>C then
I have to make a decision about whether or not to approve B.

Can I please get some back-up here?  Somebody, anybody, please back me up
on this?  I can't believe how difficult it is to drive home the point that
Approval Voting is not a ranked method.

Anyway, since Approval flunks criterion #4, it is in keeping with Arrow's
Theorem.  It flunks at least one of his criteria.



Alex