# [EM] Arrow's Theorem.

Eric Gorr eric at ericgorr.net
Mon Jul 14 21:35:02 PDT 2003

At 6:39 PM -0400 7/14/03, Rob Speer wrote:
>Approval voting is independent from irrelevant alternatives. If a
>candidate is removed from the ballot, and people's preferences remain
>the same - they do not strategically change their votes - then the
>winner will still win.

Borrowing the defintion of IIA from:

http://www.wikipedia.org/wiki/Independence_of_irrelevant_alternatives
if one option (X) wins the election, and a new alternative (Y) is
added, only X or Y will win the election.

Let's say that there were three options A, B & C with the following ballots:
(Each voter only voted for a single candidate)

A: 50
B: 26
C: 10

A wins.

Now, add, option D, which happens to be close to option A, but with
some critical difference such that votes are now split between A & D.

A: 25
B: 26
C: 10
D: 25

B Wins and Approval fails IIA.

The vital point here would seem to be that if the voters vote for no
more then a single option (which they can do under Approval),
Approval is equivalent to Plurality and Plurality does not satisfy
Arrow's Theorem.

So, where did I go wrong?

--
== Eric Gorr ========= http://www.ericgorr.net ========= ICQ:9293199 ===
"Therefore the considerations of the intelligent always include both
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