# [EM] Arrow's Theorem. - what ask more than STV

Stephane Rouillon stephane.rouillon at sympatico.ca
Mon Jul 14 21:59:06 PDT 2003

```The difference between Mr. Speer version and yours,
is your interpretation of this:

>"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."

He supposes removing some candidate would not change voters's (yes/no)
threshold's
position. You suppose it could. Theorically, you are both right. Voters do not
change
their preferences order. They only change the part they choose to explicitly
express on the ballot.

On another subject, what ask more than STV, I still answer SPPA.
It is an improved-STV, fully proportional and with only one candiate
per party per voter so main complains I have just read from our Australian
colleague
vanish...

S. Rouillon

Eric Gorr a écrit :

> 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
> benefit and harm." - Sun Tzu
> == Insults, like violence, are the last refuge of the incompetent... ===
> ----
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```

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