[EM] Saari's Basic Argument

Steve Barney barnes99 at vaxa.cis.uwosh.edu
Thu Jan 16 14:10:51 PST 2003

```Forest:

Isn't that just another way of saying Kemeny's Rule does not respect cyclic
symmetry?

SB

>From: Forest Simmons <fsimmons at pcc.edu>
>To:  <election-methods-list at eskimo.com>
>Subject: RE: [EM] Saari's Basic Argument
>
>On Wed, 15 Jan 2003, Alex Small wrote:
>
>...
>
>> I'm not convinced
>> that symmetry is a particularly compelling reason to pick an election
>> method,
>
>...
>
>especially not the symmetry of {ABC,BCA,CAB}, which has a rotational bias.
>
>True, it favors no candidate, but it does favor its three orders over the
>other three orders.
>
>One way to see this is that the average Kemeny distance from any order of
>the cycle to the three orders in the cycle is (0+2+2)/3, while the average
>Kemeny distance from a fully ranked order outside the cycle to orders of
>the cycle is (1+1+3)/3.
>
>On the other hand reverse symmetry has no effect on the Kemeny distance:
>
>If xyz is any order of the three candidates, and {rst, tsr} is any
>opposite pair, then the average Kemeny distance (d(xyz,rst)+d(xyz,tsr))/2
>is 3/2.
>
>So removal of a reverse pair cannot affect the Kemeny order.
>
>In the fully ranked three candidate case the Kemeny order is the same as
>the Ranked Pairs order, etc.
>
>Forest

Steve Barney

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