# Saari and Cyclic Ambiguities

Michael Rouse mrouse at cdsnet.net
Fri Mar 29 16:54:42 PST 2002

```How about 1-2-2-2-2 or 2-2-3-3-3? If I figured right, the Borda count order
changes when you remove the ties, and in the later case the winner changes
(if I counted right, which may be a problem since I'm figuring it during a
tech support call :)

Mike Rouse
mrouse at cdsnet.net

----- Original Message -----
From: "Adam Tarr" <atarr at purdue.edu>
To: <election-methods-list at eskimo.com>
Sent: Friday, March 29, 2002 12:37 PM
Subject: Re: Saari and Cyclic Ambiguities

>
> >5: ABCDE
> >6: BCDEA
> >7: CDEAB
> >8: DEABC
> >9: EABCD
>
> The only ranked method discussed here that does NOT hand this election to
E
> is IRV.
>
> Borda count reduces this to
>
> 1: BCDEA
> 2: CDEAB
> 3: DEABC
> 4: EABCD
>
> And the Borda scores are 20, 15, 15, 17, 30, for A, B, C, D, and E,
> respectively.  E wins by a huge margin.
>
> In Condorcet voting, the Smith/Schwartz set is every candidate, there are
> no ties, and every voter expressed a full ballot.  So all the Condorcet
> methods are pretty much the same.  Ranked pairs overturns D>E and C>E (in
> that order).  SSD drops C>E, B>D, D>A, A>C, E>B, and D>E, (in that
> order).  Both results leave E unbeaten.
>
> In IRV, A is eliminated first, then C, then E (by a count of 11B 15C
> 9E).  E gets screwed by having the wrong votes transfer.  B wins the
> election, even though B finished dead last in Borda Count and only beats
> one candidate pairwise.
>
> If the Approval cutoff is consistent, then Approval elects E as
> well.  Plurality of course elects E as well.  So really, only IRV can
screw
> this one up.  It's not tremendously illustrative (sorry).
>