Saari and Cyclic Ambiguities

Michael Rouse mrouse at cdsnet.net
Fri Mar 29 08:56:56 PST 2002

```Here's a cyclic ambiguity (a five-way circular tie) to try with various
voting systems:
5: ABCDE
6: BCDEA
7: CDEAB
8: DEABC
9: EABCD

So A>(B, C), B>(C, D), C>(D, E), D>(A, E), and E>(A, B).

You could also look at

5: ACEBD
6: BDACE
7: CEBDA
8: DACEB
9: EBDAC

where A>(C, E), B> (A, D), C>(B, E), D>(A, C) and E>(B, D)

The diagrams of these circular ties look like a pentagram, which is kind of
cool. Within these two diagrams you could also mix up the relative strengths
(56789, 65798, 75967, etc) to see where various voting methods differ. Any
ideas on how Saari would unravel the ties?

Michael Rouse
mrouse at cdsnet.net

----- Original Message -----
From: <DEMOREP1 at aol.com>
To: <election-methods-list at eskimo.com>
Sent: Friday, March 29, 2002 8:03 AM
Subject: RE: Saari and Cyclic Ambiguities

> Alex wrote in part-
>
> Saari pointed out that cyclic ambiguities come from a "Condorcet profile"
>
> or "symmetric profile".  If the electorate consists of 3 groups
>
>
> 35 A>B>C
>
> 33 B>C>A
>
> 32 C>A>B
>
>
> we can "decompose" the electorate into
>
>
> 32 A>B>C  +  3 A>B>C
>
> 32 B>C>A  +  1 B>C>A
>
> 32 C>A>B
> ----
> D- Selectively ignoring ANY votes in my local area is STILL a major
election
> felony.
>
> Who has a YES majority ???
>
> Saari can appear at any time on this list and be roasted accordingly.
>

```