# Circular ties revisited

DEMOREP1 at aol.com DEMOREP1 at aol.com
Mon Jun 8 21:58:31 PDT 1998

```I agree- Welcome back Mike Ossipoff !

In further developments--

Assume a circular tie using number voting (1,2, etc.)
Assume that 3 choices have majority acceptability.

The three pairings are thus--

A      1A + 2CA   *
B      1B + 2CB

B      1B + 2AB   *
C      1C + 2AC

C      1C + 2BC   *
A      1A + 2BA

where the 1 means the number of first choice votes and the 2 means the number
of second choice votes and * means the winner in the pairing (such that
A>B>C>A).

Assume that one of the winning pairings has the fewest votes.
I now suggest that such fewest votes winner be a loser for tie breaker

With 4 or more choices in a circular tie, there would be successive
eliminations of each remaining winner having the lowest number of votes in

Example-  If left beats top, then it is a win (W). If not it is a loss (L).
The W's are the number of votes that produced the win.
A     B     C     D
A       X     W     L     W
B       L     X     W     L
C       W     L     X     L
D       L     W     W     X

A>B, A>D, B>C, C>A, D>B, D>C
A>B>C>A>D,  D>B>C

Was the above Condorcet's solution to the circular tie ???

I am not sure due to Mr. C's somewhat cryptic translated comments.

The death of Mr. C due to the fanatics of the 1789 French Revolution set back
Democracy and rational voting methods for single winners for some 200 years.
What a terrible loss-- similar to earlier mindless/ savage barbarians
attempting to destroy advances in civilization.

```