Circular Tie Percentages???

Steve Eppley seppley at
Tue Nov 19 08:55:09 PST 1996

Donald D asked:
>Do any of you have any figures on what percent of Condorcet
>elections will end in a Circular Tie?

None, since they don't *end* there.  The Condorcet rule of electing
the one with the smallest largest loss breaks the circular tie.

A more serious answer depends on the number of candidates, the number 
of voters, and on political intangibles relating to the voters' and 
candidates' views on the important issues of the day.  I saw a table 
in Ordeshook's book which ignored the views on issues by assuming 
randomness, and the probability of a circular tie in this artificial 
scenario increased with candidates and voters to far larger than 20%.
I think it goes to 100% as candidates and voters increase to infinity
if the voters vote randomly.

A companion question which might be of more relevance is how often 
will there be a circularity in which the candidates involved all have 
a pair-loss with a full majority of "votes against."  

Perhaps the most relevant question is why do you ask?: when the
voters' preferences are circular, who do you suggest electing if not
the one who would upset the fewest voters?

---Steve     (Steve Eppley    seppley at

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