Condorcet Winner Probabilities - A Statistical Perspective
| dc.creator | Krishnamoorthy, M. S. | |
| dc.creator | Raghavachari, M. | |
| dc.date | 2005-11-05 | |
| dc.date.accessioned | 2026-07-07T08:07:21Z | |
| dc.date.available | 2026-07-07T08:07:21Z | |
| dc.description | A Condorcet voting scheme chooses a winning candidate as one who defeats all others in pairwise majority rule. We provide a review which includes the rigorous mathematical treatment for calculating the limiting probability of a Condorcet winner for any number of candidates and value of $n$ odd or even and with arbitrary ran k order probabilities, when the voters are independent. We provide a compact and complete Table for the limiting probability of a Condorcet winner with three candidates and arbitrary rank order probabilities. We present a simple proof of a result of May to show the limiting probability of a Condorcet winner tends to zero as the number of candidates tends to infinity. We show for the first time that the limiting probability of a Condorcet winner for any given number of candidates $m$ is monotone decreasing in $m$ for the equally likely case. This, in turn, settles the conjectures of Kelly and Buckley and Westen for the case $n \to \infty$. We prove the validity of Gillett's conjecture on the minimum value of the probability of a Condorcet winner for $m=3$ and any $n$. We generalize this result for any $m$ and $n$ and obtain the minimum solution and the minimum probability of a Condorcet winner. | |
| dc.description | 27 pages 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0511140 | |
| dc.identifier | http://arxiv.org/abs/math/0511140 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130916 | |
| dc.subject | Statistics Theory | |
| dc.subject | 62P15 | |
| dc.title | Condorcet Winner Probabilities - A Statistical Perspective | |
| dc.type | text |