TY - Journal Article
T1 - On the likelihood of Condorcet's profiles
T3 - Social Choice and Welfare
JF - Social Choice and Welfare
VL - 19
IS - 1
SP - 193
EP - 206
A1 - Valognes, Fabrice
A2 - Tataru, Monica
A2 - Merlin, Vincent R
PB - Springer
PY - 2002
UR - https://bonnus.ulb.uni-bonn.de/SummonRecord/FETCH-repec_primary_sprsochwe_v_3a19_3ay_3a2002_3ai_3a1_3ap_3a193_206_htm0
N2 - Consider a group of individuals who have to collectively choose an outcome from a finite set of feasible alternatives. A scoring or positional rule is an aggregation procedure where each voter awards a given number of points, wj, to the alternative she ranks in jth position in her preference ordering; The outcome chosen is then the alternative that receives the highest number of points. A Condorcet or majority winner is a candidate who obtains more votes than her opponents in any pairwise comparison. Condorcet [4] showed that all positional rules fail to satisfy the majority criterion. Furthermore, he supplied a famous example where all the positional rules select simultaneously the same winner while the majority rule picks another one. Let P* be the probability of such events in three-candidate elections. We apply the techniques of Merlin et al. [17] to evaluate P* for a large population under the Impartial Culture condition. With these assumptions, such a paradox occurs in 1.808% of the cases.
ER -