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# Properties of scoring run-off rules

by

Vincent Merlin, CNRS and Universite de Caen

May 27, 2004
2:30 pm
Bailey Hall 207

Refreshments at 2:15 pm in common room

## Abstract:

Scoring rules are among the most popular decision schemes. Consider a society of n individuals which has to rank collectively a set of m alternatives. A scoring rule is defined by a scoring vector w = (w1, w2, . . . , wr, . . . , wm), with w1 > wm and wr greater than or equal to wr+1. Thus, each voter gives w1 points to the alternatives she prefers, w2 points to her second choice, and so on down to wm points for the alternative she ranks at the bottom of her preference. Then, the alternatives are ranked according to the total number of points they received. Another way to use scoring rules is to eliminate progressively the alternatives on the basis of the total scores they obtain at each stage. For example, in the French presidential election, each voter first votes for her preferred candidate (w = (1, 0, . . . 0)) and the top two most popular candidates go to the run-off for a final confrontation. While the literature on scoring rules is quite important, including many charac-terization results (see for example Smith (1973), Young (1974a,1974b,1975)), only few papers deal with the properties of scoring runoff rules (Richelon (1980), Smith (1973)). In particular, no axiomatic characterization has been provided. The objec-tive of the current study is to adapt the definition of the scoring run off rules to the framework that has been used by Young and Levenglick (1978) for the characteriza-tion of the Kemeny rule. In this context, the scoring run-off rules satisfy neutrality, anonymity, and a weak version of the consistency axiom. A weak independence condition is also met by all the scoring run-off rules with eliminate the alternatives one by one.

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