Some characterizations of resolute majority rules

Abstract

AbstractIn this paper we consider decision functions in which voters have three options and one of them is abstention or indifference and the output is a binary decision between two alternatives so that a tie is not possible. These resolute decision functions appear frequently in grading, in some sport competitions, in voting situations in which the status quo is put to the vote, etc. It is a more restricted case of the voting context considered in the seminal article by Kenneth May on decision functions, published in Econometrica in 1952, because the output set does not admit a tie. Among these resolute decision functions we focus on the study of majority functions, in which the number of favorable votes to an alternative must be strictly greater than the number of votes against it. This work provides an axiomatic characterization for the set of majority functions and for the relative majority function with status quo bias. Both characterizations are based on weaker versions of neutrality. Other complementary characterizations are also provided.