Seminario 14-06-2023

Salón de Graos (Facultade de Matemáticas) e Online

13:00- 13:45

Dani Samaniego
Universitat Politècnica de Catalunya

Some axiomatizations and enumerations of majority simple games with abstention

In this talk 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. 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, like the yes-quota functions, are also provided.
Also we will mention the formulas for the number of these majority functions in terms of the number of voters, in order to give an idea of the size of these sets.