The Simple Majority Rule in a Three-Valued Logic Framework

Abstract

Relying on a Łukasiewiczian three-valued logic, I define and study logical operators that can be easily compared with aggregation rules like the simple and absolute majority, the jury rule or the extended Pareto rule. An axiomatization of the simple majority binary operator is constructed and an Arrow-type impossibility theorem is proved. I also show that some binary operators, like the simple majority operator, can be extended to the general case, while others, like the absolute majority operator, resist all attempts to be so extended.