General Characteristics Of The Simple Majority Rule

In the first chapter, we generalize Asan's weak path independence and Woeginger's reducibility to subsocieties for two alternatives to any set of alternatives. Given a society of finite individuals and any set of alternatives, we discuss the sufficiency and necessity condition or sufficiency condition when the social welfare function is a majority rule; Given a society of finite individuals and finite set of alternatives, we define the majority rule as a social choice rule and give some sufficiency and necessity conditions when the social choice rule is the majority rule in the second chapter.