# Impossibility theorems in the arrovian framework

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## Abstract

Given a set of outcomes that affect the welfare of the members of a group, K.J. Arrow imposed the following five conditions on the ordering of the outcomes as a function of the preferences of the individual group members, and then proved that the conditions are logically inconsistent:- The social choice rule is defined for a large family of assignments of transitive orderings to individuals.- The social ordering itself is always transitive.- The social choice rule is not dictatorial. (An individual is a dictator if the social ordering ranks an outcome x strictly above another outcome y whenever that individual strictly prefers x to y.)- If everyone in the group strictly prefers outcome x to outcome y, then x should rank strictly above y in the social ordering.- The social ordering of any two outcomes depends only on the way that the individuals in the group order those same two outcomes.The chapter proves Arrow's theorem and investigates the possibility of uncovering a satisfactory social choice rule by relaxing the conditions while remaining within the Arrovian framework, which is identified by the following five characteristics:- The outcome set is unstructured.- The society is finite and fixed.- Only information about the ordering of the outcome set is used to convey information about individual welfare.- The output of the social choice process is an ordering of the outcome set.- Strategic play by individuals is not considered.

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