(The Impossibility of) Deliberation‐Consistent Social Choice

Arrow’s Impossibility Theorem on Social Choice Systems

Social choice theory is a field that concerns methods of aggregating individual interests to determine net social preferences. Arrow’s Impossibility Theorem states that no social choice system can satisfy all requirements in a collection of “reasonable” criteria. We make the notion of “reasonable” voting systems precise by stating the four properties that voting systems must have in order to be...

Social Choice and Legitimacy The Possibilities of Impossibility

A general impossibility result on strategy-proof social choice hyperfunctions

A social choice hyperfunction picks a non-empty set of alternatives at each admissible preference profile over sets of alternatives. We analyze the manipulability of social choice hyperfunctions. We identify a domain D of lexicographic orderings which exhibits an impossibility of the Gibbard-Satterthwaite type. Moreover, this impossibility is inherited by all well-known superdomains of D. As mo...

Some Results for Impossibility Theorems of Social Welfare Function and Social Choice Function

We present some results on social welfare function and social choice function. First, we replace weak Pareto principle of Arrow’s axioms with strong Pareto principle, and then show that assuming unrestricted domain property, independence of irrelevant alternatives and strong Pareto principle on a social welfare function in Arrow’s sense leads to the existence of first to nth commanders whose st...

Arrow’s Impossibility Theorem: The Logic of Dictatorship and the Meaning of Social Choice

The paper pays critical tribute to Arrow’s (1951) analysis of social choice by focusing on a number of the foundational, conceptual and interpretational issues to which it gives rise. It begins with a discussion of justifications of other formal requirements, namely unrestricted domain, Pareto optimality and independence of irrelevant alternatives, before proceeding to a detailed analysis of th...