We study the aggregation of partial orders into a complete ordering, and prove both possibility and impossibility results in this context. First, we show that the standard independence of irrelevant alternatives condition is stronger here since even dictatorial aggregation rules may fail to...

We reappraise the Arrow problem by studying the aggregation of choice functions. We do so in the general framework of judgment aggregation, in which choice functions are naturally representable by specifying, for each menu A and each alternative x in A, whether x is choosable from A, or not. Our...

Extensive measurement is the standard measurement-theoretic approach for constructing a ratio scale. It involves the comparison of objects that can be concatenated in an additively representable way. This paper studies the implications of extensively measurable welfare for social choice theory....

We present simple and direct arguments to characterize strongly group strategy-proof social choice functions whose range is of cardinality two. The underlying society is of arbitrary cardinality, and agents can be indifferent among alternatives.

Politicians, CEOs and various other types of dictators make social choices that influence both their own and others' welfare. When a dictator's preferred alternative differs from recipients', it is unclear which preferences they aggregate and how they determine this set of admissible...

Some economists in the Austrian tradition interpret the Arrow Impossibility Theorem (AIT) as support for their laissez-faire standpoint. They presume that the AIT cannot be applied in market settings, but in the context of voting, it adds weight to their arguments against the possibility of...

We derive a very general ("Janus") money demand function, which reflects backward and forward-looking habit formation. This generality offers an explanation for the breakdown of money-demand functions and policy relevance of monetary aggregates. Integrating our Janus money demand into a...

Consider a setting in which individual strict preferences need to be aggregated into a social strict preference relation. For two alternatives and an odd number of agents, it follows from May’s Theorem that the majority aggregation rule is the only one satisfying anonymity, neutrality, and...

Can the exchange rate be stationary in levels? We answer this question in the negative by proving an impossibility theorem, built upon the absence of arbitrage in international economies. We establish the sufficient conditions for the exchange rate to not be a stationary process in levels, and...

The economist Kenneth J. Arrow, in Social Choice and Individual Values (1951), famously proved that a society of diverse preferences can only be ordered by dictatorship. As individual preferences are distinct, then given certain reasonable conditions, no ordering of them is feasible through...

Chapter 1. Different Country, Different Electoral System; Agendas -- Chapter 2. Electoral Rules, Properties and Impossibilities -- Chapter 3. Impossibility and Possibility Theorems; Single-peaked Preferences -- Chapter 4. Majority Judgment -- Chapter 5. Voting Power -- Chapter 6. An Alternative...

We know that ex-post Pareto efficiency is possible with strategy-proofness and weak envy-freeness while ordinally efficiency is incompatible with them. We strengthen this impossibility for random assignments and show that it prevails if ordinal efficiency is weakened to robust ex-post Pareto...

Arrow's theorem proves that no voting procedure can meet certain conditions of both fairness and logic. In this note, Grant Hayden explores the ramifications of the theorem for qualitative vote dilution. After describing Arrow's argument, Mr. Hayden considers four democratic voting procedures...

We model a situation where a set of agents must rank themselves based on their opinions. Each agent submits a message and a function determines the social ranking. We are interested in impartial social ranking functions, that is, those where the message of an agent can not change any social...

We model a situation where a set of agents must rank themselves based on their opinions. Each agent submits a message and a function determines the social ranking. We are interested in impartial social ranking functions, that is, those where the message of an agent can not change any social...

Environments with semi-ordered preferences, which may exhibit indifference intransitivity, are known to allow just-noticeable differences in preference intensity to serve as interpersonally comparable units of utility. I prove two impossibility theorems for social choice in such environments....

We know that a strategyproof mechanism does not exist that is ordinally efficient and fair in the sense of equal division lower bound. We show that this impossibility for random assignments prevails even if agents have uniform preferences where a weakly decreasing utility function determines...