Strategy-proof and individually rational social choice functions for public good economies: A note

Summary. Serizawa [3] characterized the set of strategy-proof, individually rational, no exploitative, and non-bossy social choice functions in economies with pure public goods. He left an open question whether non-bossiness is necessary for his characterization. We will prove that non-bossiness is implied by the other three axioms in his characterization. Received: October 17, 1997; revised version: January 19, 1998     

Swap-flexibility in the assignment of houses

A house allocation rule should be flexible in its response to changes in agents’ preferences. We propose a specific notion of this flexibility. An agent is said to be swap-sovereign over a pair of houses at a profile of preferences if the rule assigns her one of the houses at that profile and assigns her the other house when she instead reports preferences that simply swap the positions of the two houses. A pair of agents is said to be mutually swap-sovereign over their assignments at a profile if the rule exchanges their assignments when they together report such ‘swap preferences’. An allocation rule is individually swap-flexible if any pair of houses has a swap-sovereign agent, and is mutually swap-flexible if any pair of houses has either a swap-sovereign agent or mutually swap-sovereign agents. We show for housing markets that the top-trading-cycles rule is the unique strategy-proof, individually rational and mutually swap-flexible rule. In house allocation problems, we show that queue-based priority rules are uniquely strategy-proof, individually swap-flexible and envy non-bossy. Varying the strength of non-bossiness, we characterise the important subclasses of sequential priority rules (additionally non-bossy) and serial priority rules (additionally pair-non-bossy and pair-sovereign).     

Influence in private-goods allocation

We reinterpret the ‘bossiness’ of a private-goods allocation rule (Satterthwaite and Sonnenschein, 1981) as the ability of an agent to ‘influence’ another’s welfare with no change to her own welfare. In applications where non-bossiness is not possible, we propose simple conditions on (1) which agents may have influence (acyclicity and preservation), and (2) the welfare consequences of influence (positivity and oppositeness). We apply these conditions to three well-known bossy rules: the ‘Vickrey rule’ in single-object auctions (Vickrey, 1961) (acyclic, positive), the ‘doctor-optimal stable rule’ in matching with contracts (Hatfield and Milgrom, 2005) (acyclic, positive, preserving) and ‘generalised absorbing top-trading cycles (GATTC) rules’ in housing markets with indifferences in preferences (Aziz and Keijzer, 2011) (acyclic, opposite, preserving). Under mild restrictions, we show how the nature of influence under a strategy-proof rule determines whether or not it satisfies weak group-strategy-proofness (requires acyclicity and either positivity or preservation), weak Maskin monotonicity (acyclicity and positivity) and Pareto-efficiency (acyclicity and oppositeness). In addition, we propose an influence-related generalisation of the efficiency-adjusted deferred acceptance mechanism in school choice (Kesten, 2010), and characterise influence for strategy-proof GATTC rules in housing markets.     

Population-monotonicity and separability for economies with single-dipped preferences and the assignment of an indivisible object

We study two allocation models. In the first model, we consider the problem of allocating an infinitely divisible commodity among agents with single-dipped preferences. In the second model, a degenerate case of the first one, we study the allocation of an indivisible object to a group of agents. We consider rules that satisfy Pareto efficiency, strategy-proofness, and in addition either the consistency property separability or the solidarity property population-monotonicity. We show that the class of rules that satisfy Pareto efficiency, strategy-proofness, and separability equals the class of rules that satisfy Pareto efficiency, strategy-proofness, and non-bossiness. We also provide characterizations of all rules satisfying Pareto efficiency, strategy-proofness, and either separability or population-monotonicity. Since any such rule consists for the largest part of serial-dictatorship components, we can interpret the characterizations as impossibility results. Received: September 29, 1999; revised version: March 22, 2000