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

Summary This note is to inform about a mistake in my paper (Serizawa, 1996). In that paper, I characterized strategy-proof, individually rational, budget-balancing, non-exploitative and non-bossy social choice functions for economies with one public good and one private good. I established as Theorem 3 (page 507) that a social choice function is strategy-proof, individually rational with respect to endowment, budget-balancing, non-exploitative and non-bossy if and only if it is a scheme of semi-convex cost sharing determined by the minimum demand principle. I also exposed one example (Example 2, page 507) in order to emphasize that non-bossiness is indispensable for this characterization. I claimed that the social choice function in that example satisfies the above axioms except for non-bossiness, and is not a scheme of semi-convex cost sharing. However, the social choice function in the example is actually not strategy-proof, as shown in the simple discussion below. Therefore it is an open question whether or not a similar characterization theorem holds without non-bossiness.I thank Professor Rajat Deb, who kindly pointed out my mistake.     

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     

Implementation of individually rational social choice functions with guaranteed utilities

A simple mechanism is presented that allocates an indivisible object between two agents for almost any possible compensation rule. Furthermore, the equilibrium strategy guarantees a level of utility not less than −ε, where ε can be arbitrarily small.     

Securely implementable social choice functions in divisible and nonexcludable public good economies with quasi‐linear utility functions

This paper studies the possibility of secure implementation (Saijo et al., 2007) in divisible and nonexcludable public good economies with quasi‐linear utility functions. In these economies, although Saijo et al. (2007) showed that the Groves mechanisms (Groves, 1973) are securely implementable when the valuation functions of the public good are (i) differentiable, concave, and (ii) identified with a real number, respectively, this paper shows the following negative result: securely implementable social choice functions are dictatorial or constant when the valuation functions of the public good are strictly increasing and strictly concave.     

Strategy-proof allocation mechanisms for economies with public goods

We show that strategy-proof allocation mechanisms for economies with public goods are dictatorial—i.e., they always select an allocation in their range that maximizes the welfare of the same single individual (the dictator). Further, strategy-proof and efficient allocation mechanisms are strongly dictatorial—i.e., they select the dictator’s preferred allocation on the entire feasible set. Thus, our results reveal the extent to which the conflict between individual incentives and other properties that may be deemed desirable (e.g., fairness, equal treatment, distributive justice) pervades resource allocation problems.     

Strategy-proof allocation mechanisms for pure public goods economies when preferences are monotonic

Summary. A fundamental problem in public finance is that of allocating a␣given budget to financing the provision of public goods (education, transportation, police, etc.). In this paper it is established that when␣admissible preferences are those representable by continuous and increasing utility functions, then strategy-proof allocation mechanisms whose (undominated) range contains three or more outcomes are dictatorial on the set of profiles of strictly increasing utility functions, a dense subset of the domain in the topologies commonly used in this context. If admissible utility functions are further restricted to be strictly increasing, or if mechanisms are required to be non-wasteful, then strategy-profness leads to (full) dictatorship. Received: August 14, 1995; revised version: September 25, 1997     

Tiebout equilibria in local public good economies with spillovers

This paper analyzes the effects of spillovers on the equilibrium population distribution across jurisdictions in a local public good economy with free mobility. Spillovers are parametrized by a matrix [α_ij] where α_ij ∈ [0, 1]. When spillovers are symmetric and close to 0 or 1 (pure local public goods and pure public goods), all equilibrium jurisdiction structures are symmetric. However, any population distribution can be sustained in equilibrium for some value of the spillover parameter α. In the class of utility functions with additive externalities, we identify the unique family of utility functions for which equilibria are symmetric except for an isolated value of α. This is a class of utility functions which are linear in the public good and a power function of the private good, u(c, γ) = − A(1 − c)^β + γ. With this specification of utility, we show that an increase in α results in a more fragmented equilibrium population distribution, and that when spillovers are asymmetric and large, a jurisdiction which is more centrally located (i.e. benefits more from the public goods provided in other jurisdictions) has a larger population in equilibrium.     

A dictatorial domain for monotone social choice functions

We give a dictatorial domain for monotone and unanimous social choice functions.     

von Neumann–Morgenstern stable sets of income tax rates in public good economies

This paper studies the von Neumann–Morgenstern stable sets in a public good economy, where any allocation is achieved through a proportional income tax system. The outcome of the economy is defined to be a set of tax rates. We show that whenever the core as the set of tax rates is nonempty, it is a unique stable set. When the core is empty, the set of tax rates is a stable set if and only if the set is a singleton consisting of a tax rate satisfying a certain condition. We show the existence of such stable sets. The author is grateful to Mikio Nakayama, Jun Wako and an anonymous referee for their helpful comments and suggestions. He is also grateful to Youngsub Chun, Takuya Masuzawa and Shigeo Muto for their helpful comments.     

Communication,competition and social gift exchange in an auction for public good provision

Reverse auctions are an established policy instrument for allocating conservation contracts. While the auction mechanism has been the subject of a number of studies, less attention has been paid to the post-bidding contract phase. As contracts involving natural resource management are usually incomplete, trust becomes crucial for the effectiveness of the programme. We test the effect of communication between auctioneer and bidders on bidding behaviour and contract fulfilment using experimental economics. We combine a repeated reverse auction with an effort-level game and use a bilateral chatting tool as treatment variable. Without communication, auctioneers tended to select the lowest-priced bidders, who invested substantially less than the socially optimal level of effort when fulfilling their contract to provide the public good. Relational contracting proved important, with effort levels and profits tending to be higher when auctioneers and bidders entered into consecutive contract relationships. In the communication treatment there was no evidence of price competition, as auctioneers were more likely to accept high-priced bids. However, an overall higher price level did not lead to efficiency losses, since contractors realised higher effort levels in return, establishing a ‘social gift exchange’. Our results demonstrate the importance of trust-based relationships between the auctioneering institution and landholders.     

Empirical and public choice evidence for hyperbolic social discount rates and the implications for intergenerational discounting

The derivation of the correct discount rate for intergenerational projects in Cost Benefit Analysis is particularly contentious. Public choice has resulted in lower discretionary exponential discount rates for many intergenerational projects in Britain and the USA. This is shown to be strong indirect evidence that the true social discount rate may be a hyperbolic (rather than an exponential) function. There is also empirical evidence for this hypothesis. The hyperbolic nature of discounting is also a standard finding in the behavioural sciences. For intergenerational time frames hyperbolic discount rates should be employed together with exponential discount rates in cost-benefit sensitivity analyses.Sincere thanks to Maureen Cropper and Paul Portney for supplying their survey results and to Elaine Barrow and Phillip Judge for graphics assistance. Two anonymous referees also provided valuable comments.     

Chernoff's dual axiom,revealed preference and weak rational choice functions

A new and a weaker concept of rationalizability is introduced and its implications on the properties of individual choice are investigated. Especially, (i) it is shown that a property of choice functions, called Chernoff's dual axiom in this paper, plays a crucial role for the rationality of choice, and (ii) weakening the concept of rationalizability facilitates characterization of revealed preference relations.     

Von Neumann-Morgenstern solution social choice functions: An impossibility theorem

Recent literature has made significant progress in characterizing those social choice functions that can arise, or be “implemented,” as the equilibria of an underlying noncooperative game. This paper studies the implementability of social choice functions via cooperative games. Specifically, we show that if a social choice function arises, in each environment, as a Von Neumann-Morgenstern solution of an underlying cooperative game, whose dominance structure is monotonic and neutral, then the social choice function is essentially oligarchic, in exactly the same sense that “core” selecting choice functions are oligarchic.