The replacement principle for the provision of multiple public goods on tree networks

This article considers the provision of two public goods on tree networks where each agent has a single-peaked preference. We show that if there are at least four agents, then no social choice rule exists that satisfies efficiency and replacement-domination. In fact, these properties are incompatible, even if agents’ preferences are restricted to a smaller domain of symmetric single-peaked preferences. However, for rules on an interval, we prove that Miyagawa’s (Soc Choice Welf 18:527–541, 2001) characterization that only the left-peaks rule and the right-peaks rule satisfy both of these properties also holds on the domain of symmetric single-peaked preferences. Moreover, if agents’ peak locations are restricted to either the nodes or the endpoints of trees, rules exist on a subclass of trees. We provide a characterization of a family of such rules for this tree subclass.     

Linear cost sharing in economies with non-Samuelsonian public goods: Core equivalence

 We consider an economy with non-Samuelsonian public goods and we focus on linear cost sharing. In a linear cost sharing equilibrium all agents in the economy optimize given a certain fixed cost share to be contributed towards the provision of public goods in the economy. Hence, each agent pays a certain fraction of the total establishment costs of public goods and these cost shares are common knowledge. We show that for a certain fixed contribution scheme the resulting linear cost share equilibria are equivalent to corresponding core allocations, in which the core is based on the integral of the individual cost shares. We also show that there is no equivalence of the Foley core with cost share equilibria, even in well-behaved large economies. Received: 16 August 1995/Accepted: 29 July 1996     

Bling bling taxation and the fiscal virtues of hip hop

The article extends Ng’s (Am Econ Rev 77(1):186–191, 1987) model of optimal taxation of diamond goods—goods that are valued solely for their costliness. We extend his findings by analyzing how other goods should be taxed in the presence of pure diamond goods; modified Ramsey rules are derived in a basic single-type model as well as in a two-type model with redistribution. One key finding, that may be surprising and rather provoking, is that close complements (hip hop music) to diamond goods (bling bling) should be heavily subsidized.     

The dynamic transformation of political systems through social contract: a game theoretic approach

 We consider how the political system of the state evolves in the process of economic development. We present a dynamic public goods economy with non-overlapping generations, which confronts the free-rider problem without the state. In each generation, individuals enter under the unanimous rule a social contract of the political system, either monarchy or democracy, and then attempt to establish the state under the contracted political system. If the state is established, it provides public goods by enforcing tax on its members. Our game theoretic analysis shows: (i) the state can be established if and only if social productivity in terms of the capital stock of public goods is lower than a critical level; (ii) individuals choose democracy if social productivity is sufficiently high, while monarchy may be chosen if it is not; (iii) social productivity stochastically converges to the critical level over generations; and (iv) a simulation result shows several transformation patterns of political systems. Received: 21 June 1994/Accepted: 7 November 1995     

A Note on the Separability Principle in Economies with Single-Peaked Preferences

We consider the problem of allocating an infinitely divisible commodity among a group of agents with single-peaked preferences. A rule that has played a central role in the analysis of the problem is the so-called uniform rule. Chun (2001) proves that the uniform rule is the only rule satisfying Pareto optimality, no-envy, separability, and Ω-continuity. We obtain an alternative characterization by using a weak replication-invariance condition, called duplication-invariance, instead of Ω-continuity. Furthermore, we prove that the equal division lower bound and separability imply no-envy. Using this result, we strengthen one of Chun’s (2001) characterizations of the uniform rule by showing that the uniform rule is the only rule satisfying Pareto optimality, the equal division lower bound, separability, and either Ω-continuity or duplication-invariance.     

Strategy-proof allocation of multiple public goods

This paper characterizes strategy-proof social choice functions (SCFs), the outcome of which are multiple public goods. Feasible alternatives belong to subsets of a product set . The SCFs are not necessarily “onto”, but the weaker requirement, that every element in each category of public goods A _k is attained at some preference profile, is imposed instead. Admissible preferences are arbitrary rankings of the goods in the various categories, while a separability restriction concerning preferences among the various categories is assumed. It is found that the range of the SCF is uniquely decomposed into a product set in general coarser than the original product set, and that the SCF must be dictatorial on each component B _l . If the range cannot be decomposed, a form of the Gibbard–Satterthwaite theorem with a restricted preference domain is obtained.     

Aggregation of coarse preferences

We consider weak preference orderings over a set A _n of n alternatives. An individual preference is of refinement?≤n if it first partitions A _n into ? subsets of `tied' alternatives, and then ranks these subsets within a linear ordering. When ?<n, preferences are coarse. It is shown that, if the refinement of preferences does not exceed ?, a super majority rule (within non-abstaining voters) with rate 1− 1/? is necessary and sufficient to rule out Condorcet cycles of any length. It is argued moreover how the coarser the individual preferences, (1) the smaller the rate of super majority necessary to rule out cycles `in probability'; (2) the more probable the pairwise comparisons of alternatives, for any given super majority rule. Received: 29 June 1999/Accepted: 25 February 2000     

Unequivocal majority and Maskin-monotonicity

The unequivocal majority of a social choice rule is a number of agents such that whenever at least this many agents agree on the top alternative, then this alternative (and only this) is chosen. The smaller the unequivocal majority is, the closer it is to the standard (and accepted) majority concept. The question is how small can the unequivocal majority be and still permit the Nash-implementability of the social choice rule; i.e., its Maskin-monotonicity. We show that the smallest unequivocal majority compatible with Maskin-monotonicity is n- ë \fracn-1m û{n-\left\lfloor \frac{n-1}{m} \right\rfloor} , where n ≥ 3 is the number of agents and m ≥ 3 is the number of alternatives. This value is equal to the minimal number required for a majority to ensure the non-existence of cycles in pairwise comparisons. Our result has a twofold implication: (1) there is no Condorcet consistent social choice rule satisfying Maskin-monotonicity and (2) a social choice rule satisfies k-Condorcet consistency and Maskin-monotonicity if and only if k 3 n- ë \fracn-1m û{k\geq n-\left\lfloor \frac{n-1}{m}\right\rfloor}.     

Choice rules with fuzzy preferences: Some characterizations

Consider an agent with fuzzy preferences. This agent, however, has to make exact choices when faced with different feasible sets of alternatives. What rule does he follow in making such choices? This paper provides an axiomatic characterization of a class of binary choice rules called the α satisfying rule. When α=1, this rule is the Orlovsky choice rule. On the other hand, for α≤1/2, the rule coincides with the M _α rule that has been extensively analyzed in the literature on fuzzy preferences. Received: 3 August 1995/Accepted: 19 November 1997     

On the equilibrium of voting games with abstention and several levels of approval

We study the core of “(j, k) simple games”, where voters choose one level of approval from among j possible levels, partitioning the society into j coalitions, and each possible partition facing k levels of approval in the output (Freixas and Zwicker in Soc Choice Welf 21:399–431, 2003). We consider the case of (j, 2) simple games, including voting games in which each voter may cast a “yes” or “no” vote, or abstain (j = 3). A necessary and sufficient condition for the non-emptiness of the core of such games is provided, with an important application to weighted symmetric (j, 2) simple games. These results generalize the literature, and provide a characterization of constitutions under which a society would allow a given number of candidates to compete for leadership without running the risk of political instability. We apply these results to well-known voting systems and social choice institutions including the relative majority rule, the two-thirds relative majority rule, the United States Senate, and the United Nations Security Council.     

Use of urban marine habitats by foraging wading birds

Wading birds (i.e, Ardeidae: herons, egrets, and bitterns) are a guild of waterbirds that forage in coastal habitats which in the US and Europe are often located in close proximity to urban centers. However, the use of urban marine habitats may have consequences for bird populations, as birds can be subject to stress from increased levels of passive and active human disturbance. We examined the effects of human disturbance, available foraging habitat, and prey abundance on wading bird density and species richness at 17 urban coastal sites in Narragansett Bay, Rhode Island USA. The sites represented a gradient of immediately adjacent residential and commercial land use (e.g., 0.0–67.7% urban land use within a 30.5 m buffer of the sites) within an urban matrix (i.e., all sites were located within a suburban center with a population of about 85,000 people). Wading bird density (0.62 ± 0.12 birds ha⁻¹) and species richness (average 4.49 ± 0.37 species across all sites) were not influenced by passive human disturbance as measured by the extent of urban land surrounding a site. However, wading bird density and species richness both decreased significantly as active disturbance (i.e., number of boats moored or docked upstream of the site) increased (r = −0.56, F = 6.85, p = 0.019 and r = −0.73, F = 16.6, p = 0.001, respectively). In addition, both density (r = 0.72, F = 16.2, p = 0.001) and species richness (r = 0.72, F = 16.2, p = 0.001) increased concomitantly with a prey index that combines the density of fish and invertebrates on which the birds feed with the amount of available shallow water foraging habitat at a site. Our results suggest that wading birds i) may not be negatively affected by urban land surrounding estuarine foraging areas in and of itself; and ii) may be utilizing urban areas in the absence of high levels of active disturbance to take advantage of potentially enhanced prey resources. In the case where the benefits of foraging at a site outweigh the costs related to human disturbance, urban marine habitats may need to be considered for restoration or protection from further increases in active human disturbance.     

On the social stability of coalitional property rights regimes

We present a model of coalitional property rights (CPR) regimes– regimes in which ownership of a good is attributable to coalitions of various sizes. Specifically, for each good, we define a legal structure that specifies the legal coalitions of individuals that share a communal claim to that good. Generally, each legal coalition may use exclusionary rules to allocate its holdings internally. These rules allow eligible subcoalitions to recontract by expropriating some fraction of the legal coalition's endowment. We then ask: what types of CPR regimes are socially stable in the sense of having a nonempty core? We give conditions on the legal structure and the primitives of the economy that achieve social stability in this sense. We emphasize two cases of particular interest. ( I ) Unanimity. Unanimity is required for a legal coalition to recontract against (block) the status quo. In this case, the core is nonempty under standard assumptions. Each agent's ability to veto an alternative allocation allows a partial characterization in terms of the economies that are privatized by dividing up the communal endowment among the members of each legal coalition. We show that in some economies' collective vs private ownership matters in terms of social stability. ( II ) Exclusion. Many eligible subcoalitions can expropriate the legal coalition's entire endowment. An example is the collection of simple majorities. The presence of cycles can easily lead to social instability. We show that if endowment holdings are sufficiently “specialized” and each agent's “veto power” sufficiently large, then stability can be achieved despite the presence of cycles in some goods. Received: 30 June 1993/Accepted: 28 February 1998     

Development and Psychometric Evaluation of a 10-Item Short Form Inventory of Gambling Situations

The Inventory of Gambling Situations (IGS-63; Turner and Littman-Sharp, Inventory of gambling situations users guide, 2006) is a 63-item measure of high-risk gambling situations. It assesses gambling across 10 situational subscales that load onto two higher-order factors: negative and positive situations (Stewart et al. Psychology of Addictive Behaviors, 22:257–268, 2008). While the IGS-63 has excellent psychometric properties (Littman-Sharp et al., The Inventory of Gambling Situations: Reliability, factor structure, and validity (IGS Technical Manual), in press) its length may preclude its use in time-limited contexts. The purpose of this study was to develop and validate a 10-item short-form of the IGS (IGS-10). Each IGS-10 item reflects one of the ten subscale categories from the IGS-63, with two items from the original subscales included as examples for each IGS-10 item. The IGS-10 was administered to 180 undergraduate gamblers along with the IGS-63 and the Problem Gambling Severity Index (PGSI; Ferris and Wynne, Canadian Problem Gambling Index: Final report, 2001). IGS-10 items showed convergent validity with the corresponding IGS-63 subscales (r’s = .60–.73). Principal components analysis of the IGS-10 revealed two factors: negative (α = .84) and positive (α = .85). PGSI scores correlated significantly with all IGS-10 items (r’s = .33–.58) and with both IGS-10 higher-order subscales (r’s = .66 [negative] and .49 [positive]), supporting the criterion validity of the IGS-10. Since minimal information is lost when using the IGS-10, the short form may prove particularly useful when respondent burden prevents using the full IGS-63.     

Can faster income growth reduce well-being?

In his book Luxury Fever: Why Money Fails to Satisfy in an Era of Excess (1999) economist Robert Frank describes a number of significant trends in the U.S., and to a lesser extent in other industrial economies, since the late 1970s: rapidly rising incomes, for those at the upper end of the income scale, increasing hours of work, and increased consumerism (share of consumption of ‘status goods’). We demonstrate that the first development can parsimoniously account for the latter two. Our novel specification of the utility function simultaneously incorporates a relative-consumption effect for status goods and non-homotheticity of preferences between status and non-status goods, and we also allow for endogenous labour–leisure choice. It is possible that well-being has declined, notwithstanding the faster income growth, or at least not risen pari passu with the growth in earnings. Comparisons are made with other studies, and policy implications briefly discussed.

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Topological aggregation, the case of an infinite population

 The literature on infinite Chichilnisky rules considers two forms of anonymity: a weak and a strong. This note introduces a third form: bounded anonymity. It allows us to prove an infinite analogue of the “Chichilnisky– Heal-resolution” close to the original theorem: a compact parafinite CW-complex X admits a bounded anonymous infinite rule if and only if X is contractible. Furthermore, bounded anonymity is shown to be compatible with the finite and the [0, 1]-continuum version of anonymity and allows the construction of convex means in infinite populations. With X=[0, 1], the set of linear bounded anonymous rules coincides with the set of medial limits. Received: 30 October 1993/Accepted: 22 April 1996     

A CLEAR AND PRESENT MINORITY: HETEROGENEITY IN THE SOURCE OF ENDOWMENTS AND THE PROVISION OF PUBLIC GOODS

We conduct public goods experiments in which participant groups are heterogeneous in regards to the source of their endowments. We find that this dimension of heterogeneity significantly reduces contributions to the public good, yielding strong support for the Nash prediction of minimal contributions. These minimal contributions arise in environments in which there exists a clear minority in terms of source of endowments. We discuss these results in light of current research on the influence of heterogeneous populations on public goods provision and redistributive policies. (JEL C9, D63, H4, J15)     

The benefit and sacrifice principles of taxation: A synthesis

The implications of equal sacrifice taxation have only been pursued in a very narrow context. This note applies this principle to the problem of levying taxes to provide public goods. Its purpose is to determine how taxes used to finance public goods must be structured in order to benefit each agent equally. This tax structure may be viewed as a benchmark against which to compare tax regimes with redistributive intent. Equality of taxation, therefore, as a maxim of politics, means equality of sacrifice.  . . This standard, like other standards of perfection, cannot be completely realized; but the first object in every practical discussion should be to know what perfection is.  J. S. Mill Received: 10 April 1997/Accepted: 16 November 1998     

Aggregation of smooth preferences

Suppose p is a smooth preference profile (for a society, N) belonging to a domain P ^N . Let σ be a voting rule, and σ(p)(x) be the set of alternatives in the space, W, which is preferred to x. The equilibrium E(σ(p)) is the set {x∈W:σ(p)(x) is empty}. A sufficient condition for existence of E(σ(p)) when p is convex is that a “dual”, or generalized gradient, dσ(p)(x), is non-empty at all x. Under certain conditions the dual “field”, dσ(p), admits a “social gradient field”Γ(p). Γ is called an “aggregator” on the domain P ^N if Γ is continuous for all p in P ^N . It is shown here that the “minmax” voting rule, σ, admits an aggregator when P ^N is the set of smooth, convex preference profiles (on a compact, convex topological vector space, W) and P ^N is endowed with a C ¹-topology. An aggregator can also be constructed on a domain of smooth, non-convex preferences when W is the compact interval. The construction of an aggregator for a general political economy is also discussed. Some remarks are addressed to the relationship between these results and the Chichilnisky-Heal theorem on the non-existence of a preference aggregator when P ^N is not contractible. Received: 4 July 1995 / Accepted: 26 August 1996     

Game Theoretical Formulations of The Olson Problem*

Abstract This paper takes up one of the basic themes of Mancur Olson's Logic of Collective Action (Harvard University Press 1965). that is a group size as a cause of suboptimal provision of collective or public goods. A general framework is developed for classifying collective action situations involving public goods provisions. This framework focuses on the two characteristics: relations between contribution and provision, and rivalness or jointness in consumption of the collective goods. This framework distinguishes six types of collective actions, for each of which a game theoretical formulation is developed to obtain. models concerning social movements against (or for) new legislations, a petition for the recall of an official, a strike, lobbying, building a lighthouse, creation of a database, etc. These models, formulated either as an N-person chicken game or as an N-person prisoner's dilemma game. are examined with respect to how a group size affects non-cooperative equilibria and their Paretooptimality. There is no group size effect in the collective action situations formulated as an N-person chicken game, while large groups may suffer from suboptimal provision of the public goods in the collective action situations formulated as an N-person prisoner's dilemma game. Two types of the group size effect in N-person prisoner's dilemmas must be distinguished. In some cases. “no contribution” is the equilibrium regardless of the group size. but increase in the group size makes the equilibrium Pareto-deficient. In other cases, increase in the group size changes the equilibrium from the Pareto-efficient one with N contributors to the deficient one with no contributors.     

The geometry of implementation: a necessary and sufficient condition for straightforward games

 We characterize games which induce truthful revelation of the players’ preferences, either as dominant strategies (straightforward games) or in Nash equilibria. Strategies are statements of individual preferences on R ⁿ . Outcomes are social preferences. Preferences over outcomes are defined by a distance from a bliss point. We prove that g is straightforward if and only if g is locally constant or dictatorial (LCD), i.e., coordinate-wise either a constant or a projection map locally for almost all strategy profiles. We also establish that: (i) If a game is straightforward and respects unanimity, then the map g must be continuous, (ii) Straightforwardness is a nowhere dense property, (iii) There exist differentiable straightforward games which are non-dictatorial. (iv) If a social choice rule is Nash implementable, then it is straightforward and locally constant or dictatorial. Received: 30 December 1994/Accepted: 22 April 1996