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}.     

On the Average Minimum Size of a Manipulating Coalition

We study the asymptotic average minimum manipulating coalition size as a characteristic of quality of a voting rule and show its serious drawback. We suggest using the asymptotic average threshold coalition size instead. We prove that, in large electorates, the asymptotic average threshold coalition size is maximised among all scoring rules by the Borda rule when the number m of alternatives is 3 or 4, and by -approval voting when m ≥ 5.     

Ensuring every candidate wins under positional voting

Given a fixed set of voter preferences, different candidates may win outright given different scoring rules. We investigate how many voters are able to allow all n candidates to win for some scoring rule. We will say that these voters impose a disordering on these candidates. The minimum number of voters it takes to impose a disordering on three candidates is nine. For four candidates, six voters are necessary, for five candidates, four voters are necessary, and it takes only three voters to disorder nine candidates. In general, we prove that m voters can disorder n candidates when m and n are both greater than or equal to three, except when m = 3 and n ≤ 8, when n = 3 and m ≤ 8, and when n = 4 and m = 4 or 5.     

Existence of a multicameral core

When a single group uses majority rule to select a set of policies from an n-dimensional compact and convex set, a core generally exists if and only if n = 1. Finding analogous conditions for core existence when an n-dimensional action requires agreement from m groups has been an open problem. This paper provides a solution to this problem by establishing sufficient conditions for core existence and characterizing the location and dimensionality of the core for settings in which voters have Euclidean preferences. The conditions establish that a core may exist in any number of dimensions whenever n ≤ m as long as there is sufficient preference homogeneity within groups and heterogeneity between groups. With m > 1 the core is however generically empty for . These results provide a generalization of the median voter theorem and of non-existence results for contexts of concern to students of multiparty negotiation, comparative politics and international relations.     

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.     

Subgame perfect implementation of voting rules via randomized mechanisms

We characterize completely ordinal and onto choice rules that are subgame perfect of Nash equilibrium (SPE) implementable via randomized mechanisms under strict preferences. The characterization is very operationalizable, and allows us to analyse SPE implementability of voting rules. We show that no scoring rule is SPE implementable. However, the top-cycle and the uncovered correspondences as well as plurality with runoff and any strongly Condorcet consistent voting rule can be SPE implemented. Therefore our results are favourable to majority based voting rules over scoring rules. Nevertheless, we show that many interesting Condorcet consistent but not strongly Condorcet consistent rules, such as the Copeland rule, the Kramer rule and the Simpson rule, cannot be SPE implemented.     

Strategy-proofness and the reluctance to make large lies: the case of weak orders

This article incorporates agents’ reluctance to make a large lie into an analysis. A social choice rule is D(k)-proof if the rule is nonmanipulable by false preferences within k distance from the sincere one, where k is a positive integer. If D(k)-proofness is not logically equivalent to strategy-proofness, then agents’ reluctance to make a large lie embodied in D(k)-proofness is effective to construct a nonmanipulable rule. This article considers weak orders as agents’ preferences. I prove that on the universal domain, D(k)-proofness is equivalent to strategy-proofness if and only if k ≥ m ? 1, where m is the number of alternatives. Moreover, I find a sufficient condition on a domain for the equivalence of D(1)-proofness and strategy-proofness.     

A characterization of the Walras rule

This paper has three purposes. First, we refine the characterization of the Walras rule proposed by Nagahisa (JET 1991) over a more natural and simple domain than the one he employed. We show that the Walras rule is the only social choice rule defined over the domain and satisfying Individual Rationality, Pareto Efficiency, and Local Independence. Second, assuming endowments to be collectively owned, we show that the Walras rule operated from equal division is the only social choice rule satisfying No Envy, Pareto Efficiency, and Local Independence. Third, we show that for every social choice rule satisfying Individual Rationality and Pareto Efficiency, Local Independence is equivalent to a condition of Nash implementation with a game form satisfying convexity.This article is a revised version of Toyama University Working Paper No. 141. We are grateful to Professors William Thomson, Shinsuke Nakamura, Tomoichi Shinotsuka and two anonymous referees for their detailed comments. Nagahisa is grateful for hospitality of the economics department of the University of Rochester.     

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     

Allocating multiple estates among agents with single-peaked preferences

We consider the problem of allocating multiple social endowments (estates) of a perfectly divisible commodity among a group of agents with single-peaked preferences when each agent’s share can come from at most one estate. We inquire if well-known single-estate rules, such as the Uniform rule, the Proportional rule or the fixed-path rules can be coupled with a matching rule so as to achieve efficiency in the multi-estate level. On the class of problems where all agents have symmetric preferences, any efficient single-estate rule can be extended to an efficient multi-estate rule. If we allow asymmetric preferences however, this is no more the case. For nondictatorial single-estate rules that satisfy efficiency, strategy proofness, consistency, and resource monotonicity, an efficient extension to multiple estates is impossible. A similar impossibility also holds for single-estate rules that satisfy efficiency, peak-only, and a weak fairness property. We would like to express our gratitude to Bhaskar Dutta, Semih Koray, Hervé Moulin, and Yuntong Wang as well as an associate editor and two anonymous referees of this journal for detailed comments and suggestions. We also thank the seminar participants at Bilkent University, Indian Statistical Institute, Bilgi University, University of Warwick, ASSET 2003, and BWED XXVI.     

Ecological functions of an impounded marsh and three natural estuarine marshes along Woodbridge River,NY/NJ Harbor

An impounded estuarine marsh scheduled for restoration in 2003 and three nearby unimpounded marshes (Spartina alterniflora, S. patens/Iva frutescens, and Phragmites australis) in highly urbanized NY/NJ Harbor were studied to assess the impact of impoundment on marsh structure and function and to identify trajectories of ecosystem change following removal of the levee. Aboveground biomass was greater in the Phragmites and S. alterniflora marshes (706–809 g/m²) as compared to the S. patens/I. frutescens and impounded marshes (378–588 g/m²). Macro-organic matter (0–30 cm) was similar across all marshes (7452–9212 g/m²). The S. patens/Iva frutescens marsh had the lowest aboveground biomass, but contained more plant species (2.8 species/0.25 m²) and greater species diversity (H = 1.33) than the other marshes (1.3–2.0 species/0.25 m², H = 0.16–0.78). Rates of sediment and nutrient accumulation were lower in the impounded marsh (335 g sediment/m²/yr, 97 g C/m²/yr, 6.5 g N/m²/yr, and 0.9 g P/m²/yr) than in the reference marshes (422–1515 g sediment/m²/yr; 111–160 g C/m²/yr; 7–10 g N/m²/yr; 1.6–2.8 g P/m²/yr). Our results indicate that the impounded marsh does not contain the high species diversity of the high marsh, nor does it provide the same level of functions as naturally inundated marshes. Reintroduction of tidal inundation to the impounded marsh will enhance water quality benefits and favor development of S. alterniflora salt marsh community structure.     

The TAL-Family of Rules for Bankruptcy Problems

This paper analyzes a family of rules for bankruptcy problems that generalizes the Talmud rule (T) and encompasses both the constrained equal-awards rule (A) and the constrained equal-losses rule (L). The family is defined by means of a parameter that can be interpreted as a measure of the distributive power of the rule. We provide a systematic study of the structural properties of the rules within the family and its connections with the existing literature.     

The Moulin–Shenker rule

The Moulin–Shenker rule is a non-linear solution concept for solving heterogeneous cost sharing problems. It is the unique continuous rule with the properties scale invariance, bounds on cost shares and self-consistency. I am indebted to several anonymous referees and especially to Hervé Moulin for many useful suggestions.     

On asymptotic strategy-proofness of the plurality and the run-off rules

In this paper we prove that the plurality rule and the run-off procedure are asymptotically strategy-proof for any number of alternatives and that the proportion of profiles, at which a successful attempt to manipulate might take place, is in both cases bounded from above by , where n is the number of participating agents and K does not depend on n. We also prove that for the plurality rule the proportion of manipulable profiles is asymptotically bounded from below by , where k also does not depend on n. Received: 10 February 2000/Accepted: 19 October 2000     

Balanced consistency and balanced cost reduction for sequencing problems

We investigate the implications of balanced consistency and balanced cost reduction in the context of sequencing problems. Balanced consistency requires that the effect on the payoff from the departure of one agent to another agent should be equal between any two agents. On the other hand, balanced cost reduction requires that if one agent leaves a problem, then the total payoffs of the remaining agents should be affected by the amount previously assigned to the leaving agent. We show that the minimal transfer rule is the only rule satisfying efficiency and Pareto indifference together with either one of our two main axioms, balanced consistency and balanced cost reduction.     

SYMMETRIC SCORING RULES AND A NEW CHARACTERIZATION OF THE BORDA COUNT

Young developed a classic axiomatization of the Borda rule almost 50 years ago. He proved it is the only voting rule satisfying the normative properties of decisiveness, neutrality, reinforcement, faithfulness and cancellation. Often overlooked is that the uniqueness of Borda applies only to variable populations. We present a different set of properties which only Borda satisfies when both the set of voters and the set of alternatives can vary. It is also shown Borda is the only scoring rule which will satisfy all of the new properties when the number of voters stays fixed. (JEL D71, D02, H00)     

Rainfall interception by Santa Monica's municipal urban forest

Effects of urban forests on rainfall interception and runoff reduction have been conceptualized, but not well quantified. In this study rainfall interception by street and park trees in Santa Monica, California is simulated. A mass and energy balance rainfall interception model is used to simulate rainfall interception processes (e.g., gross precipitation, free throughfall, canopy drip, stemflow, and evaporation). Annual rainfall interception by the 29,299 street and park trees was 193,168 m³ (6.6 m³/tree), or 1.6% of total precipitation. The annual value of avoided stormwater treatment and flood control costs associated with reduced runoff was $110,890 ($3.60/tree). Interception rate varied with tree species and sizes. Rainfall interception ranged from 15.3% (0.8 m³/tree) for a small Jacaranda mimosifolia (3.5 cm diameter at breast height) to 66.5% (20.8 m³/tree) for a mature Tristania conferta (38.1 cm). In a 25-year storm, interception by all street and park trees was 12,139.5 m³ (0.4%), each tree yielding $0.60 (0.4 m³/tree) in avoided flood control costs. Rainfall interception varied seasonally, averaging 14.8% during a 21.7 mm winter storm and 79.5% during a 20.3 mm summer storm for a large, deciduous Platanus acerifolia tree. Effects of differences in temporal precipitation patterns, tree population traits, and pruning practices on interception in Santa Monica, Modesto, and Sacramento, California are described.     

Single-peaked preferences with several commodities

We consider the problem of allocating m commodities among n agents with single-peaked preferences. When m≥2 and n=2 any strategy-proof and efficient solution is dictatorial. We propose an extension of the Uniform Rule that (in the two-agents case) is the only one that satisfies strategy-proofness, envy-freeness, and a weak requirement related to efficiency. Alternatively, the envy-freeness property may be replaced by weak-anonymity. Received: 7 November 1997/Accepted: 1 August 2000     

Bargaining over a finite set of alternatives

We analyze bilateral bargaining over a finite set of alternatives. We look for "good" ordinal solutions to such problems and show that Unanimity Compromise and Rational Compromise are the only bargaining rules that satisfy a basic set of properties. We then extend our analysis to admit problems with countably infinite alternatives. We show that, on this class, no bargaining rule choosing finite subsets of alternatives can be neutral. When rephrased in the utility framework of Nash (1950), this implies that there is no ordinal bargaining rule that is finite-valued. Professor Sertel passed away on January 25, 2003.     

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