Cooperative production with unequal skills: The solidarity approach to compensation

We consider a simple production model and we assume that agents have unequal production skills which can in no way be attributed to their responsibility. We study how it is possible, if at all, to compensate for differential skills by applying Rawls's idea of a collective sharing in the benefits of skills. For this purpose, we introduce an axiom of solidarity, according to which agents should all be affected in the same direction if the profile of personal skills changes. We show that particular allocation rules are characterized be combining this axiom with a requirement of non-discrimination among preferences, or with a property capturing Nozick's idea of guaranteeing a minimal benefit from one's own skill. Received: 1 July 1996/Accepted: 25 May 1998     

Information and preference aggregation

We investigate the implications of relaxing Arrow's independence of irrelevant alternatives axiom while retaining transitivity and the Pareto condition. Even a small relaxation opens a floodgate of possibilities for nondictatorial and efficient social choice. Received: 20 August 1997/Accepted: 29 September 1998     

Aggregation of preferences with a variable set of alternatives

A social choice correspondence called the Essential set is studied with the help of an axiom called Cloning Consistency. Cloning consistency is the requirement that the formal choice rule be insensitive to the replication of alternatives. The Essential set is the support of the optimal mixed strategies in a symmetric two-party electoral competition game. Received: 24 March 1998/Accepted: 3 March 1999     

On rationalizability of choice functions: A characterization of the median

In this paper we characterize choice behaviour that picks the median element from a set of feasible alternatives. It is easily seen that this choice behaviour violates most of the standard consistency conditions for set contraction and set expansion. The paper offers a complete characterization in terms of pure choice function conditions, and contrasts the new axiom set with the traditional consistency conditions. It also suggests alternative external references which could explain the choice of the median. Received: 2 June 1997/Accepted: 27 July 1998     

Inequality orderings and unit consistency

The paper examines the implications of the newly proposed unit consistency axiom for partial inequality orderings. We first show that some intermediate Lorenz dominance conditions violate the axiom. We then characterize a class of intermediate Lorenz orderings and demonstrate that the only unit-consistent member is the one related to Krtscha (Models and measurement of welfare and inequality. Springer, Heidelberg, 1994)’s intermediate notion of inequality which has recently been investigated by Zoli (A surplus sharing approach to the measurement of inequality. Discussion paper no. 98/25, University of York, 1998; Logic, game, theory and social choice. Tilburg University Press, Tilburg, 1999) and Yoshida (Soc Choice Welf 24:557–574, 2005). Finally, we provide a general characterization for unit-consistent Lorenz orderings and the Krtscha-type dominance again turns out to be the only one that is intermediate and unit-consistent.     

Extended Pareto rules and relative utilitarianism

This paper introduces the “Extended Pareto” axiom on Social Welfare Functions and gives a characterization of the axiom when it is assumed that the Social Welfare Functions that satisfy it in a framework of preferences over lotteries also satisfy the restrictions (on the domain and range of preferences) implied by the von-Neumann Morgenstern axioms. With the addition of 2 other axioms: “Anonymity” and a weak version of Arrow's Independence of Irrelevant Alternatives axiom: “Weak IIA” it is shown that there is a unique Social Welfare Function called “Relative Utilitarianism” that consists of normalising individual utilities between 0 and 1 and adding them. Received: 7 June 1994 / Accepted: 28 April 1997     

Transitive and acyclic rationality indicators of fuzzy choice functions on base domain

In the present paper we introduce the indicators of the fuzzy transitive congruence axiom, fuzzy direct-revelation axiom and fuzzy acyclic congruence axiom. These indicators measure the degree to which a fuzzy choice function satisfies these axioms. We use the indicators of fuzzy transitive congruence axiom and fuzzy acyclic congruence axiom to calculate the minimum degree to which the direct fuzzy revealed preference relation is the transitive and acyclic respectively. We established that (i) the degree to which the fuzzy choice function is full rational is the degree to which it satisfies fuzzy transitive congruence axiom and (ii) the degree to which the fuzzy choice function is acyclic rational is the minimum degree to which it satisfies fuzzy direct-revelation axiom and its fuzzy revealed preference is acyclic. We show that a similarity relation on the set of fuzzy choice functions preserves the indicators of fuzzy transitive congruence axiom, fuzzy direct-revelation axiom, fuzzy acyclic congruence axiom and (transitive and acyclic) rationality indicators.     

On the power of poverty orderings

This paper investigates the possibility of increasing the ordering power of additively separable poverty measures beyond the condition of second degree stochastic dominance by considering third degree stochastic dominance. For a fixed poverty line, the ordering power can be significantly enhanced by using the third degree criterion. For a range of poverty lines, the marginal power of the third degree criterion over the second degree depends critically upon the lower bound of the range; if the lower bound poverty line is arbitrarily close to zero, the two criteria coincide. The implications of a strong version of the transfer sensitivity axiom are also considered. Received: 20 November 1995/Accepted: 16 February 1998     

Consistency, dummy and independence of irrelevant strategies for strategic games

The relationships between the consistency (CONS) principle and two other axioms, dummy (DUM) and independence of irrelevant strategies (IIS) for solution concepts on families of strategic form games are studied. If a solution satisfies DUM and IIS, then it also satisfies CONS (Peleg and Tijs 1996). The converse of this proposition is not true: CONS implies neither DUM nor IIS as shown in two simple examples, using the concept of coalition-proof Nash equilibrium. The axiom of weak dummy (WDUM) is introduced. WDUM, along with IIS, implies CONS. Moreover, CONS implies WDUM. Received: 13 August 1998/Accepted: 19 January 1999     

A characterization of the Nash bargaining solution

We characterize the Nash bargaining solution replacing the axiom of Independence of Irrelevant Alternatives with three independent axioms: Independence of Non-Individually Rational Alternatives, Twisting, and Disagreement Point Convexity. We give a non-cooperative bargaining interpretation to this last axiom. Received: 4 September 2000/Accepted: 6 September 2001     

Consistent comparison of pro-poor growth

This article contributes to the literature of pro-poor growth measurement by introducing and characterizing a growth-rate consistency axiom. The axiom states that if one growth pattern is judged to be more pro-poor than another growth pattern at a given growth rate, then the pro-poor ranking between the two growth patterns should remain the same at a higher growth rate. We show that summary pro-poor measures such as poverty-growth elasticities may violate this axiom. We then characterize a special dominance condition under which a given summary pro-poor measure will satisfy the growth-rate consistency axiom. Finally, we establish a general growth-rate dominance condition under which all summary pro-poor measures will respect the growth-rate consistency axiom.     

Weakest collective rationality and the Nash bargaining solution

We propose a new axiom, weakest collective rationality (WCR) which is weaker than both weak Pareto optimality (WPO) in Nash’s (Econometrica 18:155–162, 1950) original characterization and strong individual rationality (SIR) in Roth’s (Math Oper Res 2:64–65, 1977) characterization of the Nash bargaining solution. We then characterize the Nash solution by symmetry (SYM), scale invariance (SI), independence of irrelevant alternatives (IIA) and our weakest collective rationality (WCR) axiom.     

Sequential path independence and social choice

Arrow's general impossibility theorem shows that every Paretian social choice function which satisfies independence of irrelevant alternatives and the Axiom of Sequential Path Independence is necessarily dictatorial. It is shown that the existence of a dictator can be established without invoking full path independence. We propose an axiom of weak path independence of a sequential choice procedure. This axiom turns out to be independent of the factor that is critical in obtaining dictatorship or oligarchy results in the choice theoretic framework.     

Shapley–Shubik methods in cost sharing problems with technological cooperation

In the discrete cost sharing model with technological cooperation (Bahel and Trudeau in Int J Game Theory 42:439–460, 2013a), we study the implications of a number of properties that strengthen the well-known dummy axiom. Our main axiom, which requires that costless units of demands do not affect the cost shares, is used to characterize two classes of rules. Combined with anonymity and a specific stability property, this requirement picks up sharing methods that allow the full compensation of at most one technological contribution. If instead we strengthen the well-known dummy property to include agents whose technological contribution is offset by the cost of their demand, we are left with an adaptation of the Shapley–Shubik method that treats technologies as private and rewards their contributions. Our results provide two interesting axiomatizations for the adaptations of the Shapley–Shubik rule to our framework.     

Are Condorcet procedures so bad according to the reinforcement axiom?

A Condorcet social choice procedure elects the candidate that beats every other candidate under simple majority when such a candidate exists. The reinforcement axiom roughly states that given two groups of individuals, if these two groups select the same alternative, then this alternative must also be selected by their union. Condorcet social choice procedures are known to violate this axiom. Our goal in this paper is to put this important voting theory result into perspective. We then proceed by evaluating how frequently this phenomenon is susceptible to occur.     

Maximal domains of preferences preserving strategy-proofness for generalized median voter schemes

We characterize the maximal sets of preferences under which generalized median voter schemes are strategy-proof. Those domains are defined by a qualified version of single-peakedness, which depends on the distribution of power among agents implied by each generalized median voter scheme. Received: 28 April 1997/Accepted: 30 January 1998     

Anonymity in large societies

In a social choice model with an infinite number of agents, there may occur “equal size” coalitions that a preference aggregation rule should treat in the same manner. We introduce an axiom of equal treatment with respect to a measure of coalition size and explore its interaction with common axioms of social choice. We show that, provided the measure space is sufficiently rich in coalitions of the same measure, the new axiom is the natural extension of the concept of anonymity, and in particular plays a similar role in the characterization of preference aggregation rules.     

Single-peakedness and strategy-proofness of generalized median voter schemes

We identify, in a continuous multidimensional framework, a maximal domain of preferences compatible with strategy-proofness for a given generalized median voter scheme. It turns out that these domains are a variation of single-peakedness. A similar but stronger result for the discrete case and single-peakedness has been already obtained by Barberà et al. (1999). However, both results are independent and their proofs involve different arguments. Received: 27 July 1998/Accepted: 11 September 2000