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.     

The solidarity axiom for quasi-linear social choice problems

Recently, Moulin gave various axiomatic characterizations of solutions to quasi-linear social choice problems. He used a consistency axiom, which relates solutions for societies of different sizes, in addition to some basic axioms. In this paper, we introduce another axiom relating solutions for societies of different sizes, called the Solidarity Axiom. This axiom demands that when additional agents enter the scene, all of the original agents be affected in the same direction, i.e., all of them gain or all of them lose. Our main result is a complete characterization of solutions satisfying the solidarity axiom, in addition to Pareto optimality, anonymity and two normalization axioms. All solutions satisfying these five axioms are in the egalitarian spirit; each solution assigns to every agent an equal share of the surplus over some reference level, but uses a different method to compute the reference level. Then, using additional milder axioms, we give further characterization results concerning various subfamilies.I am extremely grateful to Professor William Thomson for his numerous comments which have considerably improved the exposition of the paper. I would like to thank Professor Hervé Moulin for helpful discussions and insightful comments. The comments from an editor and a referee of this journal are also gratefully acknowledged. I retain, however, full responsibility for any shortcommings     

The reinforcement axiom under sequential positional rules

The reinforcement axiom roughly states that when an alternative is selected by two different constituencies, it must also be selected by their union. Hare and Coombs rules are special cases of sequential positional voting rules, which are known to violate this axiom. In this article, we first show that reinforcement can be violated by all such rules. We then evaluate, by the use of Monte Carlo simulations and the Fishburn–Gehrlein technique, the proportion of profiles at which this phenomenon occurs.     

Arrow’s Axiom and Full Rationality for Fuzzy Choice Functions

A classical result for crisp choice functions shows the equivalence between Arrow axiom and the property of full rationality. In this paper we study a fuzzy form of Arrow axiom formulated in terms of the subsethood degree and of the degree of equality (of fuzzy sets). We prove that a fuzzy choice function satisfies Fuzzy Arrow Axiom if and only if it is (fuzzy) full rational. We also show that these conditions are also equivalent with weak and strong fuzzy congruence axioms WFCA and SFCA. It is studied the Arrow index, a new concept that indicates the degree to which a fuzzy choice function satisfies the Fuzzy Arrow Axiom. The author wishes to express her gratitude to the two anonymous reviewers for their valuable comments and discussions that contributed to a higher quality of the paper. Some of their comments can be found in the final version of the paper. An abstract of this paper was presented at the First Spain Italy Netherlands Meeting on Game Theory SING, Maastricht, The Netherlands, June 2005.     

The Might Have Been and Could Be of Religion in Social Theory

Religion may well be the most inscrutable surd of social theory, which began late in the 19^th century dismissing the subject. Not even the renewal of interest in religion in the 1960s did much to make religion a respectable topic in social theory. It is possible that social theory's troubles are, in part, due to its refusal to think about religion. Close examination of social theories of Greek religion suggest, for principal example, that religion is perfectly able to thrive alongside the profane provided both are founded on principles of finitude, which in turn may be said to be the foundational axiom of any socially organized religion. The value of a social theory of religion, thus defined, may be seen as a way out of the current controversies over the politics of redistribution and politics of recognition. Any coherent principles of social justice, whether economic or cultural, may only be possible if one begins with the idea that all human arrangements are, first and foremost, limited—that is to say: finite; hence, strictly speaking, religious. Durkheim got this only partly right.     

Uniform trade rules for uncleared markets

We analyze markets in which the price of a traded commodity is such that the supply and the demand are unequal. Under standard assumptions, the agents then have single peaked preferences on their consumption or production choices. For such markets, we propose a class of Uniform trade rules each of which determines the volume of trade as the median of total demand, total supply, and an exogenous constant. Then these rules allocate this volume “uniformly” on either side of the market. We evaluate these “trade rules” on the basis of some standard axioms in the literature. We show that they uniquely satisfy Pareto optimality, strategy proofness, no-envy, and an informational simplicity axiom that we introduce. We also analyze the implications of anonymity, renegotiation proofness, and voluntary trade on this domain.     

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.     

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.     

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.     

A measure of distance between judgment sets

In the literature on judgment aggregation, an important open question is how to measure the distance between any two judgment sets. This is relevant for issues of social choice: if two individuals hold different beliefs then we might want to find a compromise that lies somewhere between them. We propose a set of axioms that determine a measure of distance uniquely. This measure differs from the widely used Hamming metric. The difference between Hamming’s metric and ours boils down to one axiom. Given judgment sets A and B, this axiom says that if the propositions in ${A \cap B}$ jointly imply that the propositions in A?B share the same truth value, then the disagreement between A and B over those propositions in A?B should be counted as a single disagreement. We consider the application of our metric to judgment aggregation, and also use the metric to measure the distance between preference rankings.     

Maximal symmetry and the Nash solution

The Nash Bargaining Solution is characterised by using the new axiom of Maximal Symmetry in place of Nash's Independence of Irrelevant Alternatives and Symmetry. This axiom expresses the idea that a fair arbitrator should treat symmetric alternatives in the same way, subject to the feasibility constraint. An advantage of the proposed characterisations is that they are valid on a wide set of domains, in particular domains including, or consisting of, non-convex problems. Received: 16 March 1998/Accepted: 13 October 1998     

Pairwise Strategy-Proofness and Self-Enforcing Manipulation

“Strategy-proofness” is one of the axioms that are most frequently used in the recent literature on social choice theory. It requires that by misrepresenting his preferences, no agent can manipulate the outcome of the social choice rule in his favor. The stronger requirement of “group strategy-proofness” is also often employed to obtain clear characterization results of social choice rules. Group strategy-proofness requires that no group of agents can manipulate the outcome in their favors. In this paper, we advocate “effective pairwise strategy-proofness.” It is the requirement that the social choice rule should be immune to unilateral manipulation and “self-enforcing” pairwise manipulation in the sense that no agent of a pair has the incentive to betray his partner. We apply the axiom of effective pairwise strategy-proofness to three types of economies: public good economy, pure exchange economy, and allotment economy. Although effective pairwise strategy-proofness is seemingly a much weaker axiom than group strategy-proofness, effective pairwise strategy-proofness characterizes social choice rules that are analyzed by using different axioms in the literature.     

Characterizations of the cycle-complete and folk solutions for minimum cost spanning tree problems

Minimum cost spanning tree problems connect agents efficiently to a source when agents are located at different points and the cost of using an edge is fixed. The folk and cycle-complete cost sharing solutions always offer core allocations. We provide similar characterizations for both. A new property is based on the following observation: when all agents have the same cost to connect to the source, we can connect one of them to the source then connect all other agents to him, as if he was the source. Cost sharing should also be done in these two steps. We also use some common properties: core selection, piecewise linearity and an independence property. The solutions are differentiated by properties that apply when the cheapest edge to the source gets cheaper. Either the savings are equally distributed among all agents (folk) or the agent on that edge gets all of the savings (cycle-complete).     

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.     

Some thoughts on graduate education in sociology

Examining the question of graduate education in sociology raises issues about the way we perceive our discipline and its future. Multiple theoretical perspectives and applied vs. basic interests need not fractionate the discipline if we orient ourselves to those skills which comprise the essence of sociological work; and the idea of a disciplinary core will be more easily operationalized if we construct graduate curricula with these skills in mind. How we practice our discipline will be a far more significant determinant of both its future and the content of graduate training than our normative pronouncements about what ought to be. His recent publications, both with Les Whitbeck, include “Knowledge Use as Knowledge Creation” inKnowledge (1986), and “Sources of Knowledge for Practice” in theJournal of Applied Behavioral Science (forthcoming).     

Flexibility of choice versus reduction of ambiguity

This paper explores the problem of a social planner willing to improve the welfare of individuals who are unable to compare all available alternatives. The optimal decision trades off the individuals’ desire for flexibility versus their aversion towards ambiguous choice situations. We introduce an axiom system that formalizes this idea. Our main result characterizes the preference maximizing opportunity set. It is a maximal set that consists of mutually comparable alternatives. It also has the property that it maximizes the sum of the distances between its ordered elements for some appropriate pseudometric imposed on the set of possible choices.     

Developing Family Therapy Skills on a Shoe String Budget: A Peer Supervision and Training Approach

Family therapy skills are an essential tool when working with young children and their families, yet accessing family therapy training and supervision in workplace settings has become more difficult. Skills enhancement may be obtained through formal training in accredited courses, a costly undertaking, in which clinicians most often carry the entire cost for the training. In this paper, we propose that specific family therapy skills relevant to working with families of young children can be developed within a peer group format. The peer training described in this paper is extremely cost effective, easy to set up, specifically tailored to our unique training needs and the characteristics of the population of families we are working with. Further, the training allows us to develop fresh and creative ways of skills acquisition, our own ‘curriculum’, with flexible use of training techniques, depending on our particular needs at a given time. We conclude with some of the disadvantages of the model and propose ideas for future development.     

Vetoer and tie-making group theorems for indifference-transitive aggregation rules

A binary relation is indifference-transitive if its symmetric part satisfies the transitivity axiom. We investigated the properties of Arrovian aggregation rules that generate acyclic and indifference-transitive social preferences. We proved that there exists unique vetoer in the rule if the number of alternatives is greater than or equal to four. We provided a classification of decisive structures in aggregation rules where the number of alternatives is equal to three. Furthermore, we showed that the coexistence of a vetoer and a tie-making group, which generates social indifference, is inevitable if the rule satisfies the indifference unanimity. The relationship between the vetoer and the tie-making group, i.e., whether the vetoer belongs to the tie-making group or not, determines the power structure of the rule.     

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