# Walter Bossert's research while affiliated with Université de Montréal and other places

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## Publications (203)

This paper provides an axiomatic analysis of sufficientarian social evaluation. Sufficientarianism has emerged as an increasingly important notion of distributive justice. We propose a class of principles that we label generalized critical-level sufficientarian orderings. The distinguishing feature of our new class is that its members exhibit const...

This paper provides a characterization of a new class of ordinal poverty measures that are defined by means of the aggregate generalized poverty gap. To be precise, we propose to use the sum of the differences between the transformed fixed poverty line and the transformed level of income of each person below the line as our measure. If the transfor...

We present a unified approach to the design of social index numbers. Our starting point is a model that employs an exogenously given partition of the population into subgroups. Three classes of group-dependent measures of deprivation are characterized. The three groups are nested and, beginning with the largest of these, we narrow them down by succ...

We examine the notion of a price index as the solution to the problem of minimizing the distance between the index values and the vector of price ratios. To do so, the choice of a suitable distance function is of crucial importance. We use a generalized least-squares criterion for this purpose and show that the generalized quasilinear functions are...

In this study, we provide a characterization of the class of proportional bargaining solutions introduced by Kalai. Our result differs from earlier axiomatizations in that we use a property that we label individual disagreement point concavity. This property is a weakening of disagreement point concavity used by Chun and Thomson. An application ill...

David Donaldson describes his graduate studies at Stanford with Kenneth Arrow and Hirofumi Uzawa, his meeting with Charles Blackorby, his collaborations with Walter Bossert and John Weymark, his work on utilitarianism, poverty measurement, inequality, commenting on John Harsanyi, John Broome and others.

Pierre Daunou, a contemporary of Borda and Condorcet during the era of the French Revolution and active debates on alternative voting rules, proposed a rule that chooses the strong Condorcet winner if there is one, otherwise eliminates Condorcet losers and uses plurality voting on the remaining candidates. We characterize his rule which combines po...

We examine some ordinal measures of inequality that are familiar from the literature. These measures have a quite simple structure in that their values are determined by combinations of specific summary statistics such as the extreme values and the arithmetic mean of a distribution. In spite of their common appearance, there seem to be no axiomatiz...

A new property of collective choice rules that we refer to as superset robustness is introduced, and we employ it in several characterization results. The axiom requires that if all individual preference orderings expand weakly (in the sense of set inclusion), then the corresponding social preference relation must also expand weakly. In other words...

Resilience has become an important topic in many social sciences. Numerous individual choices and economic and demographic outcomes are likely to be influenced by people's resilience. School performance, work absenteeism and burnout, longevity, the quality of sleep and health-risk behaviors such as substance abuse are some examples. Similarly, it i...

The paper proposes a general definition of positionalist voting rules. Unlike the commonly-employed scoring rules, our notion of positionalism allows for non-linear criteria to be included in the requisite class. We define a voting rule as positionalist if, for any profile of strict individual orderings, any two alternatives are compared collective...

The paper discusses a one-parameter generalization of individual relative deprivation measures to a two-period setting that differs from earlier approaches. The parameter is, by definition, independent of the income distributions under consideration—it is to be chosen by a social planner. Its value has an intuitive interpretation: it represents the...

We axiomatize the class of mixed utilitarian–maximin social welfare orderings. These orderings are convex combinations of utilitarianism and the maximin rule. Our first step is to show that the conjunction of the weak Suppes–Sen principle, the Pigou–Dalton transfer principle, continuity and the composite transfer principle is equivalent to the exis...

We analyze the decisiveness structures associated with acyclical collective choice rules. In particular, we examine the consequences of adding anonymity to weak Pareto, thereby complementing earlier results on acyclical social choice. Both finite and countably infinite populations are considered. As established in contributions by Donald Brown and...

We examine voting rules that are inspired by Dodgson’s method of marks (to be distinguished from the procedure that is commonly referred to as Dodgson’s rule) by means of two criteria. Each voter decides how to allocate a vote budget (which is common to all voters, and need not be exhausted) to the candidates. Our first criterion is a richness cond...

We propose a class of measures of welfare change that are based on the generalized Gini social welfare functions. We analyze these measures in the context of a second-order dominance property that is akin to generalized Lorenz dominance as introduced by Shorrocks (Economica 50:3–17, 1983) and Kakwani (Advances in econometrics, vol 3. JAI Press, Gre...

We propose a characterization of a popular index of multidimensional poverty which, as a special case, generates a measure of material deprivation. This index is the weighted sum of the functioning failures. The important feature of the variables that may be relevant for poverty assessments is that they are discrete in nature. Thus, poverty measure...

We examine the measurement of individual poverty in an intertemporal context. Our aim is to capture the importance of persistence in a state of poverty and we characterize a corresponding individual intertemporal poverty measure. Our first axiom requires that intertemporal poverty is identical to static poverty in the degenerate single-period case....

One unit of a good has to be divided among a group of agents who each are entitled to a minimal share, and these shares sum up to less than one. The associated set of choice problems consists of the unit simplex and all its full-dimensional subsimplices with the same orientation. We characterize all choice rules that are independent of irrelevant a...

This paper analyzes the effects of the inclusion of the past experiences in measuring current material deprivation. The method followed generalizes the proposal of Bossert et al. (Intertemporal material deprivation. Routledge, London, pp. 128–142, 2014) by adapting the class of indices on the measurement of poverty over time of Dutta et al. (Soc Ch...

This paper provides a brief introduction to the use and usefulness of Suzumura consistency, a coherence requirement for binary relations that weakens transitivity. The property was introduced by Suzumura in the context of collective choice but, as demonstrated in some recent contributions, its applicability reaches beyond the boundaries of social-c...

We propose an alternative articulation of the Benthamite greatest-happiness-of-the-greatest-number principle. With ordinally measurable and interpersonally non-comparable utilities, the rule chooses those feasible alternatives that maximize the number of individuals who end up with their greatest element. This rule is tantamount to the plurality ru...

We propose and characterize a new measure of rank mobility. The index is given by the head count of those whose positions change in the move from one period to the next divided by population size. The interpretation of this head-count ratio is straightforward and intuitive. In addition, we illustrate how the measure can be decomposed into an index...

We propose an alternative articulation of the Benthamite greatest-happiness-of-the-greatest-number principle. With ordinally measurable and interpersonally non-comparable utilities, the rule chooses those feasible alternatives that maximize the number of individuals who end up with their greatest element. This rule is tantamount to the plurality ru...

We provide a characterization of a class of rank-mobility measures. These measures generalize the Kemeny measure that is well-known from the literature on measuring the distance between orderings. We use replication invariance to ensure that our measures are applicable in variable-population settings. The rank-based approach to mobility has a natur...

We generalize the classical expected-utility criterion by weakening transitivity to Suzumura consistency. In the absence of full transitivity, reflexivity and completeness no longer follow as a consequence of the system of axioms employed and a richer class of rankings of probability distributions results. This class is characterized by means of st...

We provide a brief survey of some literature on intertemporal social choice theory in a multi-profile setting. As is well-known, Arrow’s impossibility result hinges on the assumption that the population is finite. For infinite populations, there exist non-dictatorial social welfare functions satisfying Arrow’s axioms and they can be described by th...

Single-basined preferences generalize single-dipped preferences by allowing for multiple worst elements. Single-dipped and single-basined preferences have played an important role in areas such as voting, strategy-proofness and matching problems. We examine the notion of single-basinedness in a choice-theoretic setting, with the set of all compact...

An aggregation rule maps each profile of individual strict preference orderings over a set of alternatives into a social ordering over that set. We call such a rule strategy-proof if misreporting one's preference never produces a different social ordering that is between the original ordering and one's own preference. After describing two examples...

Kin selection theorists argue that evolution in social contexts will lead organisms to behave as if maximizing their inclusive, as opposed to personal, fitness. The inclusive fitness concept allows biologists to treat organisms as akin to rational agents seeking to maximize a utility function. Here we develop this idea and place it on a firm footin...

We characterize a generalization of the linear index of individual deprivation. Our class allows for an income increase of a higher-income individual to have a stronger impact the closer they occur to the income of the person under consideration.

The interview was conducted on October 4, 2007, during a Workshop associated with the 2007 Condorcet lectures delivered by Kotaro Suzumura on October 4 and 5, 2007 at the University of Caen. It was revised and expanded substantially on the occasion of Bossert’s visit to Waseda University, where Suzumura taught social choice theory and public philos...

This article illustrates how axiomatic social choice theory can be used in the evaluation of measures of group fitness for a biological hierarchy, thereby contributing to the dialogue between the philosophy of biology and social choice theory. It provides an axiomatic characterization of the ordering underlying the Michod–Viossat–Solari–Hurand–Nede...

A choice function is backwards-induction rationalizable if there exists a finite perfect-information extensive-form game such that for each subset of alternatives, the backwards-induction outcome of the restriction of the game to that subset of alternatives coincides with the choice from that subset. We prove that every choice function is backwards...

Extensive social choice theory is used to study the problem of measuring group fitness in a two-level biological hierarchy. Both fixed and variable group size are considered. Axioms are identified that imply that the group measure satisfies a form of consequentialism in which group fitness only depends on the viabilities and fecundities of the indi...

We provide a systematic treatment of the notion of economic insecurity, assuming that an individual’s sentiment of insecurity depends on the current wealth level and its variations experienced in the past. We think of wealth as a comprehensive variable encompassing anything that may help in coping with adverse occurrences. The current wealth level...

We examine the measurement of multidimensional poverty and material deprivation following the counting approach. In contrast to earlier contributions, dimensions of well-being are not forced to be equally important but different weights can be assigned to different dimensions. We characterize a class of individual measures reflecting this feature....

In a seminal contribution, Hansson (1976) demonstrates that the collection of decisive coalitions associated with an Arrovian social welfare function forms an ultrafilter. He goes on to show that if transitivity is weakened to quasi-transitivity as the coherence property imposed on a social relation, the set of decisive coalitions is a filter. We e...

We examine properties of binary relations that complement quasi-transitivity and Suzumura consistency in the sense that they, together with the original axiom(s), are equivalent to transitivity. In general, the conjunction of quasi-transitivity and Suzumura consistency is strictly weaker than transitivity but in the case of collective choice rules...

In decision-making involving multiple criteria or attributes, a deci-sion maker first identifies all relevant evaluative attributes in making decisions. Then, a dominance principle is often invoked whenever ap-plicable: whenever an option x is better than an option y in terms of some attribute and no worse than y in terms of any other attributes, t...

The goal of this paper is to contribute to the economic literature on ethnic and cultural diversity by proposing a new index that is informationally richer and more flexible than the commonly used ‘ethno-linguistic fractionalization’ (ELF) index. We characterize a measure of diversity among individuals that takes as a primitive the individuals, as...

In an infinite-horizon setting, Ferejohn and Page showed that any social welfare function satisfying Arrow’s axioms and stationarity
must be a dictatorship of the first generation. Packel strengthened this result by proving that no collective choice rule
generating complete social preferences can satisfy unlimited domain, weak Pareto and stationari...

We employ the theory of rational choice to examine whether observable choices from feasible sets of prospects can be generated
by the optimization of some underlying decision criterion under uncertainty. Rather than focusing on a specific theory of
choice, our objective is to formulate a general approach that is designed to cover the various decisi...

To test the joint hypothesis that players in a noncooperative game (allowing mixtures over pure strategies) consult an independent preference relation and select a Nash equilibrium, it suffices to study the reaction of the revealed collective choice upon changes in the space of strategies available to the players. The joint hypothesis is supported...

This paper aims at investigating empirically the relationship between self-declared satis-faction with life and an individual's well-being as measured by the indices of deprivation and social exclusion proposed in the income distribution literature. Results on European countries show that life satisfaction decreases with an increase in deprivation...

We find conditions on the order on subsets of a finite set which are necessary and sufficient for the relative ranking of
any two subsets in this order to be determined by their extreme elements relative to an abstract convex geometry. It turns
out that this question is closely related to the rationalisability of path independent choice functions b...

We examine the measurement of multidimensional poverty following the counting approach. In contrast to earlier contributions, dimensions of human well-being are not forced to be equally important but different weights can be assigned to different dimensions. We characterize a class of individual multidimensional poverty measures re-flecting this fe...

This chapter reviews the welfarist approach to population ethics. This chapter provides an overview of the critical-level utilitarian population principles and their generalized counterparts, examine important properties of these principles and discuss their relationships to other variable population social evaluation rules. The chapter illustrates...

We find conditions on the order on subsets of a finite set which are necessary and sufficient for the relative ranking of any two subsets in this order to be determined by their extreme elements relative to an abstract convex geometry. It turns out that this question is closely related to the rationalisability of path independent choice functions b...

The rationalizability of a choice function on general domains by means of an ordering has been analyzed thoroughly by Richter (1966; 1971), Hansson (1968), and Suzumura (1977). Moreover, characterizations of various versions of consistent rationalizability have appeared in Bossert, Sprumont, and Suzumura (2005a). However, not much seems to be known...

We examine the measurement of individual poverty in an intertemporal context. Our aim is to capture the importance of persistence in a state of poverty and we characterize a corresponding individual intertemporal poverty measure. Our first axiom requires that intertemporal poverty is identical to static poverty in the degenerate single-period case....

The phenomenon of income polarization is generally associated with a disappearing middle class but there does not seem to be a generally accepted definition of this notion. We characterize classes of polarization quasi-orderings and polarization measures in a framework where there are two income groups separated by the median. The axioms we employ...

We characterize a class of collective choice rules such that collective preference relations are consistent. Consistency is a weakening of transitivity and a strengthening of acyclicity requiring that there be no cycles with at least one strict preference, which excludes the possibility of a “money pump.” The properties of collective choice rules u...

Binary relations are at the heart of much of economic theory, both in the context of individual choice and in multi-agent
decision problems. A fundamental coherence requirement imposed on a relation is the well-known transitivity axiom. If a relation
is interpreted as a goodness relation, transitivity postulates that whenever one alternative is at...

Experimental evidence on gender differences demonstrates that women are generally less trusting and more reciprocating than men in Investment Games. However, existing studies typically use a narrow population consisting of college students. To test the robustness of these findings, we report on an experiment using 18-84-year old participants recrui...

Ever since Sen’s (1993, 1997) criticism on the notion of internal consistency or menu independence of choice, there exists a widespread perception that the standard revealed preference approach to the theory of rational choice has difficulties in coping with the existence of external norms, or the information a menu of choice might convey to a deci...

Since the late 1970s there has been a dramatic shift of focus in social choice theory, with structured sets of alternatives and restricted domains of the sort encountered in economic problems coming to the fore. This article provides an overview of some of the recent contributions to four topics in normative social choice theory in which economic m...

This version: June 29, 2008 Ever since Sen (1993) criticized the notion of internal consistency of choice, there exists a widespread perception that the standard rationalizability approach to the theory of choice has difficulties in coping with the existence of external norms. We introduce a concept of norm-conditional rationalizability and show th...

This paper examines principles for social evaluation under uncertainty in environments with a variable population. In contrast
to most of the literature, we employ a model that is formulated in terms of prospects rather than lotteries. Starting from
a fixed-population result, a multi-profile variant of Harsanyi’s social aggregation theorem is exten...

Ever since Sen (1993) criticized the notion of internal consistency of choice, there exists a wide spread perception that the standard rationalizability approach to the theory of choice has difficulties coping with the existence of external social norms. This paper introduces a concept of norm-conditional rationalizability and shows that external s...

Social exclusion manifests itself in the persistent relative lack of an individual's access to functionings compared with other members of society, and we model it as being in a state of deprivation over time. We view deprivation as having two basic determinants: the lack of identification with other members of society, and the aggregate alienation...

We reconsider the problem of ordering infinite utility streams. As has been established in earlier contributions, if no representability condition is imposed, there exist strongly Paretian and finitely anonymous orderings of intertemporal utility streams. We examine the possibility of adding suitably formulated versions of classical equity conditio...

A social-evaluation functional assigns a social ranking of alternatives to each information profile in its domain. In the classical multi-profile model of social choice, profiles are restricted to welfare information: all non-welfare information is implicitly assumed to be fixed. Because of this, the conventional approach does not allow us to disce...

The rationalizability of a choice function by means of a transitive relation has been analyzed thoroughly in the literature. However, not much seems to be known when transitivity is weakened to quasi-transitivity or acyclicity. Such weakenings are particularly relevant in the context of social choice. We describe the logical relationships between t...

We introduce a one-parameter class of individual deprivation measures. Motivated by a suggestion of Runciman, we modify Yitzhaki’s index by multiplying it by a function that is interpreted as measuring the part of deprivation generated by an agent’s observation that others in his reference group move on to a higher level of income than himself. The...

We provide an axiomatization of Yitzhaki's index of individual deprivation. Our result differs from an earlier characterization due to Ebert and Moyes in the way the reference group of an individual is represented in the model.

Consistency, a natural weakening of transitivity introduced in a seminal contribution by Suzumura (1976b), has turned out to be an interesting and promising concept in a variety of areas within economic theory. This paper summarizes its recent applications and provides some new observations in welfarist social choice and in population ethics. In pa...

Although the theory of greatest-element rationalizability and maximal-element rationalizability under general domains and without full transitivity of rationalizing relations is well-developed in the literature, these standard notions of rational choice are often considered to be too demanding. An alternative definition of rationality of choice is...

This paper proposes a definition of relative uncertainty aversion for decision models under complete uncertainty. It is shown that, for a large class of decision rules characterized by a set of plausible axioms, the new criterion yields a complete ranking of those rules with respect to the relative degree of uncertainty aversion they represent. In...

This note reexamines the single-profile approach to social-choice theory. If an alternative is interpreted as a social state of affairs or a history of the world, it can be argued that a multi-profile approach is inappropriate because the information profile is determined by the set of alternatives. However, single-profile approaches are criticized...

In the past quarter century, there has been a dramatic shift of focus in social choice theory, with structured sets of alternatives and restricted domains of the sort encountered in economic problems coming to the fore. This article provides an overview of some of the recent contributions to four topics in normative social choice theory in which ec...

Public policies frequently involve choices of alternatives in which the size and the composition of the population may vary. Examples are the allocation of resources to prenatal care and the design of aid packages to developing countries. In order to assess the corresponding feasible choices on normative grounds, criteria for social evaluation that...

The proof of Theorem 2 in our paper [Soc. Choice Welfare 24, No. 2, 253–267 (2005; Zbl 1100.91021)] is incorrect, due to the erroneous substitution of an earlier version in the production process. Here the correct proof is given along with a statement of the result.

This book presents an exploration of the idea of the common or social good, extended so that alternatives with different populations can be ranked. The approach is, in the main, welfarist, basing rankings on the well-being, broadly conceived, of those who are alive (or ever lived). The axiomatic method is employed, and topics investigated include:...

The goal of this paper is to characterize a generalized ethno-linguistic frac-tionalization index that combines information on population shares with information on similarities among groups and individuals. We show that the generalized index is a nat-ural extension of the ethno-linguistic fractionalization index and is also simple to compute. The...

In this paper we consider variations of Koopmans' (1960) postulates and demonstrate that these lead to a class of social preferences that is wider than discounted utilitarianism. We formulate a utilitiarian condition (PFL), and introduce a one-sided equity condition (HEF) stating that a sacrifice of the present generation leading to a uniform gain...

Intertemporal social-evaluation rules provide us with social criteria that can be used to assess the relative desirability of utility distributions across generations. The trade-offs between the well-being of different generations implicit in each such rule reflect the underlying ethical position on issues of intergenerational equity or justice. We...

We examine the maximal-element rationalizability of choice functions with arbitrary domains. While rationality formulated in terms of the choice of greatest elements according to a rationalizing relation has been analyzed relatively thoroughly in the earlier literature, this is not the case for maximal-element rationalizability, except when it coin...

The rationalizability of a choice function on an arbitrary domain under various coherence properties has received a considerable amount of attention both in the long-established and in the recent literature. Because domain closedness conditions play an important role in much of rational choice theory, we examine the consequences of these requiremen...

Public policies often involve choices of alternatives in which the size and the composition of the population may vary. Examples are the allocation of resources to prenatal care and the design of aid packages to developing countries. In order to assess the corresponding feasible choices on normative grounds, criteria for social evaluation that are...

This paper characterizes welfarist social evaluation in a multi-profile setting where, in addition to multiple utility profiles, there may be more than one profile of non-welfare information. We prove a new version of the welfarism theorem in this alternative framework, and we demonstrate that adding a plausible and weak anonymity property to the w...

The rationalizability of a choice function on arbitrary domains by means of a transitive relation has been analyzed thoroughly in the literature. Moreover, characterizations of various versions of consistent rationalizability have appeared in recent contributions. However, not much seems to be known when the coherence property of quasi-transitivity...

Consistency of a binary relation requires any preference cycle to involve indifference only. It has been shown that consistency is necessary and sufficient for the existence of an ordering extension of a binary relation. It is therefore of interest to examine the rationalizability of choice functions by means of consistent relations. We describe th...

This paper, which is to be published as a chapter in the Oxford Handbook of Political Economy, provides an introduction to social-choice theory with interpersonal comparisons of well-being. We argue that the most promising route of escape from the negative conclusion of Arrow's theorem is to use a richer informational environment than ordinal measu...

This paper revisits Diamond’s classical impossibility result regarding the ordering of infinite utility streams. We show that if no representability condition is imposed, there do exist strongly Paretian and finitely anonymous orderings of intertemporal utility streams with attractive additional properties. We extend a possibility theorem due to Sv...

In this paper, we consider the Coase theorem in a non cooperative game framework. In particular, we explore the robustness of the Coase theorem with respect to the ?nal distribution of alienable property rights which constitutes, as far as we know, a less cultivated ?eld of research. In our framework, in order to reach e� ciency, agents have to sti...

In Arrovian [Arrow (1951, 1963)] social choice theory, the objective is to construct a social welfare function—a mapping which assigns a social preference ordering to each admissible profile of individual preferences—satisfying several a priori appealing conditions. Arrow showed that the only social welfare functions satisfying his axioms are dicta...

This paper provides new versions of Harsanyi’s social aggregation theorem that are formulated in terms of prospects rather than lotteries. Strengthening an earlier result, fixed-population ex-ante utilitarianism is characterized in a multi-profile setting with fixed probabilities. In addition, we extend the social aggregation theorem to social-eval...

This chapter provides a survey of utilitarian theories of justice. We review and discuss axiomatizations of utilitarian and generalized-utilitarian social-evaluation functionals in a welfarist framework. Section 2 introduces, along with some basic definitions, social-evaluation functionals. Furthermore, we discuss several information-invariance ass...

We provide a characterization of selection correspondences in two-person exchange economies that can be core rationalized in the sense that there exists a preference profile with some standard properties that generates the observed choices as the set of core elements of the economy for any given endowment vector. The approach followed in this paper...

We consider a cooperative model of bargaining where the location of the disagreement point may be uncertain. Based on the maximin criterion, we formulate an ex ante efficiency condition and characterize the class of bargaining solutions satisfying this axiom. These solutions are generalizations of the monotone path solutions. Adding individual rati...

It is well-known that non-cooperative and cooperative game theory may yield different solutions to games. These differences are particularly dramatic in the case of truels, or three-person duels, in which the players may fire sequentially or simultaneously, over one round or n rounds. Representative solution concepts (Nash and subgame-perfect equil...