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Among the reasons behind the choice behavior of an individual taking a stochastic form are her potential indifference or indecisiveness between certain alternatives, and/or her willingness to experiment in the sense of occasionally deviating from choosing a best alternative to give a try to other options. We introduce methods of identifying if and when a stochastic choice model may be thought of as arising due to any one of these three reasons. Each of these methods furnishes a natural way of making deterministic welfare comparisons within any model that is “rationalized” as such. In turn, we apply these methods, and characterize the associated welfare orderings, in the case of several well‐known classes of stochastic choice models.

We model situations of choice under uncertainty where one is exogenously given information about the unknown states as a “suggested prior” (as in weather forecasts, betting odds provided by bookmakers, success likelihoods provided by medical doctors, estimates given by financial analysts, etc.). We wish to understand when a decision maker would adopt the suggested prior as her own subjective beliefs, yielding fully to the power of suggestion. We find that this happens under surprisingly weak conditions: If a preference relation, may it be complete or incomplete, (1) uses the information it is given consistently (in the sense of being state-neutral) and (2) believes that events that are suggested to occur with zero probability will indeed not occur, then it is not only probabilistically sophisticated, but also holds the suggested beliefs as actual beliefs. If the agent is a (subjective) expected utility maximizer, this happens even in the absence of condition (2).

We say that a group is fully preorderable if every (left- and right-) translation invariant preorder on it can be extended to a translation invariant total preorder. Such groups arise naturally in applications, and relate closely to orderable and fully orderable groups (which were studied extensively since the seminal works of Philip Hall and A. I. Mal’cev in the 1950s). Our first main result provides a purely group-theoretic characterization of fully preorderable groups by means of a condition that goes back to Ohnishi (Osaka Math. J. 2, 161–164 16). In particular, this result implies that every fully orderable group is fully preorderable, but not conversely. Our second main result shows that every locally nilpotent group is fully preorderable, but a solvable group need not be fully preorderable. Several applications of these results concerning the inheritance of full preorderability, connections between full preorderability and full orderability, vector preordered groups, and total extensions of translation invariant binary relations on a group, are provided.

This paper begins by observing that any reflexive binary (preference) relation (over risky prospects) that satisfies the independence axiom admits a form of expected utility representation. We refer to this representation notion as the coalitional minmax expected utility representation. By adding the remaining properties of the expected utility theorem, namely, continuity, completeness, and transitivity, one by one, we find how this representation gets sharper and sharper, thereby deducing the versions of this classical theorem in which any combination of these properties is dropped from its statement. This approach also allows us to weaken transitivity in this theorem, rather than eliminate it entirely, say, to quasitransitivity or acyclicity. Apart from providing a unified dissection of the expected utility theorem, these results are relevant for the growing literature on boundedly rational choice in which revealed preference relations often lack the properties of completeness and/or transitivity (but often satisfy the independence axiom). They are also especially suitable for the (yet overlooked) case in which the decision‐maker is made up of distinct individuals and, consequently, transitivity is routinely violated. Finally, and perhaps more importantly, we show that our representation theorems allow us to answer many economic questions that are posed in terms of nontransitive/incomplete preferences, say, about the maximization of preferences, the existence of Nash equilibrium, the preference for portfolio diversification, and the possibility of the preference reversal phenomenon.

We obtain variants of the classical von Neumann-Morgenstern expected utility theorem, with and without the completeness axiom, in which the derived Bernoulli utility functions are Lipschitz. The prize space in these results is an arbitrary separable metric space, and the utility functions may be unbounded. The main ingredient of our results is a novel (behavioral) axiom on the underlying preference relations which is satisfied by virtually all stochastic orders. The proof of the main representation theorem is built on the fact that the completion of the Kantorovich-Rubinstein space is the canonical predual of the Banach space of Lipschitz functions that vanish at a fixed point. Two applications are given, one to the theory of non-expected utility theory, and the other to the theory of decision-making under uncertainty., 29 pages

The theoretical literature on (non-random) choice largely follows the route of Richter (1966) by working in abstract environments and by stipulating that we see all choices of an agent from a given feasible set. On the other hand, empirical work on consumption choice using revealed preference analysis is done following the approach of Afriat (1967), which assumes that we observe only one (and not necessarily all) of the potential choices of an agent. These two approaches are structurally different and they are treated in the literature in isolation from each other. This paper introduces a framework in which both approaches can be formulated in tandem. We prove a rationalizability theorem in this framework that simultaneously generalizes the fundamental results of Afriat and Richter, along with many of their variants.

The objective of this paper is to provide continuous utility representation theorems analogous to Debreu's classic utility representation theorem, albeit for preference relations that may fail to be complete and/or transitive. Specifically, we show that every (continuous and) reflexive binary relation on a (compact) metric space can be represented by means of the maxmin, or dually, minmax, of a (compact) set of (compact) sets of continuous utility functions. This notion of “maxmin multi-utility representation,” generalizes the recently proposed notions of “multi-utility representation” for preorders and “justifiable preferences” for complete and quasitransitive relations. As such, our main representation theorems lead to some new characterizations of these special cases as well.

This paper develops axiomatically a revealed preference theory of reference-dependent choice behavior. Instead of taking the reference for an agent as exogenously given in the description of a choice problem, we suitably relax the Weak Axiom of Revealed Preference to obtain, endogenously, the existence of reference alternatives as well as the structure of choice behavior conditional on those alternatives. We show how this model captures some well-known choice patterns such as the attraction effect. (JEL D11, D81)

Our primary query is to find conditions under which the closure of a preorder on a topological space remains transitive. We study this problem for translation invariant preorders on topological groups. The results are fairly positive; we find that the closure of preorders and normal orders remain as such in this context. The same is true for factor orders as well under quite general conditions. In turn, in the context of topological linear spaces, these results allow us to obtain a simple condition under which the order-duals with respect to a vector order and its closure coincide. Various order-theoretic applications of these results are also provided in the paper.

We use the revealed preference method to derive a model of individual decision making when the endowment of an agent provides a reference point that may influence her choices. This model generalizes the classical rational choice model, which views choice as a consequence of “utility maximization†. Instead, our model sees choice as arising from “psychologically constrained utility maximization†, where the constraints are induced by one's initial endowment. In particular, this model produces status quo bias as a natural consequence (but not necessarily the endowment effect). A range of economic applications identify the predictive and explanatory strength of the model. In particular, we demonstrate that the status quo bias phenomenon reduces the size of the substitution effect in problems of consumption choice.

This paper provides a systematic solvability analysis for (generalized) variational inequalities on separable Hilbert lattices. By contrast to a large part of the existing literature, our approach is lattice-theoretic, and is not based on topological fixed point theory. This allows us to establish the solvability of certain types of (generalized) variational inequalities without requiring the involved (set-valued) maps be hemicontinuous or monotonic. Some of our results generalize those obtained in the context of nonlinear complementarity problems in earlier work, and appear to have scope for applications. This is illustrated by means of several applications to fixed point theory, optimization, and game theory.

We develop the ordinal theory of (semi)continuous multi-utility representation for incomplete preference relations. We investigate the cases in which the representing sets of utility functions are either arbitrary or finite, and those cases in which the maps contained in these sets are required to be (semi)continuous. With the exception of the case where the representing set is required to be finite, we find that the requirements of such representations are surprisingly weak, pointing to a wide range of applicability of the representation theorems reported here. Some applications to decision theory under uncertainty and consumer theory are also considered.

We revisit the fixed point problem for the sum of a compact operator and a continuous function, where the domain on which these maps are defined is not necessarily convex, the former map is allowed to be multi-valued, and the latter to be a semicontraction and/or a suitable nonexpansive map. In this setup, guaranteeing the existence of fixed points is impossible, but two types of invariant-like sets are found to exist.

For a society that consists of at least three individuals, we show that a social choice rule is Maskin monotonic if and only if it is Nash implementable by means of a mechanism that is stochastic or a mechanism that contains (arbitrary) awards. In equilibrium, the mechanisms do not have any stochastic elements and do not involve any awards. Thus, loosely speaking, one can drop the no-veto power postulate from Maskin's classic theorem on Nash implementability, provided that the notion of a mechanism is suitably generalized, thereby narrowing the gap between the properties of Maskin monotonicity and Nash implementability. Moreover, using the standard notion of a mechanism, we prove that Nash implementability is equivalent to Maskin monotonicity with renegotiation: this is a pure improvement over a well-known result of Maskin and Moore [Maskin, E., Moore, J., 1999. Implementation and renegotiation, Rev. Econ. Studies 66, 39–56].

We derive a representation theorem for time preferences (on the prize-time space) which identifies a novel notion of relative discounting as the key ingredient. This representation covers a variety of time preference models, including the standard exponential and hyperbolic discounting models and certain non-transitive time preferences, such as the similarity-based and subadditive discounting models. Our axiomatic work thus unifies a number of seemingly disparate time preference structures, thereby providing a tractable mathematical format that allows for investigating certain economic environments without subscribing to a particular time preference model. This point is illustrated by means of an application to sequential bargaining theory.

We study if (and when) the intersections and unions of social choice rules that are implementable with respect to a certain equilibrium concept are themselves implementable with respect to that equilibrium concept. Our results for dominant strategy equilibrium are mostly of negative nature; similarly, the intersection of Nash implementable SCCs need not be Nash implementable. On the other hand, we find that the union of any set of Nash implementable social choice rules is Nash implementable (for societies of at least three constituents). This last observation allows us to formulate the notion of the largest Nash implementable subcorrespondence of a social choice rule.

A major problem of the positive theory of income taxation is to explain why statutory income tax schedules in practice are marginal-rate progressive. While it is commonly believed that this is but a simple consequence of the fact that the number of relatively poor voters exceeds that of richer voters in general, putting this contention in a voting equilibrium context is not a trivial task. We do this here in the context of nonlinear taxation and attempt to provide a formal argument in support of this heuristic claim. We first establish the existence of mixed strategy equilibria and identify certain cases in which marginal-rate progressive taxes are chosen almost surely by the political parties. Unfortunately, we also find that if the tax policy space is not artificially constrained, the support of at least one equilibrium cannot be contained within the set of marginal-rate progressive taxes.

A commonly held belief in economics is that an individual's preferences that are revealed by her choices must be complete. This paper takes issue with this position by showing that one may be able to distinguish between indifference and indecisiveness of an agent upon observing her choice behavior. We relax the standard Weak Axiom of Revealed Preferences (WARP) and show that a potent theory of individual choice (with and without risk) can be founded on this weaker axiom when it is coupled with some other standard postulates. The most notable features here are that an agent is allowed to be indifferent between certain alternatives and indecisive about others. Moreover, an outside observer can identify which of these actually occur upon examining the (observable) choice behavior of the decision maker. As an application, we also show how our theory may be able to cope with the classical preference reversal phenomenon.

We weaken the no-veto power condition of Maskin [Maskin, E.,1999. Nash equilibrium and welfare optimality. Rev. Econ. Stud. 66, 23–38] to limited veto power, and prove that any monotonic social choice rule is Nash implementable if it satisfies this weaker condition. The result is obtained by using the canonical Maskin mechanism without modification . An immediate corollary is that the weak core is Nash implementable in any coalitional game environment. An example is given to show that the strong core need not be implementable, even when it is monotonic.

Motivated by the empirical findings concerning the importance of one's current situation on her choice behavior, the main objective of this paper is to propose a rational choice theory that allows for the presence of a status quo bias, and that incorporates the standard choice theory as a special case. We follow a revealed preference approach, and obtain two nested models of rational choice that allow phenomena like the status quo bias and the endowment effect, and that are applicable in any choice situation to which the standard (static) choice model applies.

We study axiomatically the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteries by means of a set of von Neumann-Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multi-utility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a well-defined sense.

This paper provides a variety of sufficient conditions for the existence of a nonzero fixed point of a power-bounded linear operator defined on a real Banach space. In the case of power-bounded positive operators on a Banach lattice, among the conditions we provide are not being strongly stable along with commuting with a compact operator or being quasicompact. These results apply directly to Markov operators. In the case of an arbitrary power-bounded operator on a Hilbert space, being uniformly asymptotically regular and not strongly stable guarantees the existence of a nonzero fixed point.

We consider the problem of representing a (possibly) incomplete preference relation by means of a vector-valued utility function. Continuous and semicontinuous representation results are reported in the case of preference relations that are, in a sense, not “too incomplete.” These results generalize some of the classical utility representation theorems of the theory of individual choice and paves the way towards developing a consumer theory that realistically allows individuals to exhibit some “indecisiveness” on occasion. Journal of Economic Literature Classification Number: D11.

This paper introduces a technique for mobility dominance and compares the degree of earnings mobility of men in the USA from 1970 to 1995. The highest mobility is found in the 1975–1980 or 1980–1985 periods.

We introduce a procedural model of risky choice in which an individual is endowed with a core preference relation that may be highly incomplete. She can, however, derive further rankings of alternatives from her core preferences by means of a procedure based on the independence axiom. We find that the preferences that are generated from an initial set of rankings according to this procedure can be represented by means of a "set" of von Neumann-Morgenstern utility functions, thereby allowing for incompleteness of preference relations. The proposed theory also yields new characterizations of the stochastic dominance orderings. Copyright 2002 by the Economics Department of the University of Pennsylvania and Osaka University Institute of Social and Economic Research Association

Even relatively poor people oppose high rates of redistribution because of the anticipation that they or their children may move up the income ladder. This hypothesis commonly advanced as an explanation of why most democracies do not engage in large-scale expropriation and highly progressive redistribution. But is it compatible with everyone -- especially the poor -- holding rational expectations that not everyone can simultaneously expect to end up richer than average? This paper establishes the formal basis for the POUM hypothesis. There is a range of incomes below the mean where agents oppose lasting redistributions if (and, in a sense, only if) tomorrow's expected income is increasing and concave in today's income. The laissez-faire coalition is larger, the more concave the transition function and the longer the policy horizon. We illustrate the general analysis with an example (calibrated to the U.S.) where, in every period, 3/4 of families are poorer than average, yet a 2/3 majority has expected future incomes above the mean, and therefore desires low tax rates for all future generations. We also analyze empirical mobility matrices from the PSID and find that the POUM effect is indeed a significant feature of the data.

We study the evolution of preferences via payoff monotonic dynamics in strategic environments with and without complete information. It is known that, with complete information and subgroup matching, empirically plausible interdependent preference relations may entail the local instability of individualistic preferences (which target directly the maximization of material payoffs/fitness). In contrast, under incomplete information (unobservability of preference types), we show that independent preferences are globally stable in a large set of environments and locally stable in essentially any standard environment, provided that the number of subgroups that form in the society is large. Since these results are obtained within the context of a very general model, they may be thought of as providing an evolutionary rationale for the prevalence of individualistic preferences. Journal of Economic Literature Classification Numbers: C72, D42.

We axiomatically investigate the problem of rationalizing bargaining solutions by social welfare functions that are linear in every rank-ordered subset of R n + . Such functions, the so-called Choquet integrals, have been widely used in the theories of collective and individual choice. We refer to bargaining solutions that can be rationalized by Choquet integrals as Choquet bargaining solutions. Our main result is a complete characterization of Choquet bargaining solutions. As a corollary of our main result, we also obtain a characterization of the generalized Gini bargaining solutions introduced by Blackorby et al. (1994, Econometrica 62 , 1161–1178). Journal of Economic Literature Classification Numbers: D71, C78.

We study certain classes of supermodular and submodular games which are symmetric with respect to material payoffs but in which not all players seek to maximize their material payoffs. Specifically, a subset of players have negatively interdependent preferences and care not only about their own material payoffs but also about their payoffs relative to others. We identify sufficient conditions under which members of the latter group have a strategic advantage in the following sense: at all intragroup symmetric equilibria of the game, they earn strictly higher material payoffs than do players who seek to maximize their material payoffs. The conditions are satisfied by a number of games of economic importance. We discuss the implications of these findings for the evolutionary theory of preference formation and the theory of strategic delegation. Journal of Economic Literature Classification Numbers: C72, D62.

We consider a small set of elementary properties for income movement measures, and show that there is essentially only one measure that satisfies all of these properties: the per capita aggregate change in log-incomes. We demonstrate next that this movement-mobility measure has a number of appealing descriptive and normative properties, and provide a formal generalization of our basic characterization theorem drawing from the related literature on poverty measurement. Finally, we present here an empirical application in which we show by using our new measure that there has been a broad-based increase in income movement in the United States between the 1970s and 1980s.

The variance of logarithms is a widely used inequality measure which is well known to disagree with the Lorenz criterion. Up to now, the extent and likelihood of this inconsistency were thought to be vanishingly small. We find that this view is mistaken : the extent of the disgreement can be extremely large; the likelihood is far from negligible. (This abstract was borrowed from another version of this item.)

This paper studies the conditions under which the basic results of the revealed preference theory can be established on the domain of choice problems which include non-convex feasible sets; the exercise is closely related to the works of Peters and Wakker (1991) and Bossert (1994). We show that while no continuous choice function can satisfy strong Pareto optimality over the class of all compact and comprehensive choice problems, strong Pareto optimality, Arrow's choice axiom, upper hemicontinuity and a weak compromisation postulate turn out to be necessary and sufficient to represent choice correspondences by continuous, strictly increasing and quasiconcave real-valued functions. Some applications of our main findings to axiomatic bargaining theory are also studied.

The sequential generalized Lorenz (SGL) ordering is introduced by Atkinson and Bourguignon (1987) to rank heterogeneous income distributions. It is well-known that this ordering has a strong utilitarian support. In this note, we show that one does not have to be a utilitarian to accept this welfare ordering: the SGL ordering is supported by all increasing SWFs which record an increase in overall welfare when a (cardinal) welfare transfer is made from less needy to needier.

The Lorenz–Pareto optimal frontier of a collective choice problem identifies a subset of all Pareto optimal outcomes which are not inegalitarian according to the Lorenz criterion. An inequality averse choice function must thus be Lorenz–Pareto optimal in the sense that it should never `choose' an outcome outside the Lorenz–Pareto frontier of any choice problem. We study the basic properties of the Lorenz–Pareto optimal choice functions and, in particular, obtain necessary and sufficient conditions for rationalizability and representability of such choice functions. Several applications to the theory of Nash bargaining are also outlined.

Given a set of longitudinal data pertaining to two populations, a question of interest is the following: Which population has experienced a greater extent of income mobility? The aim of the present paper is to develop a systematic way of answering this question. We first put forth four axioms for income movement-mobility indices, and show that a familiar class of measures is characterized by these axioms. An unambiguous (partial) ordering is then defined as the intersection of the (complete) orderings induced by the mobility measures which belong to the characterized class; a transformation of income distributions is "more mobile" than another if, and only if, the former is ranked higher than the latter for all mobility measures which satisfy our axioms. Unfortunately, our mobility ordering depends on a parameter, and therefore, it is not readily apparent how one can apply it to panel data directly. In the second part of the paper, therefore, we derive several sets of parameter-free necessary and sufficient conditions which allow one to use the proposed mobility ordering in making unambiguous income mobility comparisons in practice.

We show that a marginal rate progressive tax always defeats a marginal rate regressive tax under pairwise majority voting (so long as the latter collects at least as much revenue as the former one) irrespective of whether the voters care at all about their relative incomes or not.

I study the problem of ranking distributions of opportunity sets on the basis of equality. The analysis begins by developing alternative ways of formulating the notion of equalizing transfers in the context of opportunity distributions. It is readily observed that any such formulation must rely on agents' preferences over individual opportunity sets, and therefore, a theory of opportunity inequality measurement must be conditional upon the “social” opportunity set ranking one postulates. Unfortunately, the results make it clear that such a theory can be constructed only when one uses the cardinality ordering of Pattanaik and Xu (1990). More precisely put, I show that it is essentially impossible to extend Dalton's transfer principle to the context of opportunity distributions unless one is content with ranking the opportunity sets only on the basis of their cardinalities. Journal of Economic Literature Classification Numbers: D31, D63, D71.

We propose the principle of equal sacrifice to determine the class of “vertically inequitable” progressive taxes. A necessary condition for an income tax function to be equal sacrifice is formulated, and hence, a subclass of progressive taxes which cannot inflict the same sacrifice upon all individuals relative toanystrictly increasing and concave utility function is determined. Conversely, it is shown in a general framework that any convex (thus progressive) tax function satisfies the principle of equal sacrifice. Our findings point to the fact that equal sacrifice under progressive income taxation depends heavily upon the degree of marginal rate (as opposed to average rate) progressivity.Journal of Economic LiteratureClassification Numbers: D63, H20.

Income mobility may be seen as arising from two sources: (i) the transfer of income among individuals with total income held constant, and (ii) a change in the total amount of income available. In this paper, we propose several sensible properties defining the concept of income mobility and show that an easily applicable measure of mobility is uniquely implied by these properties. We also show that the resulting measure is additively decomposable into the two sources listed above, namely, mobility due to the transfer of income within a given structure and mobility due to economic growth or contraction. Finally, these results are compared and contrasted with other mobility concepts and measures in the literature. Journal of Economic Literature : Classification Numbers: D31, D63.

This paper starts from the premise that the concept of income inequality is ill-defined, and hence, it studies the measurement of income inequality from a fuzzy set theoretical point of view. It is argued that the standard (fuzzy) transitivity concepts are not compatible with fuzzy inequality orderings which respect Lorenz ordering. For instance, we show that there does not exist a max-min transitive fuzzy relation on a given income distribution space which ranks distributions unambiguously according to the Lorenz criterion whenever they can actually be ranked by it. Weakening the imposed transitivity concept, it is possible to escape from the noted impossibility theorems. We introduce some alternative transitivity concepts for fuzzy relations, and subsequently, construct a class of fuzzy orderings which preserve Lorenz ordering and satisfy these alternative transitivities. It is also shown that fuzzy measurement can be used to construct confidence intervals for the crisp conclusions of inequality indices.

In an influential article by Young ( Journal of Economic Theory , 1988, 44, 321–335), it is shown that the traditional equal sacrifice principles in taxation can be justified from a non-utilitarian perspective by proving that equal sacrifice is, in fact, a consequence of more primitive concepts of distributive justice. This result is obtained in a distribution theoretic setting where total revenue to be raised is fixed. The present paper studies the same question in a setting where the basic problem is to determine a tax function without any reference to the total tax revenue (a setting which is familiar from the theory of progressive taxation) and shows that (i) there exists a utility function (which is continuous and strictly increasing) relative to which all agents sacrifice equally if and only if the tax function is incentive preserving; and (ii) any convex (hence progressive) and incentive preserving tax function equalizes sacrifice relative to a utility function which is continuous, strictly increasing and concave.

The generalized Hamming distance is commonly used in determining a closest crisp relation to a given fuzzy relation (which, in turn, is crucial in studying exact choices originating from fuzzy preferences). This note illustrates a difficulty attached to this practice, and proposes an alternative metric which is intuitively more appropriate in the case of fuzzy preferences. Some implications of this new metric on finding the nearest exact relation to a fuzzy preference ordering and on the understanding of the max-min transitivity property are also discussed.