Single-Plateaued Choice

Single-plateaued preferences generalize single-peaked preferences by allowing for multiple best elements. These preferences have played an important role in areas such as voting, strategy-proofness and matching problems. We examine the notion of singleplateauedness in a choice-theoretic setting. Single-plateaued choice is characterized by means of a collinear interval continuity property in the presence of independence of irrelevant alternatives. Further results establish that our notion of single-plateauedness conforms to the motivation underlying the term and we analyze the consequences of alternative continuity properties. The importance of basic assumptions such as closedness and convexity is discussed. Journal of Economic Literature Classification Nos.: D11, D71.

Single-plateaued choice

Single-plateaued preferences generalize single-peaked preferences by allowing for multiple best elements. These preferences have played an important role in areas such as voting, strategy-proofness and matching problems. We examine the notion of single-plateauedness in a choice-theoretic setting. Single-plateaued choice is characterized by means of a collinear interval continuity property in the presence of independence of irrelevant alternatives. Further results establish that our notion of single-plateauedness conforms to the motivation underlying the term and we analyze the consequences of alternative continuity properties. The importance of basic assumptions such as closedness and convexity is discussed. Journal of Economic Literature Classification Nos.: D11, D71.

Extensive Social Choice and the Measurement of Group Fitness in Biological Hierarchies

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 individuals at the lower level in the hierarchy. This kind of consequentialism can take account of the group fitness advantages of germ-soma specialization, which is not possible with an alternative social choice framework proposed by Okasha, but which is an essential feature of the index of group fitness for a multicellular organism introduced by Michod, Viossat, Solari, Hurand, and Nedelcu to analyze the unicellular-multicellular evolutionary transition. The new framework is also used to analyze the fitness decoupling between levels that takes place during an evolutionary transition.

Multi-Profile Intertemporal Social Choice

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 nondictatorial social welfare functions satisfying Arrow’s axioms and they can be described by their corresponding collections of decisive coalitions. We review contributions that explore whether this possibility in the infinite-population context allows for a richer class of social welfare functions in an intergenerational model. Different notions of stationarity formulated for individual and for social preferences are examined. Journal of Economic Literature Classification No.: D71.

Every Choice Function is Backwards-Induction Rationalizable

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-induction rationalizable.

A dynamic sequential route choice model for micro-simulation

Dans les études sur le transport, les modèles de choix de route décrivent la sélection par un utilisateur d’un chemin, depuis son origine jusqu’à sa destination. Plus précisément, il s’agit de trouver dans un réseau composé d’arcs et de sommets la suite d’arcs reliant deux sommets, suivant des critères donnés. Nous considérons dans le présent travail l’application de la programmation dynamique pour représenter le processus de choix, en considérant le choix d’un chemin comme une séquence de choix d’arcs. De plus, nous mettons en œuvre les techniques d’approximation en programmation dynamique afin de représenter la connaissance imparfaite de l’état réseau, en particulier pour les arcs éloignés du point actuel. Plus précisément, à chaque fois qu’un utilisateur atteint une intersection, il considère l’utilité d’un certain nombre d’arcs futurs, puis une estimation est faite pour le restant du chemin jusqu’à la destination. Le modèle de choix de route est implanté dans le cadre d’un modèle de simulation de trafic par événements discrets. Le modèle ainsi construit est testé sur un modèle de réseau routier réel afin d’étudier sa performance.

Single-basined choice

Single-basined preferences generalize single-dipped preferences by allowing for multiple worst elements. These 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. In conjunction with independence of irrelevant alternatives, single-basined choice implies a structure that conforms to the motivation underlying our definition. We also establish the consequenes of requiring single-basined choice correspondences to be upper semicontinuous, and of the revealed preference relation to be Suzumura consistent. Journal of Economic Literature.

Bayesian inference and model comparison for random choice structures

We complete the development of a testing ground for axioms of discrete stochastic choice. Our contribution here is to develop new posterior simulation methods for Bayesian inference, suitable for a class of prior distributions introduced by McCausland and Marley (2013). These prior distributions are joint distributions over various choice distributions over choice sets of di fferent sizes. Since choice distributions over di fferent choice sets can be mutually dependent, previous methods relying on conjugate prior distributions do not apply. We demonstrate by analyzing data from a previously reported experiment and report evidence for and against various axioms.

Welfare criteria from choice: the sequential solution

We study the problem of deriving a complete welfare ordering from a choice function. Under the sequential solution, the best alternative is the alternative chosen from the universal set; the second best is the one chosen when the best alternative is removed; and so on. We show that this is the only completion of Bernheim and Rangel's (2009) welfare relation that satisfies two natural axioms: neutrality, which ensures that the names of the alternatives are welfare-irrelevant; and persistence, which stipulates that every choice function between two welfare-identical choice functions must exhibit the same welfare ordering.

Population Ethics, Social Choice Theory, and Two problems in the Measurement of Economic Poverty

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A simple model of two-stage choice

I provide choice-theoretic foundations for a simple two-stage model, called transitive shortlist methods, where choices are made by sequentially by applying a pair of transitive preferences (or rationales) to eliminate inferior alternatives. Despite its simplicity, the model accommodates a wide range of choice phenomena including the status quo bias, framing, homophily, compromise, and limited willpower. I establish that the model can be succinctly characterized in terms of some well-documented context effects in choice. I also show that the underlying rationales are straightforward to determine from readily observable reversals in choice. Finally, I highlight the usefulness of these results in a variety of applications.

Strategy-proof choice of acts : a preliminary study

We model social choices as acts mapping states of the world to (social) outcomes. A (social choice) rule assigns an act to every profile of subjective expected utility preferences over acts. A rule is strategy-proof if no agent ever has an incentive to misrepresent her beliefs about the world or her valuation of the outcomes; it is ex-post efficient if the act selected at any given preference profile picks a Pareto-efficient outcome in every state of the world. We show that every two-agent ex-post efficient and strategy-proof rule is a top selection: the chosen act picks the most preferred outcome of some (possibly different) agent in every state of the world. The states in which an agent’s top outcome is selected cannot vary with the reported valuations of the outcomes but may change with the reported beliefs. We give a complete characterization of the ex-post efficient and strategy-proof rules in the two-agent, two-state case, and we identify a rich class of such rules in the two-agent case.