Threshold-Based Belief Change: Rankings and Semiorders

In this paper we study changes of beliefs in a ranking-theoretic setting using non-extremal implausibility thresholds for belief.  We represent implausibilities as ranks and introduce natural rank changes subject to a minimal change criterion. We show that many of the traditional AGM postulates for revision and contraction are preserved, except for the postulate of Preservation which is invalid. The diagnosis for belief contraction is similar, but not exactly the same. We demonstrate that the one-shot versions of both revision and contraction can be represented as revisions based on semiorders, but in two subtly different ways. We provide sets of postulates that are sound and complete in the sense that they allow us to prove representation theorems.  We show that, and explain why, the classical duality between revision and contraction, as exhibited by the Levi and Harper identities, is partly broken by threshold-based belief changes. We also study the logic of iterated threshold-based revision and contraction. The traditional Darwiche-Pearl postulates for iterated revision continue to hold, as well as two additional postulates that characterize ranking-based revision as a restricted `improvement' operator. We investigate the dual notion of iterated threshold-based belief contraction and provide a new set of postulates for it, characterizing contraction as a restricted 'degrading' operator

Essays in organization formation and decision making

This thesis consists of three essays in microeconomic theory. The first two are about the formation of organizations, and the third is about individual or organizational decision making in ambiguous settings. In the first essay I explore the implications of costs associated with binding agreements on equilibrium agreement structures. Establishing binding agreements is often costly in real world economies. These contracting costs are usually regarded as harmful by economists as the costs decrease the gains from cooperation. They affect which agreements form by changing the incentives of agents, potentially prevent the establishment of efficient contracts. Using an alternating offers bargaining model of coalition formation I show that the presence of transaction costs can lead to an efficient outcome in situations where inefficiency arises in equilibrium without these costs. These results provide new insights for policies targeting transaction costs. There are many situations in Economics and Political Science that involve limited possibilities for firms or parties to organize themselves into groups, mostly due to regulatory restrictions. In addition, in these settings the surplus of a given group often depends on the organizational structures formed outside of the group. The second essay introduces a coalition formation model that is able to analyze markets with both restricted cooperation and externalities across coalitions. This concept allows a more realistic modeling, opening the possibility to use this framework to analyze the welfare effects of mergers. In the third essay I propose a new model of decision making under uncertainty with multiple priors that is, unlike the well-known model of Gilboa and Schmeidler (1989), able to express attitude towards ambiguity. In addition, the decision does not necessarily depend on the two extreme (worst case and best case) priors as in the model of Ghirardato et al. (2001). I use choice correspondences by lexicographic semiorders that are generalizations of the choice functions defined in Manzini and Mariotti (2012). I also provide a method constructing lexicographic semiorders for choosing from ambiguous acts

Decision Making and Trade without Probabilities

What is a rational decision-maker supposed to do when facing an unfamiliar problem, where there is uncertainty but no basis for making probabilistic assessments? One answer is to use a form of expected utility theory, and assume that agents assign their own subjective probabilities to each element of the (presumably known) state space. In contrast, this paper presents a model in which agents do not form subjective probabilities over the elements of the state space, but nonetheless use new information to update their beliefs about what the elements of the state space are. This model is shown to lead to different predictions about trading behavior in a simple asset market under uncertainty. A controlled laboratory experiment tests the predictions of this model against those of expected utility theory and against the hypothesis that subjects act na¨ıvely and non-strategically. The results suggest that a lack of subjective probabilities does not imply irrational or unpredictable behavior, but instead allows individuals to use both what they know and knowledge of what they do not know in their decision making. Comment un décideur rationnel est-il censé réagir face à un problème qui ne lui est pas familier lorsquâil existe une certaine incertitude, et en lâabsence dâune base sur laquelle effectuer des estimations probabilistes? Une solution consiste à utiliser une forme de la théorie de lâutilité espérée et de présumer que les agents attribuent leurs propres probabilités subjectives à chaque élément de la représentation dâétat (sans doute connue). Par contraste, notre article présente un modèle où les agents ne forment pas de probabilités subjectives sur les éléments de la représentation dâétat, mais utilisent de nouveaux renseignements afin de mettre à jour leurs croyances sur les éléments formant la représentation dâétat. Le comportement des échanges avec ce modèle dans un marché dâactifs simple et incertain nous mène à des prédictions différentes. En utilisant une expérience contrôlée en laboratoire, nous avons vérifié les prédictions de ce modèle contre celles de la théorie de lâutilité espérée et contre lâhypothèse que les sujets agissent avec naïveté et sans recourir à une stratégie. Les résultats suggèrent quâun manque de probabilités subjectives nâimplique pas un comportement irrationnel ou imprévisible, mais permet plutôt aux individus dâutiliser autant lâinformation quâils possèdent que la connaissance de lâinformation quâils ne possèdent pas dans leur prise de décision.Uncertainty; non-expected utility; incomplete preferences; ambiguity., Incertitude, utilité non espérée, préférences incomplètes, ambiguïté.

Preference Modelling

This paper provides the reader with a presentation of preference modelling fundamental notions as well as some recent results in this field. Preference modelling is an inevitable step in a variety of fields: economy, sociology, psychology, mathematical programming, even medicine, archaeology, and obviously decision analysis. Our notation and some basic definitions, such as those of binary relation, properties and ordered sets, are presented at the beginning of the paper. We start by discussing different reasons for constructing a model or preference. We then go through a number of issues that influence the construction of preference models. Different formalisations besides classical logic such as fuzzy sets and non-classical logics become necessary. We then present different types of preference structures reflecting the behavior of a decision-maker: classical, extended and valued ones. It is relevant to have a numerical representation of preferences: functional representations, value functions. The concepts of thresholds and minimal representation are also introduced in this section. In section 7, we briefly explore the concept of deontic logic (logic of preference) and other formalisms associated with "compact representation of preferences" introduced for special purpoes. We end the paper with some concluding remarks

On strengthening the logic of iterated belief revision: proper ordinal interval operators

Darwiche and Pearl’s seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. However, most of the suggestions for doing so have been radical enough to result in a dubious ‘reductionist’ principle that identifies belief states with orderings of worlds. The present paper offers a more modest strengthening of Darwiche and Pearl’s proposal. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles govern the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the family that these principles characterise, which subsumes both lexicographic and restrained revision, can be represented as relating belief states that are associated with a ‘proper ordinal interval’ assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of a large number of AGM era postulates

A Humean Theory of Choice of which Rationality May Be One Consequence

For the reader who considers economic theory of choice as a special case of a more general theory of action, Hume's discussion of the determinants of action in the Treatise of Human Nature (1739-1740), in the Enquiry on Human Understanding (1748), and in the Dissertation on Passions (1757), deserves attention. However, according to some modern commentators, Hume does not seem to have given any evidence which would favour what we nowadays consider as the kind of rationality involved in modern theories of rational choice. On the contrary, this paper arrives to the conclusion that consistency between preferences and choice, like the usual properties of completeness and transitivity, may be considered as outcomes of a mental process, described by means of a decision algorithm which aims at representing Hume's theory of choice.Hume; rationality; decision; passion; desire; preference; will; choice; rationalité; décision; désir; préférences, volonté; choix

Introduction to social choice and welfare

Social choice theory is concerned with the evaluation of alternative methods of collective decision-making, as well as with the logical foundations of welfare economics. In turn, welfare economics is concerned with the critical scrutiny of the performance of actual and/or imaginary economic systems, as well as with the critique, design and implementation of alternative economic policies. The Handbook of Social Choice and Welfare, which is edited by Kenneth Arrow, Amartya Sen and Kotaro Suzumura, presents, in two volumes, essays on past and on-going work in social choice theory and welfare economics. This paper is written as an extensive introduction to the Handbook with the purpose of placing the broad issues examined in the two volumes in better perspective, discussing the historical background of social choice theory, the vistas opened by Arrow's Social Choice and Individual Values, the famous "socialist planning" controversy, and the theoretical and practical significance of social choice theory.social choice theory, welfare economics, socialist planning controversy, social welfare function, Arrovian impossibility theorems, voting schemes, implementation theory, equity and justice, welfare and rights, functioning and capability, procedural fairness