Preference-based arguments for probabilism

Economic Theory, 2011

This paper analyzes preferences in the presence of ambiguity that are rational in the sense of satisfying the classical ordering condition as well as monotonicity. Under technical conditions that are natural in an Anscombe-Aumann environment, we show that even for such general preference model it is possible to identify a set of priors, as first envisioned by . We then discuss ambiguity attitudes, as well as unambiguous acts and events, for the class of rational preferences we consider.

De Finetti's concept of exchangeability provides a way to formalize the intuitive idea of similarity and its role as guide in decision making. His classic representation theorem states that exchangeable expected utility preferences can be expressed in terms of a subjective beliefs on parameters. De Finetti's representation is inextricably linked to expected utility as it simultaneously identifies the parameters and Bayesian beliefs about them. This paper studies the implications of exchangeability assuming that preferences are monotone, transitive and continuous, but otherwise incomplete and/or fail probabilistic sophistication. The central tool in our analysis is a new subjective ergodic theorem which takes as primitive preferences, rather than probabilities (as in standard ergodic theory). Using this theorem, we identify the i.i.d. parametrization as sufficient for all preferences in our class. A special case of the result is de Finetti's classic representation. We also prove: (1) a novel derivation of subjective probabilities based on frequencies;

Journal of Economic Theory, 2021

We prove that a random choice rule satisfies Luce's Choice Axiom if and only if its support is a choice correspondence that satisfies the Weak Axiom of Revealed Preference, thus it consists of alternatives that are optimal according to some preference, and random choice then occurs according to a tie breaking among such alternatives that satisfies Renyi's Conditioning Axiom. Our result shows that the Choice Axiom is, in a precise formal sense, a probabilistic version of the Weak Axiom. It thus supports Luce's view of his own axiom as a "canon of probabilistic rationality." * This paper combines and supersedes two independent works: Paper 6 (Lindberg, 2012b) of the thesis of Lindberg (2012a) and a working paper of Cerreia-Vioglio Maccheroni, Marinacci, and Rustichini (2016). We thank Sean Horan, Marco Pavan (the editor), an anonymous associate editor, and two anonymous referees for very helpful comments, as well as the ERC (grants SDDM-TEA and INDIMACRO) and a PRIN grant (2017CY2NCA) for financial support.

2018

OF THE DISSERTATION Three Essays in the Theory of Preferences by SEYED HASSAN NOSRATABADI Dissertation Director: Oriol Carbonell-Nicolau This dissertation consists of three chapters. The first chapter addresses the classical questions of utility representation and maximization. It relaxes the notion of weak upper continuity (Campbell and Walker (1990)) to obtain a property called partial weak upper continuity and shows that both maximization of preferences and representation by a utility function can be achieved under this new property. The rest of this dissertation focuses on extending revealed preference theory to accommodate behavioral anomalies observed in the experimental data. In particular, I offer a framework to expand the theory of revealed preferences to the case where a DM’s choice is not completely identified with a single preferences. In Chapter 2, I use a divide and conquer procedure in order to expand the revealed preference theory to accommodate behavioral anomalies ...

Preference Change, 2009

In this paper we consider preference over objects. We show how this preference can be derived from priorities, properties of these objects, a concept which is initially from optimality theory. We do this both in the case when an agent has complete information and in the case when an agent only has beliefs about the properties. After the single agent case we also consider the multi-agent case. In each of these cases, we construct preference logics, some of them extending the standard logic of belief. This leads to interesting connections between preference and beliefs. We strengthen the usual completeness results for logics of this kind to representation theorems. The representation theorems describe the reasoning that is valid for preference relations that have been obtained from priorities. In the multi-agent case, these representation theorems are strengthened to the special cases of cooperative and competitive agents. We study preference change with regard to changes of the priority sequence, and change of beliefs. We apply the dynamic epistemic logic approach, and in consequence reduction axioms are presented. We conclude with some possible directions for future work.

Economics Letters, 2017

We provide a taxonomy of 4 known models of rationalization with (possibly) incomplete preferences. • We provide a novel characterization of rationalizability that gives a new interpretation of WARP. • Our taxonomy provides a novel axiomatic rationale for a moderate attraction effect.

Reasoning Rationality and Probability, 2008

This paper discusses pragmatic arguments for 'rationality constraints' on a decision maker's state of mind-on her beliefs or preferences. Arguments of this kind purport to show that a violator of a given constraint can be made to act to her guaranteed disadvantage. To put it dramatically, she can be exploited by a clever bookie, who doesn't need to know more than the agent to be exploited in order to set up his exploitation scheme. The locus classicus for such arguments is Frank Ramsey's essay on "Truth and Probability", where the general idea is floated for the first time: If anyone's mental condition violated these laws [= the laws of probability], … [h]e could have a book made against him by a cunning bettor and would then stand to lose in any event. (Ramsey 1990 (1926), p. 78) Well-known examples of pragmatic arguments are synchronic Dutch Books, for the standard probability axioms, diachronic Dutch Books, for the more controversial principles of reflection and conditionalization, and Money Pumps, for the acyclicity requirement on preferences. When one examines these examples, one thing stands out: The proposed exploitation setups share a common feature. Suppose an agent is logically and mathematically competent. Assume also that she prefers being better off than worse off and acts accordingly. Then, as we shall see, even if she violates a given constraint, she cannot be exploited unless she is disunified in her decision-making. By this I mean that exploitation is possible only if the agent makes decisions on various issues * This paper is an expanded and extensively revised version of my contribution to a collection of essays on Isaac Levi's philosophy (cf. Rabinowicz 2006). Along with several other changes, it responds to some criticisms made by Levi in his reply (Levi 2006). I am indebted to several people for comments and discussion. Luc Bovens and John Broome have been especially helpful in this respect. My work on this subject was supported by a research grant from The Bank of Sweden's Tercentenary Foundation and was partly conducted during my stay at The Swedish Collegium for Advanced Study in the Social Sciences (SCASSS) in Uppsala. I am indebted to the participants of my seminar at SCASSS in 2004, for their useful comments. Some of the material in this paper was presented at the Ramsey Centennial conference in Cambridge in 2003, at a workshop on philosophy and probability in Bielefeld that same year, at a workshop on logic in games, language and computation in Amsterdam in 2004, at a conference on rationality and patterns of reasoning in Bertinoro that same year, and at seminars in Canberra (Social and Political Theory, Research School for Social Sciences), Stanford (department of philosophy) and Lund (departments of philosophy and economics). I would like to thank the organizers and the participants of these events.

2002

Written by an international assembly of distinguished philosophers, the Blackwell Philosophy Guides create a groundbreaking student resource -a complete critical survey of the central themes and issues of philosophy today. Focusing and advancing key arguments throughout, each essay incorporates essential background material serving to clarify the history and logic of the relevant topic. Accordingly, these volumes will be a valuable resource for a broad range of students and readers, including professional philosophers.

Preferences. Berlin; New York: de Gruyter, 1998

Theories of rational decision normally distinguish basic and other preferences, using only the former for calculating the utility function of an agent. The idea behind the distinction is that, on the one hand, a theory of rational decision must allow criticism of at least a part of the agent's actual preferences; on the other hand, so as not to lose touch with the agent's real interests, it must rely on his factual preferences. Different decision theories have declared as basic various sets of preferences, thereby arriving at very different utility functions. Therefore, the question of which preferences shall be basic is of large practical importance. Nonetheless, it has rarely been discussed.