Peter C. Fishburn (1936–2021)

Theory and Decision -     

Betting on Machina’s reflection example: an experiment on ambiguity

In a recent article, Machina (Am Econ Rev forthcoming, 2008) suggested choice problems in the spirit of Ellsberg (Q J Econ 75:643–669, 1961), which challenge tail-separability, an implication of Choquet expected utility (CEU), to a similar extent as the Ellsberg paradox challenged the sure-thing principle implied by subjective expected utility (SEU). We have tested choice behavior for bets on one of Machina’s choice problems, the reflection example. Our results indicate that tail-separability is violated by a large majority of subjects (over 70% of the sample). These empirical findings complement the theoretical analysis of Machina (Am Econ Rev forthcoming, 2008) and, together, they confirm the need for new approaches in the analysis of ambiguity for decision making.     

A parametric analysis of prospect theory’s functionals for the general population

This article presents the results of an experiment that completely measures the utility function and probability weighting function for different positive and negative monetary outcomes, using a representative sample of N = 1,935 from the general public. The results confirm earlier findings in the lab, suggesting that utility is less pronounced than what is found in classical measurements where expected utility is assumed. Utility for losses is found to be convex, consistent with diminishing sensitivity, and the obtained loss-aversion coefficient of 1.6 is moderate but in agreement with contemporary evidence. The estimated probability weighting functions have an inverse-S shape and they imply pessimism in both domains. These results show that probability weighting is also an important phenomenon in the general population. Women and lower educated individuals are found to be more risk averse, in agreement with common findings. In contrast to previous studies that ascribed gender differences in risk attitudes solely to differences in the degree utility curvature, however, our results show that this finding is primarily driven by loss aversion and, for women, also by a more pessimistic psychological response toward the probability of obtaining the best possible outcome.     

A linear generalization of Stackelberg’s model

We study an extension of Stackelberg’s model in which many firms can produce at many different times. Demand is affine, while cost is linear. In this setting, we investigate whether Stackelberg’s results in a two-firm game are robust when the number of firms increases. We show that firms may not need to anticipate further entries, leaders might earn less than in the simultaneous game, and, whatever its cost and its time of entry, the firm’s entry always improves welfare.     

Pascal’s and Tabarrok’s Wagers

In a recent paper A. Tabarrok [Believe in Pascal’s Wager? Have I Got a Deal for You!, Theory and Decision 48, 123--128, 2000] argued that a believer who accepts Pascal’s Wager should in addition accept payment of any given fee in return for a given increase in the probability of reaching God. However the conclusion is obtained from manipulations of infinities which are not valid in an expected utility model. In this note, an alternative model is formulated in which Tabarrok’s conclusion can be obtained.     

Machiavelli’s Soderini and the problem of necessity

Drawing principally on a particular example discussed by Machiavelli, this article seeks to clarify the concept of necessity and assess the Machiavellian contentions that evil-doing is in politics often necessary and justified. The example indicates that claims of necessity are best construed as allegations that evil-doing is “indispensable.” The example also indicates that these allegations are often suspect because these typically reflect limited information and knowledge and often biases and rationalizations as well, although this is not stressed by Machiavelli. Instead, Machiavelli stresses the dangers and difficulties statesmen often confront when seeking to secure important political ends or avoid costly failures, dangers and difficulties which he believes are ultimately related to the nature of human beings and the character of political elites. With respect to the morality of evil-doing, Machiavelli is suggestive of different kinds and forms of justification. Five kinds are described, and all are found unsatisfactory.     

The Philosophical Dimension of Marx’s Economic Critique

In Marx’s critique of capitalism, the economic critique is closely related to the philosophical critique. Marx’s philosophical critique established the     

Drawing Inspiration from Marx’s Diagnosis of Modernity

本文认为,尽管马克思没有使用过“现代性”这一概念,却是最早对现代社会和现代性做出全面诊断的重要思想家。马克思从经济哲学的独特眼光出发,通过对以资本主义为特征的现代社会的生活现象——商品、货币、资本、异化的分析,对现代性的本质做出了深刻的阐述,为当代学者的现代性反思提供了重要的启示。     

The senator’s tale: the development of Bremen’s bourgeoisie in the post-1945 era

Were members of the German bourgeoisie capable of forming the foundation for a new self-understanding of post-1945German society? Or did they prove to be unsuited as agents of Germany’s new beginning? This article seeks to answer these questions by focusing on historical developments in the early phase of the Federal Republic of Germany as reflected in the biography of one prominent representative of the German bourgeoisie. Theodor Spitta, who was born in 1873, was elected in 1911as a senator for life in the government of the Free Hanse City of Bremen. Spitta was an outstanding representative of a generation socialized under the last German Kaiser, a generation which perceived itself as part of a politically liberal Bremen bourgeoisie. He feared the gradual decline, indeed the disintegration of his class. None the less – or perhaps for that very reason – he committed himself to the goal of restoring a regionally specific form of bourgeois life in the city of Bremen. Although Spitta declared a ‘farewell to the bourgeoisie’ in his autobiographical texts, that did not prevent him from actively pursuing the revival of a unique urban-bourgeois ‘spirit’. This spirit was to serve as a tool in promoting Bremen’s central political goal in post-1945Germany: the preservation of the city-state’s unique status within Germany’s federal system.     

America’s policy thinking in the age of Trump

What is striking in Trumpian economics – supply-side economics too – is the omission of economic growth. There is no awareness that nations at the frontier need indigenous innovation to have ample growth. The take-offs into sustained growth in 19th century Britain and America were fueled by dynamism from the grassroots up. Moreover, this stunted economics has no room for the rewards from participating in the economy besides the market wage – for the satisfaction of succeeding at what one is doing, the sense of flourishing as one’s career unfolds, and the thrill of venturing into the unknown.     

On Hobbes’s state of nature and game theory

Hobbes’s state of nature is often analyzed in two-person two-action non-cooperative games. By definition, this literature only focuses on duels. Yet, if we consider general games, i.e., with more than two agents, analyzing Hobbes’s state of nature in terms of duel is not completely satisfactory, since it is a very specific interpretation of the war of all against all. Therefore, we propose a definition of the state of nature for games with an arbitrary number of players. We show that this definition coincides with the strategy profile considered as the state of nature in two-person games. Furthermore, we study what we call rational states of nature (that is, strategy profiles which are both states of nature and Nash equilibria). We show that in rational states of nature, the utility level of any agent is equal to his maximin payoff. We also show that rational states of nature always exist in inessential games. Finally, we prove the existence of states of nature in a class of (not necessarily inessential) symmetric games.     

The effect of unconditional preferences on Sen’s paradox

Theory and Decision - Sen’s Liberal paradox describes a conflict between weak Pareto, minimal liberalism, and either transitivity or a best element over a domain of individual preferences....