1,074 research outputs found

    von Neumann-Morgenstern and Savage Theorems for Causal Decision Making

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    Causal thinking and decision making under uncertainty are fundamental aspects of intelligent reasoning. Decision making under uncertainty has been well studied when information is considered at the associative (probabilistic) level. The classical Theorems of von Neumann-Morgenstern and Savage provide a formal criterion for rational choice using purely associative information. Causal inference often yields uncertainty about the exact causal structure, so we consider what kinds of decisions are possible in those conditions. In this work, we consider decision problems in which available actions and consequences are causally connected. After recalling a previous causal decision making result, which relies on a known causal model, we consider the case in which the causal mechanism that controls some environment is unknown to a rational decision maker. In this setting we state and prove a causal version of Savage's Theorem, which we then use to develop a notion of causal games with its respective causal Nash equilibrium. These results highlight the importance of causal models in decision making and the variety of potential applications.Comment: Submitted to Journal of Causal Inferenc

    The Collapse of Interwar Vienna: Oskar Morgenstern’s Community, 1925 - 1950

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    From the perspective of science, art and intellectual life in general, Interwar Vienna was one of the most vibrant communities in modern European history. Within the field of economics, it was home to, amongst others, Ludwig von Mises, Friedrich von Hayek, Hans Mayer, Gottfried Haberler, Fritz Machlup, Oskar Morgenstern, Karl Menger and Abraham Wald. The community flourished after the end of World War I, and then began to suffer in the early 1930’s as a result of growing political instability and rising anti-semitism. With the Anschluss of Austria by the Third Reich in March 1938, it collapsed completely, never to recover. Drawing on the personal papers of two key participants, Oskar Morgenstern and Karl Menger, and also on the archives of the Rockefeller Foundation, this paper provides a portrait of that community, chronicling its evolution and dramatic collapse. Particular attention is paid to the milieu surrounding Morgenstern, both as director of the Rockefeller-funded Austrian Institute for Business Cycle Research and as philosophical “dissident”. In collaborating with mathematicians Menger, Wald and, later, John von Neumann, he gradually forsook his Austrian theoretical legacy. The account detailed here shows conflict and tension to have been central to both the life and death of this fabled community.

    Paradoxes versus formalism in economics. Evidence from the early years of game theory and experimental economics

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    This paper argues that the acceptance of two recent methodological advances in economics, namely game theory and laboratory experimentation, was affected by the history dependence constraining the formalization of economics. After an early period in which the two methods were coolly received by economists because their applications challenged some basic hypotheses of mainstream economics, their subsequent acceptance was the result of the corroboration of those same hypotheses. However, the recent emergence of some paradoxes has finally revealed that the effectiveness of game theory and experimental techniques in economics is improved when descriptively implausible and normatively unsatisfactory assumptions such as the centrality of individual maximization in decision theory and the definition of rationality as consistency in preferences are revised.paradoxes, game theory, experiments, individual maximization, economic rationality

    A Contextual Risk Model for the Ellsberg Paradox

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    The Allais and Ellsberg paradoxes show that the expected utility hypothesis and Savage's Sure-Thing Principle are violated in real life decisions. The popular explanation in terms of 'ambiguity aversion' is not completely accepted. On the other hand, we have recently introduced a notion of 'contextual risk' to mathematically capture what is known as 'ambiguity' in the economics literature. Situations in which contextual risk occurs cannot be modeled by Kolmogorovian classical probabilistic structures, but a non-Kolmogorovian framework with a quantum-like structure is needed. We prove in this paper that the contextual risk approach can be applied to the Ellsberg paradox, and elaborate a 'sphere model' within our 'hidden measurement formalism' which reveals that it is the overall conceptual landscape that is responsible of the disagreement between actual human decisions and the predictions of expected utility theory, which generates the paradox. This result points to the presence of a 'quantum conceptual layer' in human thought which is superposed to the usually assumed 'classical logical layer'.Comment: 6 pages, 1 figur

    Surreal Decisions

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    Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring our theory to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives

    Computable Rationality, NUTS, and the Nuclear Leviathan

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    This paper explores how the Leviathan that projects power through nuclear arms exercises a unique nuclearized sovereignty. In the case of nuclear superpowers, this sovereignty extends to wielding the power to destroy human civilization as we know it across the globe. Nuclearized sovereignty depends on a hybrid form of power encompassing human decision-makers in a hierarchical chain of command, and all of the technical and computerized functions necessary to maintain command and control at every moment of the sovereign's existence: this sovereign power cannot sleep. This article analyzes how the form of rationality that informs this hybrid exercise of power historically developed to be computable. By definition, computable rationality must be able to function without any intelligible grasp of the context or the comprehensive significance of decision-making outcomes. Thus, maintaining nuclearized sovereignty necessarily must be able to execute momentous life and death decisions without the type of sentience we usually associate with ethical individual and collective decisions
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