## Taking Chances: Essays on Rational ChoiceJ. Howard Sobel has long been recognized as an important figure in philosophical discussions of rational decision. He has done much to help formulate the concept of causal decision theory. In this volume of essays Sobel explores the Bayesian idea that rational actions maximize expected values, where an action's expected value is a weighted average of its agent's values for its possible total outcomes. Newcomb's Problem and The Prisoner's Dilemma are discussed, and Allais-type puzzles are viewed from the perspective of causal world Bayesianism. The author establishes principles for distinguishing options in decision problems, and studies ways in which perfectly rational causal maximizers can be capable of resolute choices. Sobel also views critically Gauthier's revisionist ideas about maximizing rationality. This collection will be a desideratum for anyone working in the field of rational choice theory, whether in philosophy, economics, political science, psychology or statistics. Howard Sobel's work in decision theory is certainly among the most important, interesting and challenging that is being done by philosophers. |

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### Contents

Newcomblike problems | 31 |

Not every prisoners dilemma is a Newcomb problem | 77 |

Some versions of Newcombs Problem are prisoners | 89 |

Infallible predictors | 100 |

Kent Bach on good arguments | 119 |

Maximizing and prospering | 126 |

Old wine in new bottles | 141 |

Partition theorems for causal decision theories | 174 |

A principle for agents who are sure they can make mixed choices | 215 |

Maximization stability of decision and actions in accordance with reason | 218 |

Arguments and perspectives | 227 |

Restatement and elaboration | 233 |

Useful intentions | 237 |

Senses in which the rational cannot intend irrational actions | 238 |

Forming and adopting intentions | 240 |

Magical bootstrapping and rational intentions and preferences | 243 |

Causal decision theories need partition theorems | 178 |

Two partition theorems | 181 |

Fishburn and conditional acts | 185 |

Armendt on conditional preferences | 187 |

Partitions for U and Exclusive Partitions compared | 191 |

Uses of partition theorems | 192 |

A theorem for sufficiently fine partitions | 195 |

Expected utilities and rational actions and choices | 197 |

Definitions assumptions and restrictions | 198 |

The ideal stability of rational decisions | 200 |

Principles that apply tests of expected utility to actions | 202 |

A principle that confines tests of expected utility to choices | 212 |

Rational adoption of intentions to do things that would otherwise be irrational | 246 |

Conclusion | 251 |

Postscript | 252 |

Interacting causal maximizers | 255 |

The need for coercion | 257 |

The hyperrational community | 258 |

Hyperrational games | 283 |

Utility maximizers in iterated prisoners dilemmas | 330 |

A paradox regained | 345 |

367 | |

375 | |

### Common terms and phrases

agent is sure argument assume assumption backward induction Bayesian causal decision theory causally independent certainly open chance Chapter choose circumstances Column common belief conditional probabilities confess consider credences and preferences David Gauthier decision problem Definition Desirability maximizer dominated Eells epistemic perspective equilibrium evidential Desirability expected value Gauthier given go for popcorn hyperrational games hyperrational maximizers hyperrational players ideally rational ideally stable indifferent choices intentions interaction irrational Jeffrey Jeffrey's Lemma lottery set matrix mixed strategy mixed-strategy game nearly sure Newcomb problems Newcomblike problems options outcomes partition theorems plant wheat possible practical precise choice prediction predictor principle Prisoner's Dilemma prisoners prob proposition pure strategies Rabinowicz rational actions rational agents reason relevant Row's second box sense sequence situations Sobel strictly dominated sufficiently exclusive Suppose symmetrical games take both boxes theory of rational things tion Uncle Albert utility function utility maximization utility theory versions of Newcomb's Weirich