As ive said, my goal is to argue that, insofar as dutch book arguments are. Alan hajek 2008 british journal for the philosophy of science 59. Alan hajek 2005 is explicit about the distinction between dutch book. Critics raise various objections to dutch book arguments hajek, 2009. This survey offers critical assessments of several kinds of dutch book arguments. A case can be made that probability is as vital a part of the philosophers toolkit as logic. Alan hajek, daniel hoek, jim joyce, harvey lederman, richard pettigrew, bernhard salow. I am more confident that this coin will land heads when tossed than i am. In gambling, a dutch book or lock is a set of odds and bets which guarantees a profit. British journal for the philosophy of science 59 4. Correspondingly, a natural way to argue for probabilism is. Read up on the dutch book argument, for example thesep on the dba suggested readings some nonempty subset of the following remember to email me your question. I suggest that cohens argument fails because a rawlsian ethos would involve correlates of both of rawls principles of justice.
The chapter begins with the classic argument for obedience to the probability calculus, emphasizing both its. It is associated with probabilities implied by the odds not being coherent in economics, the term usually refers to a sequence of trades that would leave one party strictly worse off and another strictly better off. Dutch book arguments have been invoked to defend various probabilistic norms of rationality. An argument is given here that a rule for belief change which under certain conditions violates probability kinematics will leave the agent open to a dutch book. Alan hajek, william harper, sally haslanger, mark kaplan, jeff kasser, louis loeb. Iff you violate probability theory, there exists a speci. Jul 17, 2007 probabilism is committed to two theses. The conclusion of the dba is that the degrees of belief, or credences, that an agent attaches to the members of a set x of sentences, statements, or propositions, should satisfy the axioms of probability. The idea originates with ramsey, who observed that an agent whose degrees of belief or credences fail to satisfy the basic axioms of probability would be vulnerable to a sure betting loss i.
Bayesian epistemology is a formal approach to various topics in epistemology that has its roots in thomas bayes work in the field of probability theory. Paul anand, prasanta pattanaik, and clemens puppe, forthcoming 2007. The dutch book argument, in the form that has become a philosophical staple, is simply invalid, and to the extent that. In chapter 8, well ask what happens to the dutch book arguments if we change certain features of the basic framework in which weve been working. Dutch book arguments, accuracy arguments for probabilism, decision theory, conditionals, bayesian philosophy of science and bayesian epistemology are among the main topics. Philosophers pursue various strategies for defending conditionalization. Dutch book arguments purport to show that rationality requires certain constraints on an agents subjective probabilities, on pain of the agent being susceptible to sure losses in corresponding bets. Dutch book arguments, in the oxford handbook of rational and social choice, ed. Chapter 9 of oxford handbook of probability and philosophy, eds. Dutch book arguments have been presented for static belief systems and for belief change by conditionalization. Oxford handbook of probability and philosophy, eds. In philosophy it is used to explore degrees of certainty of beliefs.
Symmetry arguments in probability northwestern scholars. Gillies, donald 2000, philosophical theories of probability, new york. Dutch book arguments philosophy oxford bibliographies. The dutch book argument assumes that an agents degrees of belief are linked with her betting quotients. Hajek, alan dutch book arguments, chapter 7 in the oxford handbook of rational and. Edited by paul anand, prasanta pattanaik, and clemens puppe, 173195. Depragmatized dutch book arguments philosophy of science. Fifteen arguments against hypothetical frequentism, alan hajek part 6. Multidisciplinary perspectives on risk, earthscan the goolabri symposium organized by. The consistency argument for ranking functions springerlink. In chapter 8, well ask what happens to the dutch book arguments if we. Four important arguments for probabilismthe dutch book, representation theorem.
Prasanta bandhopadhyay and malcolm forster, elsevier, forthcoming. Fifteen arguments against finite frequentism, alan hajek 25. The handbook of rational and social choice provides an overview of issues arising in work on the foundations of decision theory and social choice over the past three decades. Handbook of rational and social choice oxford scholarship. Oct 25, 2016 probability theory is a key tool of the physical, mathematical, and social sciences. We prove a dutch book theorem and converse dutch book theorem for this revised norm, and relate our results to rescorla 2018. The main point of the dutch book argument is to show that rational people must.
I construct rigorous explications of their arguments and show that they are not cogent. The subjective interpretation of probability identifies the concept with an agents degrees of belief. Suppose that agent as degrees of belief in s and s written dbs and dbs are each. Paul anand, prasanta pattanaik, and clemens puppe, forthcoming. Dutch book arguments stanford encyclopedia of philosophy. Intuitively, such a plan is irrational and easily dutch bookable. In the philosophy of mathematics he is particularly interested in set theory and.
Alan hajek 2005 is explicit about the distinction between dut. Jul 17, 2007 the paper provides an argument for the thesis that an agents degrees of disbelief should obey the ranking calculus. Objectivists believe in frequency theory definitions of probability, which refer to objective outcomes of events like coin flips. In particular, we show that degrees of belief that dont satisfy the principles will always guide action in some way that is bad or undesirable. The dutch book argument sees the incoherent agents glass as half empty, while the czech book argument sees it as half full. N2 the history of the use of symmetry arguments in probability theory is traced. Confirmation and induction internet encyclopedia of philosophy. Cohens argument that a prevailing ethos of justice would prevent a rawlsian just society from having any income inequalities. Professor of philosophy, australian national university. It is natural to represent my degrees of belief, or credences, with numerical values. Subjective probabilities, toto, the dutch book argument suggested readings. A bayesian framework modeling degrees of belief honorable mention for the 2015 apa book prize, winner of the 2014 arlt award from the council of graduate schools. Roger white 2009, evidential symmetry and mushy credence.
Pargetter, in defence of the dutch book argument, canadian journal of philosophy, 1985. I am grateful to brian skyrms, simon huttegger, and alan hajek for helpful discussion. A subjectivists guide to objective chance, david lewis 28. Four important arguments for probabilismthe dutch book, representation theorem, calibration, and gradational accuracy arguments have a strikingly similar structure. Department of philosophy, university of michigan the pragmatic character of the dutch book argument makes it unsuitable as an epi stemic justification for the fundamental probabilist dogma that rational partial beliefs must conform to the axioms of probability. Center for philosophy of science visiting fellows hajek. Many philosophers make the further step of claiming that the existence of a dutch book. Drawing on work by economic theorists mainly, but also with contributions from political science, philosophy, and psychology, the collection shows how the related areas of decision theory and social choice have developed in their applications and moved.
This book provides an overview of issues arising in work on the foundations of decision theory and social choice over the past three decades. Richard pettigrew, the dutch book arguments philpapers. Brian weatherson 1999 studies in history and philosophy of science part a 30. After a brief consideration of why these did not occur in ancient greece, the use of symmetry in probability, starting in the 17th century, is considered. This book is about a particular way we might try to establish these laws of credence. Colin howson and peter urbach, bayesian versus nonbayesian approaches 15. Dutch book arguments for the sleeping beauty, and to the strategic voting literature. Recently a number of authors have tried to avoid the failures of traditional dutch book arguments by separating them from pragmatic concerns of avoiding a sure loss. In gambling, a dutch book or lock is a set of odds and bets which guarantees a profit, regardless of the outcome of the gamble. Four important arguments for probabilism the dutch book, representation theorem. Iff youviolateprobabilitytheory,there exists a speci. Recently a number of authors have tried to avoid the failures of traditional dutch book arguments by separating them from pragmatic concerns of avoiding a sure. The pragmatic character of the dutch book argument makes it unsuitable as an epi.
Proceedings of the biennial meeting of the philosophy of science association 1992. Synthese, 2009 it also brings out curious features of doubly symmetric games with applications to the tragedy of the commons, which i am currently exploring with maurice koster and ines lindner. Philosophy may seem abstract and removed from everyday life, but the discipline offers argumentative strategies that anyone can use to sharpen their thinking. Darren bradley and hannes leitgeb, when betting odds and credences come apart. Uc berkeley logic group philosophy preliminary syllabus 20. Nonsharp credences, riskaversion, newcombs problem. The ramseyde finetti argument can be illustrated by an example. In dutch book arguments, we try to establish the principles of rationality for degrees of belief by appealing to their role in guiding decisions. One advantage of its formal method in contrast to traditional epistemology is that its concepts and theorems can be defined with a high degree of precision. Citeseerx document details isaac councill, lee giles, pradeep teregowda.
Dutch book arguments typically take the bookie to be the clever person who is assured of winning money off some irrational agent who has posted vulnerable odds, whereas at the racetrack it is the bookie who posts the odds in the first place. Typical assumptions in consumer choice theory rule. In this paper, we propose a revised norm, kolmogorovblackwell conditionalization, which avoids this problem. A philosophers guide to probability, in uncertainty. The oxford handbook of probability and philosophy alan. The main point of the dutch book argument is to show that rational people must have subjective probabilities for random events, and that these probabilities must satisfy the standard axioms of probability. Two broad approaches to justifying the laws of probability on subjectivist grounds are then discussed. Uc berkeley logic group philosophy preliminary syllabus. Kenny easwaran works in the areas of epistemology, decision theory, and the philosophy of mathematics.
Paul anand, prasanta pattanaik, and clemens puppe, forthcoming 2008. Unfortunately, the examples he uses to demonstrate the different. The latter says that an agents belief set is and will always be consistent and deductively closed iff her degrees of entrenchment satisfy the ranking axioms and are updated according to the ranktheoretic update. This consistency argument is based on the consistency theorem. Dutch book arguments for jeffrey conditionalization are invalid. A dutch book theorem for quantificational credences. In an essay in the digital magazine aeon, philosophy professor alan hajek outlines the tricks of the trade. Focuses on the dutch book and representation theorem arguments.
List of philosophical publications by alan hajek australian national university, including most counterfactuals are false, a tale of two epistemologies. The handbook of rational and social choice paul anand. This together with the theorem establishes that degrees of belief that violate the probability axioms are associated with bets that are fair in the above sense, but that lead to a sure loss. In this paper i examine defenses of this kind by howson and urbach, hellman, and christensen. Dutch book arguments show that violating the bayesian updating rule would result in preference for combinations.
84 645 335 133 361 726 217 1479 587 519 178 547 198 696 327 666 159 807 240 1110 989 1078 1051 1165 1281 1209 701 591 1321 130 863 1224 498 406