Expected Accuracy Supports Conditionalization—and Conglomerability and Reflection

Expected accuracy arguments have been used by several authors (Leitgeb and Pettigrew and Greaves and Wallace) to support the diachronic principle of conditionalization, in updates where there are only finitely many possible propositions to learn. I show that these arguments can be extended to infinite cases, giving an argument not just for conditionalization but also for principles known as ‘conglomerability’ and ‘reflection’. This shows that the expected accuracy approach is stronger than has been realized. I also argue that we should be careful to distinguish diachronic update principles from related synchronic principles for conditional probability.

[1]  Van Fraassen,et al.  A PROBLEM FOR RELATIVE INFORMATION MINIMIZERS IN PROBABILITY KINEMATICS , 1981 .

[2]  Branden Fitelson,et al.  An ‘Evidentialist’ Worry About Joyce's Argument for Probabilism , 2012 .

[3]  Brian Skyrms,et al.  Bayes or Bust , 2000 .

[4]  Bas C. van Fraassen,et al.  Belief and the problem of Ulysses and the sirens , 1995 .

[5]  A. Elga,et al.  Bayesianism, Infinite Decisions, and Binding , 2004 .

[6]  Van Fraassen,et al.  Belief and the Will , 1984 .

[7]  Richard Pettigrew,et al.  An Objective Justification of Bayesianism I: Measuring Inaccuracy* , 2010, Philosophy of Science.

[8]  L. Dubins.  Finitely Additive Conditional Probabilities, Conglomerability and Disintegrations , 1975 .

[9]  Wayne C. Myrvold.  Epistemic values and the value of learning , 2010, Synthese.

[10]  D. Bradley.  Four Problems about Self-Locating Belief , 2012 .

[11]  Alan Hájek,et al.  What Conditional Probability Could Not Be , 2003, Synthese.

[12]  Alan Hájek,et al.  What Are Degrees of Belief? , 2007, Stud Logica.

[13]  Peter Whittle,et al.  Probability via expectation , 1992 .

[14]  H. Leitgeb,et al.  An Objective Justification of Bayesianism II: The Consequences of Minimizing Inaccuracy* , 2010, Philosophy of Science.

[15]  Michael G. Titelbaum.  The Relevance of Self-Locating Beliefs , 2008 .

[16]  Christopher J. G. Meacham.  Sleeping beauty and the dynamics of de se beliefs , 2008 .

[17]  David Christensen,et al.  Clever Bookies and Coherent Beliefs , 1991 .

[18]  James M. Joyce.  Accuracy and Coherence: Prospects for an Alethic Epistemology of Partial Belief , 2009 .

[19]  Joseph B. Kadane,et al.  Rethinking the Foundations of Statistics: Statistical Implications of Finitely Additive Probability , 1999 .

[20]  David Lindley.  Scoring rules and the inevitability of probability , 1982 .

[21]  D. Gauthier.  Assure and Threaten , 1994, Ethics.

[22]  Gregory S. Kavka.  The toxin puzzle , 1983 .

[23]  David Wallace,et al.  Justifying Conditionalization: Conditionalization Maximizes Expected Epistemic Utility , 2006 .

[24]  Brian Skyrms,et al.  The Dynamics Of Rational Deliberation , 1990 .

[25]  E. McClennen.  Rationality and Dynamic Choice: Foundational Explorations , 1996 .

[26]  Jaines M. Joyce.  A Nonpragmatic Vindication of Probabilism , 1998, Philosophy of Science.

[27]  Edward S. Hinchman.  Trust and Diachronic Agency , 2003 .

[28]  Frank Arntzenius,et al.  Some Problems for Conditionalization and Reflection , 2003 .

[29]  Kenneth Krishnan Easwaran,et al.  The foundations of conditional probability , 2008 .