Dynamic consistency in the logic of decision
- PDF / 277,039 Bytes
- 12 Pages / 439.37 x 666.142 pts Page_size
- 104 Downloads / 278 Views
Dynamic consistency in the logic of decision Gerard J. Rothfus1
Ó Springer Nature B.V. 2020
Abstract Arif Ahmed has recently argued that causal decision theory is dynamically inconsistent and that we should therefore prefer evidential decision theory. However, the principal formulation of the evidential theory, Richard Jeffrey’s Logic of Decision, has a mixed record of its own when it comes to evaluating plans consistently across time. This note probes that neglected record, establishing the dynamic consistency of evidential decision theory within a restricted class of problems but then illustrating how evidentialists can fall into sequential incoherence outside of this class. Uncovering the evidentialist’s own dynamic inconsistencies reveals, contra Ahmed, that sequential choice considerations do not significantly favor the evidentialist’s theory over the causalist’s. Keywords Decision theory Newcomb’s problem Sequential choice Dynamic consistency
1 Introduction The familiar debate between Evidential Decision Theory (EDT) and its chief rival, Causal Decision Theory (CDT), has traditionally been carried out in the context of static choice. The main examples employed to motivate and arbitrate the dispute,
& Gerard J. Rothfus [email protected] 1
Department of Logic and Philosophy of Science, University of California, Irvine, USA
123
G. J. Rothfus
from Newcomb to Psycho-Button, all involve an agent tasked with making a single decision at a particular point in time.1 One of the many contributions of Arif Ahmed’s recent book has been to freshen the debate by suggesting the relevance of sequential choice arguments.2 In doing so, Ahmed uncovers an awkward feature of CDT: the agents it describes can fall prey to dynamic inconsistency when tasked with making a series of decisions across time. Ahmed takes this discovery as an argument for EDT.3 Of course, the prospects for such an argument hinge upon how EDT itself fares in the context of sequential choice. The dynamic inconsistency of CDT will provide little reason to embrace EDT if evidentialists are themselves dynamically inconsistent. Hence, advancing the EDT/CDT debate any further along the lines Ahmed has suggested requires vetting the dynamic consistency properties of EDT. Embarking upon such an investigation, it is natural to begin by considering how the principal formulation of EDT, Richard Jeffrey’s Logic of Decision,4 fares in the sort of sequential choice problems that lead to trouble for CDT and then to proceed to consider more general contexts of sequential choice. As it turns out, taking this path affords momentary comfort for the evidentialist: the dynamic consistency of EDT is guaranteed within the simple class of problems that Ahmed employs to make trouble for CDT. However, it ends in disappointment: when we countenance more general types of dynamic choice problems, the Logic of Decision fails to offer a sequentially coherent account of rational choice. The present note travels this course, with Sect. 2 offering the initial comfort, Sect. 3 su
Data Loading...
