Abstract
The first three paradoxes revolved around questions of what would be factually true, given certain assumptions. The rest concern questions of what someone called the player should do given certain situations, thereby entering the realm of decision theory. To guard the claim that these paradoxes depend on probability concepts, the possible meanings of “should” must be severely curtailed. This can be accomplished by stipulating a few intuitively obvious rules such as that given a choice between two options, the player should take the one of greater value, and also by stipulating the values assigned to relevant elements in the problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The Betting Crowd is superficially of this form (note the players aren’t given a choice) but the betting is as eliminable as the shooting. The core paradox rests on a probability question: on any round before the dice are rolled, does the player have a higher probability of winning or losing?
- 2.
We are speaking exclusively of normative decision theory which seeks the rational or optimal decision; descriptive decision theory, which seeks to understand human decision making behavior, is an experimental science in the standard sense.
- 3.
I omit the dollar signs from monetary amounts and expected values; the numbers can then be interpreted as money or as units of utility. In the latter case “expected value” should be replaced with “expected utility”.
- 4.
The usual definition of screening off is \( {\text{P}}({\text{X}}\left| {{\text{YZ}}){\text{ = P(X}}\left| {{\text{Z)}}{\text{.}}} \right.} \right.\) (Eells 1991 p. 223) This can be rewritten \( \frac{{{\text{P(XYZ)}}}}{{{\text{P(YZ)}}}}{\text{ = }}\frac{{{\text{P(XZ)}}}}{{{\text{P(Z)}}}}. \) Multiply both sides by P(YZ)/P(Z). Then \( \frac{{{\text{P(XYZ)}}}}{{{\text{P(Z)}}}}{\text{ = }}\frac{{{\text{P(XZ)}}}}{{{\text{P(Z)}}}}\frac{{{\text{P(YZ)}}}}{{{\text{P(Z)}}}} \) which is \( {\text{P(XY}}\left| {{\text{Z) = P(X}}\left| {{\text{Z)P(Y}}\left| {{\text{Z)}}} \right.} \right.} \right. \) the definition of independence conditional on Z.
- 5.
Jeffery (1983, p. 20) speaks of “the central heartland of decision theory, where probabilities conditionally on acts are expectations of their influence on relevant conditions”. This is the territory of causal problems where all decision theories work together in harmony.
- 6.
They are the clearest; the Solomon story is tarnished by the staggering immorality of Solomon’s using his royal status to coerce a married woman into adultery, the prisoner’s dilemma by gains obtained through betrayal, both of which the analyst is supposed to ignore because no evaluation is assigned to these moral matters in the problem’s specifications.
References
Eells, E. (1982). Rational Decision and Causality. Cambridge: Cambridge University.
Eells, E. (1984). Metatickles and the dynamics of deliberation. Theory and Decision, 17, 71–95.
Eells, E. (1991). Probabilistic Causality. Cambridge: Cambridge.
Gibbard, A., & Harper, W. (1978). Counterfactuals and two kinds of expected utility. Foundations and Applications of Decision Theory, Hooker, Leach & McClennen (eds.) vol. 1, D. Dordrecht: Reidel, 125–162. Reprinted in Gardenfors & Sahlin 1988, Decision, probability and utility and with abridgement in Cambell & Sowden 1985. Paradoxes of rationality and cooperation.
Jeffery, R. (1965). The Logic of Decision. New York: McGraw-Hill.
Jeffery, R. (1983). Revised edition of Jeffery (1965) University of Chicago, Chicago.
Kyburg, H. (1980). Acts and conditional probability. Theory and decision 12, 149–171.
Lewis, D. (1981). Causal decision theory. Australasian Journal of Philosophy, 59(1), 5–30. Reprinted in Lewis; 1986, and in Gardenfors & Sahlin; (1988).
Skyrms, B. (1982). Causal decision theory. The Journal of Philosophy, 79, 695–711.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2013 The Author(s)
About this chapter
Cite this chapter
Eckhardt, W. (2013). Newcomb’s Problem. In: Paradoxes in Probability Theory. SpringerBriefs in Philosophy. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5140-8_5
Download citation
DOI: https://doi.org/10.1007/978-94-007-5140-8_5
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-5139-2
Online ISBN: 978-94-007-5140-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)