Book contents
- Frontmatter
- Contents
- Conditions on orderings and acceptable-set functions
- Acknowledgments
- 1 Introduction and sketch of the main argument
- 2 The ordering principle
- 3 The independence principle
- 4 The problem of justification
- 5 Pragmatic arguments
- 6 Dynamic choice problems
- 7 Rationality conditions on dynamic choice
- 8 Consequentialist constructions
- 9 Reinterpreting dynamic consistency
- 10 A critique of the pragmatic arguments
- 11 Formalizing a pragmatic perspective
- 12 The feasibility of resolute choice
- 13 Connections
- 14 Conclusions
- 15 Postscript: projections
- Notes
- Bibliography
- Author index
- Subject index
2 - The ordering principle
Published online by Cambridge University Press: 05 February 2012
- Frontmatter
- Contents
- Conditions on orderings and acceptable-set functions
- Acknowledgments
- 1 Introduction and sketch of the main argument
- 2 The ordering principle
- 3 The independence principle
- 4 The problem of justification
- 5 Pragmatic arguments
- 6 Dynamic choice problems
- 7 Rationality conditions on dynamic choice
- 8 Consequentialist constructions
- 9 Reinterpreting dynamic consistency
- 10 A critique of the pragmatic arguments
- 11 Formalizing a pragmatic perspective
- 12 The feasibility of resolute choice
- 13 Connections
- 14 Conclusions
- 15 Postscript: projections
- Notes
- Bibliography
- Author index
- Subject index
Summary
Weak preference orderings
It is a cornerstone of the modern theory of utility and subjective probability that a rational decision maker must have coherent preferences with regard to the set of options that he faces in any decision problem. On the usual account, “coherent” is taken to mean that the agent's preference ordering over any set of options must be both connected and fully transitive. In what follows I adopt the usual convention of using P to denote the (strict) preference, I to denote the indifference, and R to denote the preference-or-indifference (weak preference), relation. Correspondingly, I take X to be the set of (mutually exclusive and exhaustive) options that define a decision problem for an agent. In terms of these conventions, connectedness and transitivity are defined in the following manner:
An agent's ordering of X is connected just in case for any x and y in X, either x R y or y R x (possibly both).
An agent's ordering of x is fully transitive just in case for any x, y, and z in X, if x R y and y R z, then x R z.
When the agent's preferences over any set of options satisfy both the connectedness and full-transitivity conditions, the convention is to speak of his preferences as constituting a weak ordering of X. The qualifier “weak” derives from the consideration that the ordering in question leaves open the possibility that two distinct elements may be ranked indifferently to one another.
- Type
- Chapter
- Information
- Rationality and Dynamic ChoiceFoundational Explorations, pp. 20 - 43Publisher: Cambridge University PressPrint publication year: 1990