A simpler and more realistic subjective decision theory
Bibliographic Data
| ID | 10813872 |
|---|---|
| Authors | Haim Gaifman (Columbia University), Yang Liu (0000-0003-1220-7044, University of Cambridge, corresponding author) |
| Year | 2018 |
| Volume | 195 |
| Issue | 10 |
| Pages | 4205-4241 |
| Publication date | 2018-10-01 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Synthese (JOURNAL) |
| Journal identifiers | ISSN: 0039-7857 • E-ISSN: 1573-0964 |
| Publisher | Springer Science and Business Media LLC (PUBLISHER) |
| DOI | 10.1007/s11229-017-1594-6 |
| OpenAlex | W2620577801 |
| Language | EN |
| Citations received | 4 |
| References cited | 12 |
In his classic book "the Foundations of Statistics" Savage develops a formal system of rational decision making. It is based on (i) a set of possible states of the world, (ii) a set of consequences, (iii) a set of acts, which are functions from states to consequences, and (iv) a preference relation over the acts, which represents the preferences of an idealized rational agent. The goal and the culmination of the enterprise is a representation theorem: any preference relation that satisfies certain arguably acceptable postulates determines a (finitely additive) probability distribution over the states and a utility assignment to the consequences, such that the preferences among acts are determined by their expected utilities. Additional problematic assumptions are however required in Savage's proofs. First, there is a Boolean algebra of events (sets of states) which determines the richness of the set of acts. The probabilities are assigned to members of this algebra. Savage's proof requires that this be a -algebra (i.e., closed under infinite countable unions and intersections), which makes for an extremely rich preference relation. On Savage's view we should not require subjective probabilities to be -additive. He therefore finds the insistence on a -algebra peculiar and is unhappy with it. But he sees no way of avoiding it. Second, the assignment of utilities requires the constant act assumption: for every consequence there is a constant act, which produces that consequence in every state. This assumption is known to be highly counterintuitive. The present work contains two mathematical
Algebra over a field · Constant (computer programming) · Countable set · Counterintuitive · Decision theory · Discrete mathematics · Epistemology · Mathematical economics · Mathematical proof · Preference · Preference relation · Pure mathematics · Relation (database) · Representation theorem · Set (abstract data type) · Sigma · Computer Science · Decision-Making and Behavioral Economics · Mathematics · Philosophy
| Unique citing works | 4 |
|---|---|
| Citations per year | 0,67 |
| Citation span | 2020 - 2025 (6) |
| Citation velocity | recent |
| Highly cited | No |
| Citation types | Neutral: 4 |