### Abstract

We reformulate expected utility theory, from the viewpoint of bounded rationality, by introducing probability grids and a cognitive bound; we restrict permissible probabilities only to decimal (ℓ-ary in general) fractions of finite depths up to a given cognitive bound. We distinguish between measurements of utilities from pure alternatives and their extensions to lotteries involving more risks. Our theory is constructive from the viewpoint of the decision maker. When a cognitive bound is small, the preference relation involves many incomparabilities, but these diminish as the cognitive bound is relaxed. Similarly, the EU hypothesis would hold more for a larger bound. The main part of the paper is a study of preferences including incomparabilities in cases with finite cognitive bounds; we give representation theorems in terms of a 2-dimensional vector-valued utility functions. We also exemplify the theory with one experimental result reported by Kahneman and Tversky.

Original language | English |
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Journal | Economic Theory |

DOIs | |

Publication status | Accepted/In press - 2019 Jan 1 |

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### Keywords

- Bounded rationality
- Cognitive bound
- Expected utility
- Incomparabilities
- Measurement of utility
- Probability grids

### ASJC Scopus subject areas

- Economics and Econometrics

### Cite this

**Expected utility theory with probability grids and preference formation.** / Kaneko, Mamoru.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Expected utility theory with probability grids and preference formation

AU - Kaneko, Mamoru

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We reformulate expected utility theory, from the viewpoint of bounded rationality, by introducing probability grids and a cognitive bound; we restrict permissible probabilities only to decimal (ℓ-ary in general) fractions of finite depths up to a given cognitive bound. We distinguish between measurements of utilities from pure alternatives and their extensions to lotteries involving more risks. Our theory is constructive from the viewpoint of the decision maker. When a cognitive bound is small, the preference relation involves many incomparabilities, but these diminish as the cognitive bound is relaxed. Similarly, the EU hypothesis would hold more for a larger bound. The main part of the paper is a study of preferences including incomparabilities in cases with finite cognitive bounds; we give representation theorems in terms of a 2-dimensional vector-valued utility functions. We also exemplify the theory with one experimental result reported by Kahneman and Tversky.

AB - We reformulate expected utility theory, from the viewpoint of bounded rationality, by introducing probability grids and a cognitive bound; we restrict permissible probabilities only to decimal (ℓ-ary in general) fractions of finite depths up to a given cognitive bound. We distinguish between measurements of utilities from pure alternatives and their extensions to lotteries involving more risks. Our theory is constructive from the viewpoint of the decision maker. When a cognitive bound is small, the preference relation involves many incomparabilities, but these diminish as the cognitive bound is relaxed. Similarly, the EU hypothesis would hold more for a larger bound. The main part of the paper is a study of preferences including incomparabilities in cases with finite cognitive bounds; we give representation theorems in terms of a 2-dimensional vector-valued utility functions. We also exemplify the theory with one experimental result reported by Kahneman and Tversky.

KW - Bounded rationality

KW - Cognitive bound

KW - Expected utility

KW - Incomparabilities

KW - Measurement of utility

KW - Probability grids

UR - http://www.scopus.com/inward/record.url?scp=85072053789&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072053789&partnerID=8YFLogxK

U2 - 10.1007/s00199-019-01225-4

DO - 10.1007/s00199-019-01225-4

M3 - Article

AN - SCOPUS:85072053789

JO - Economic Theory

JF - Economic Theory

SN - 0938-2259

ER -