### Discussion Paper

## Abstract

The paper explores utility measures by combining experiments with mathematical derivations in psychophysics paradigm. The analysis on ultimatum game experiment reveals an evidence for utility threshold and thus supports Bernoulli’s utility logarithmic law. Both experimental results and theoretical derivations show that the logarithmic law is suitable for the description of commodity choice and the power law for risk choice. The further mathematical demonstration indicates the logarithmic law for utility scaling to be a Klein–Rubin utility function, a utility function well defined in microeconomics. Based on this, the experimental utility measure is connected with the econometric model Linear Expenditure System, and presents an experimental procedure for testing the utility maximization hypothesis, which will remove a long unsettled perplexity in a fundamental stone of economics since Gossen proposed it in 1854.

## Comments and Questions

Augmenting psycology components of description of economy is certainly a topical question paving the way to a new economic ideology.

Mathematical approaches have constructed a systematic form for economics, while, psychological experimental approaches have revealed many realistic behavioral attributes for economics. They all are important. If mathematics and psychology can be combined in economics, economics will possibly become a systematic science with experimental and empirical basis.

But, whilst psycology is reclaimed to provide realism to mathematical equilibrium economics, it won't surely add "precision". Likely the opposite.

If unrealistic parables have to be completed by uncontrastable behavior assumptions, unable to be measured, where are we and where are we going to?

When will we be ready to ...[more]

... consider the possiblity of founding a social science which deserves that name? I mean, a science free of dogma, and open to relavant, realistic, assumptions, which nowadays are a priori excluded of any consideration.

In Aristotle times, physics had ever been filled with dogmas. After Galileo and Newton, physics became a science free of dogmas. It is of the result combining experimental with mathematical approaches. Comparing with Aristotle’s overall thinking way, modern science developed along an analytic path in which objects were treated by ...[more]

... experimental and mathematical decompositions. The analytic approach in modern physics concentrates on specific positive starting point, introduces operational definitions for each object, and logically stretches to the overall discipline. I think that clarifying the fundamental concepts in economics by introducing operational definitions may be an appropriate starting point. The problem that where will we finally go should be left for tomorrow. The most important is that we should have a positive and operational starting point today.

see attached file

Reply to Professor R. Duncan Luce’s report

See the attached file

I have no doubt the content of this paper is of great importance for two reasons:

1) It demonstrates the importance of Psychophysical research as the foundation for serious quantitative explorations of a foundational component of the discipline of Economics, viz, the notion of a quantifiable numerical representation of commodity ...[more]

... "value."

2) It suggests the importance of distinguishing between the utility of of risky choices and the utility of commodity choices. Once again we see a clear distinction between two kinds of economic judgment, a position I have long supported.

The analytical work reported appears to me to capture the conceptual essence of the economic argument. I have not examined the conjectures, accepted principles, or common interpretation of the analysis, but unless there is an error in notion that I have not noticed, this work appears appropriate for publication.

I am sorry to note that the author has not included references to the work of E. Galanter on power function representations of utilities, and the scaling techniques associated with this work, and that of S.S. Stevens, and others working on various metrics associated with judgements of value.

I would like to thank the second referee for his comments on my paper, and revise the paper according to his sugestions.

See the attached file