# Decision-Making Utility Function

(Redirected from Cost-Benefit Function)

A Decision-Making Utility Function is a numeric-output function that can be optimized to support a decision making task.

## References

### 2015b

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Preference_(economics) Retrieved:2015-4-4.
• In economics and other social sciences, preference refers to the set of assumptions related to ordering some alternatives, based on the degree of happiness, satisfaction, gratification, enjoyment, or utility they provide, a process which results in an optimal “choice” (whether real or theoretical). The character of the individual preferences is determined purely by taste factors, independent of considerations of prices, income, or availability of goods.

With the help of the scientific method many practical decisions of life can be modelled, resulting in testable predictions about human behavior. Although economists are usually not interested in choices or preferences in themselves, they are interested in the theory of choice because it serves as a background for empirical demand analysis.[1]

1. Cite error: Invalid `<ref>` tag; no text was provided for refs named `Arrow, Kenneth 1958`

### 2015c

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Preference_(economics)#Strict_versus_weak Retrieved:2015-4-4.
• The possibility of defining a strict preference relation [math] \succ\! [/math] from the weaker one [math] \succsim\! [/math] , and vice versa, suggest in principle an alternative approach of starting with the strict relation [math] \succ\! [/math] as the primitive concept and deriving the weaker one and the indifference relation. However, an indifference relation derived this way will generally not be transitive.[1] According to Kreps "beginning with strict preference makes it easier to discuss noncomparability possibilities".[2]
1. Cite error: Invalid `<ref>` tag; no text was provided for refs named `Barten 1982 p. 384`
2. Kreps, David. (1990). A Course in Microeconomic Theory. New Jersey: Princeton University Press

### 2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Utility#Quantifying_utility Retrieved:2014-9-23.
• It was recognized that utility could not be measured or observed directly, so instead economists devised a way to infer underlying relative utilities from observed choice. These 'revealed preferences', as they were named by Paul Samuelson, were revealed e.g. in people's willingness to pay:

Utility is taken to be correlative to Desire or Want. It has been already argued that desires cannot be measured directly, but only indirectly, by the outward phenomena to which they give rise: and that in those cases with which economics is chiefly concerned the measure is found in the price which a person is willing to pay for the fulfilment or satisfaction of his desire.[1]Template:Rp

### 2014b

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Utility Retrieved:2014-8-31.
• Utility, or usefulness, is the ability of something to satisfy needs or wants. [2] Utility is an important concept in economics and game theory, because it represents satisfaction experienced by the consumer of a good. Not coincidentally, a good is something that satisfies human wants and provides utility, for example, to a consumer making a purchase. It was recognized that one can not directly measure benefit, satisfaction or happiness from a good or service, so instead economists have devised ways of representing and measuring utility in terms of economic choices that can be counted. Economists have attempted to perfect highly abstract methods of comparing utilities by observing and calculating economic choices. In the simplest sense, economists consider utility to be revealed in people's willingness to pay different amounts for different goods.
1. Marshall, Alfred (1920). Principles of Economics. An introductory volume (8th ed.). London: Macmillan.

### 2014c

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/utility#Economic_definitions Retrieved:2014-8-31.
• In economics, utility is a representation of preferences over some set of goods and services. Preferences have a (continuous) utility representation so long as they are transitive, complete, and continuous.

Utility is usually applied by economists in such constructs as the indifference curve, which plot the combination of commodities that an individual or a society would accept to maintain a given level of satisfaction. Individual utility and social utility can be construed as the value of a utility function and a social welfare function respectively. When coupled with production or commodity constraints, under some assumptions, these functions can be used to analyze Pareto efficiency, such as illustrated by Edgeworth boxes in contract curves. Such efficiency is a central concept in welfare economics.

In finance, utility is applied to generate an individual's price for an asset called the indifference price. Utility functions are also related to risk measures, with the most common example being the entropic risk measure.There has been some controversy over the question whether the utility of a commodity can be measured or not. At one time, it was assumed that the consumer was able to say exactly how much utility he got from the commodity. The economists who made this assumption, belong to the 'Cardinalist School' (of Economics).

### 2011

• http://plato.stanford.edu/entries/preferences/#ChoFunThePro
• QUOTE: There is a strong tradition, particularly in economics, to equate preference with choice. Preference is considered to be hypothetical choice, and choice to be revealed preference.
Given an alternative set A, we can represent (hypothetical) choice as a function C that, for any given subset B of A, delivers those elements of B that a deliberating agent has not ruled out for choice. For brevity's sake we will call them 'chosen elements'. The formal definition of a choice function is as follows:

` C is a choice function for A if and only if it is a function such that for all B ⊆ A: (1) C(B) ⊆ B, and (2) if B ≠ ∅, then C(B) ≠ ∅. `

A large number of rationality properties have been proposed for choice functions. The five most important of these are described here.

`If B ⊆ A then B ∩ C(A) ⊆ C(B) (Property α, “Chernoff”)`

This property states that if some element of subset B of A is chosen from A, then it is also chosen from B. According to property α, removing some of the alternatives that are not chosen does not influence choice. This is a very basic and quite reasonable requirement of choice

### 2003

• (Korb & Nicholson, 2003) ⇒ Kevin B. Korb, and Ann E. Nicholson. (2003). “Bayesian Artificial Intelligence." Chapman & Hall/CRC.
• QUOTE: Given a general ability to order situations, and bets with definite probabilities of yielding particular situations, Frank Ramsey [231] demonstrated that we can identify particular utilities with each possible situation, yielding a utility function. If we have a utility function [math]U(O_i \vert A)[/math] over every possible outcome of a particular action [math]A[/math] we are contemplating, and if we have a probability for each such outcome [math]P(O_i \vert A)[/math], then we can compute the probability-weighted average utility for that action - otherwise known as the expected utility of the action. … It is commonly taken as axiomatic by Bayesians that agents ought to maximize their expected utility.

### 1998

• (Kohavi & Provost, 1998) ⇒ Ron Kohavi, and Foster Provost. (1998). “Glossary of Terms.” In: Machine Leanring 30(2-3).
• Utility: See Cost.
• Cost (utility/loss/payoff): A measurement of the cost to the performance task (and/or benefit) of making a prediction Y' when the actual label is y. The use of accuracy to evaluate a model assumes uniform costs of errors and uniform benefits of correct classifications.

### 1979

• (Kahneman & Tversky, 1979) ⇒ Daniel Kahneman, and Amos Tversky. (1979). “Prospect Theory: An analysis of decision under risk." Econometrica: Journal of the Econometric Society.
• QUOTE:... (iii) Risk Aversion: u is concave (u" < 0). A person is risk … on the assumption that people often know how they would behave in actual situations of choice, and on … If people are reasonably accurate in predicting their choices, the presence of common and systematic violations of ...

### 1738

• (Bernoulli, 1738) ⇒ Daniel Bernoulli. (1738). “Specimen Theoriae Novae de Mensura Sortis (Exposition of a New Theory on the Measurement of Risk)." http://www.jstor.org/discover/10.2307/1909829
• QUOTE: Ever since mathematicians first began to study the measurement of risk, there has been general agreement on the following proposition: Expected values are computed by multiplying each possible gain by the number of ways in which it can occur, and then dividing the sum of these products by the total number of possible cases.