science

Subjective expected utility

Subjective expected utility is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Subjective expected utility rather than just read about it. In short: In decision theory, subjective expected utility (SEU) is a framework for modeling how individuals make choices under uncertainty. In particular, it posits that decision-makers have 1) a subjective probability distribution over uncertain states of the world; and 2) a utility function over consequences such that their choice behavior can be described as maximizing expected utility over consequences with respect to the…

Key takeaways

Subjective expected utility belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Subjective expected utility to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Subjective expected utility from memory before moving on to harder problems.

Reference excerpt

In decision theory, subjective expected utility (SEU) is a framework for modeling how individuals make choices under uncertainty. In particular, it posits that decision-makers have 1) a subjective probability distribution over uncertain states of the world; and 2) a utility function over consequences such that their choice behavior can be described as maximizing expected utility over consequences with respect to their subjective probability. This way, the theory of subjective expected utility combines two subjective concepts: a personal utility function, and a personal probability distribution (usually based on Bayesian probability theory). SEU is a different approach from the one put forward by von Neumann and Morgenstern in that it does not take (objective) probabilities (i.e., lotteries) as given. Instead, subjective probabilities are used, which are assumed to be consistent with choice behavior. The main contribution to formalizing SEU was done by L. J. Savage in 1954 (see Savage's axioms), following previous work by Ramsey and von Neumann. Savage proved that, if the decision-maker preferences over acts satisfy some reasonable axioms, then their choices can be explained as arising from a utility function u ( x i ) {\displaystyle u(x_{i})} combined with the subjective belief that there is a probability of each outcome P ( x i ) . {\displaystyle P(x_{i}).} The subjective expected utility is the resulting expected value of the utility:

E [ u ( X ) ] = ∑ i u ( x i ) P ( x i ) . {\displaystyle \mathrm {E} [u(X)]=\sum _{i}\;u(x_{i})\;P(x_{i}).}

Experiments have shown that many individuals do not behave in a manner consistent with Savage's axioms of subjective expected utility, e.g. most prominently Allais (1953) and Ellsberg (1961).

See also Savage's subjective expected utility model

Notes

References

Charles Sanders Peirce and Joseph Jastrow (1885). "On Small Differences in Sensation". Memoirs of the National Academy of Sciences. 3: 73–83. http://psychclassics.yorku.ca/Peirce/small-diffs.htm Ramsey, Frank Plumpton; “Truth and Probability” (PDF), Chapter VII in The Foundations of Mathematics and other Logical Essays (1931). de Finetti, Bruno. "Probabilism: A Critical Essay on the Theory of Probability and on the Value of Science," (translation of 1931 article) in Erkenntnis, volume 31, September 1989. de Finetti, Bruno. 1937, “La Prévision: ses lois logiques, ses sources subjectives,” Annales de l'Institut Henri Poincaré, de Finetti, Bruno. "Foresight: its Logical Laws, Its Subjective Sources," (translation of the 1937 article in French) in H. E. Kyburg and H. E. Smokler (eds), Studies in Subjective Probability, New York: Wiley, 1964. de Finetti, Bruno. Theory of Probability, (translation by AFM Smith of 1970 book) 2 volumes, New York: Wiley, 1974–5. Donald Davidson, Patrick Suppes and Sidney Siegel (1957). Decision-Making: An Experimental Approach. Stanford University Press. Pfanzagl, J (1967). "Subjective Probability Derived from the Morgenstern–von Neumann Utility Theory". In Martin Shubik (ed.). Essays in Mathematical Economics In Honor of Oskar Morgenstern. Princeton University Press. pp. 237–251. Morgenstern, Oskar (1976). "Some Reflections on Utility". In Andrew Schotter (ed.). Selected Economic Writings of Oskar Morgenstern. New York University Press. pp. 65–70. ISBN 0-8147-7771-6.

External links Edi Karni, Johns Hopkins University (November 9, 2005). "Savages' Subjective Expected Utility Model" (PDF). Retrieved 2009-02-17.

Worked examples

Example 1 — a first encounter with Subjective expected utility

Start with the simplest possible case. Write down what Subjective expected utility claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Subjective expected utility before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Subjective expected utility ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Subjective expected utility

In research: Subjective expected utility appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Subjective expected utility in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Subjective expected utility is common in secondary-school and first-year university syllabi. It links to neighbouring topics Expected utility, Social philosophy, so understanding it makes those chapters shorter.
In everyday life: Look for Subjective expected utility outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Subjective expected utility in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Subjective expected utility means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Subjective expected utility out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Subjective expected utility in simple terms?

Why does Subjective expected utility matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Subjective expected utility?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Subjective expected utility.