Howard Raiffa
Encyclopedia
Howard Raiffa is the Frank P. Ramsey
Professor
(Emeritus) of Managerial Economics
, a joint chair held by the Business School
and the Kennedy School of Government at Harvard University
. He is an influential Bayesian decision theorist
and pioneer in the field of decision analysis
, with works in statistical decision theory, game theory
, behavioral decision theory, risk analysis, and negotiation analysis
He helped found and was the first director of the International Institute for Applied Systems Analysis.
Consider a situation in which you are required to gamble and are given two possible gambles.
Gamble A, in which you bet on the outcome of a fight between the world's greatest boxer and the world's greatest wrestler in a ring fight. (Assume you are fairly ignorant about martial arts and would have great difficulty making a choice of who to bet on.) If your chosen champion wins you win $500 otherwise you get nothing. You place your choice in a sealed envelope, which is opened after the game.
Gamble B. Draw a ball from an opaque urn known to contain 50 orange and 50 blue balls. You will receive $500 if you draw an orange ball and nothing for a blue ball. The balls have been thoroughly mixed and you should assume that all balls are equally likely to be drawn. The draw takes place after the ring match is over.
Many people would feel more unsure about taking Gamble A in which the probabilities are unknown, rather than Gamble B, in which the probabilities are easily seen to be one half for each outcome.
Raiffa argues that a decision-maker should in fact assign a subjective probability of one-half to each outcome of Gamble A, provided that no information was available that makes one outcome more likely than the other.
Raiffa argues as follows. Suppose someone has the following preferences. If forced to take Gamble A they would bet on the boxer, but if given a free choice between the gambles they would prefer Gamble B. Presumably, such a person when allowed to choose Gamble A would prefer to simply bet on the boxer rather than toss a coin to decide the matter of whether they should bet on the boxer or the wrestler. But this randomised approach is equivalent to Gamble B. So, by the axioms of substitutability and transitivity
for utilities
, they should also prefer to bet on the boxer than on Gamble B. A similar argument can be used to show that when the player has no preference between the boxer and the wrestler he should also have no preference between Gamble A and Gamble B.
(The axiom of substitutability says that if someone is indifferent between outcomes A and B and indifferent between outcomes A and C, they should be indifferent between B and C. The axiom of transitivity says that if someone prefers outcome A to B and also prefers B to C, then they should prefer A to C.)
Others, such as Daniel Ellsberg
disagree with Raiffa's reasoning and have devised alternative interpretations of decision theory. One of the most radical departures is Dempster-Shafer theory
, which rejects the use of probability theory
completely, in favour of a theory of belief functions, which do not satisfy the axioms of probability.
Frank P. Ramsey
Frank Plumpton Ramsey was a British mathematician who, in addition to mathematics, made significant and precocious contributions in philosophy and economics before his death at the age of 26...
Professor
Professor
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...
(Emeritus) of Managerial Economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
, a joint chair held by the Business School
Business school
A business school is a university-level institution that confers degrees in Business Administration. It teaches topics such as accounting, administration, economics, entrepreneurship, finance, information systems, marketing, organizational behavior, public relations, strategy, human resource...
and the Kennedy School of Government at Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
. He is an influential Bayesian decision theorist
Decision theory
Decision theory in economics, psychology, philosophy, mathematics, and statistics is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision...
and pioneer in the field of decision analysis
Decision analysis
Decision analysis is the discipline comprising the philosophy, theory, methodology, and professional practice necessary to address important decisions in a formal manner...
, with works in statistical decision theory, game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
, behavioral decision theory, risk analysis, and negotiation analysis
Negotiation
Negotiation is a dialogue between two or more people or parties, intended to reach an understanding, resolve point of difference, or gain advantage in outcome of dialogue, to produce an agreement upon courses of action, to bargain for individual or collective advantage, to craft outcomes to satisfy...
He helped found and was the first director of the International Institute for Applied Systems Analysis.
- His book Applied Statistical Decision Theory with Robert SchlaiferRobert SchlaiferRobert O. Schlaifer was a pioneer of Bayesian decision theory. At the time of his death he was William Ziegler Professor of Business Administration Emeritus of the Harvard Business School....
introduced the idea of conjugate priorConjugate priorIn Bayesian probability theory, if the posterior distributions p are in the same family as the prior probability distribution p, the prior and posterior are then called conjugate distributions, and the prior is called a conjugate prior for the likelihood...
distributions. - A lecture of his in the 1960s concerning the use of Bayesian methods for betting on horses gave John Craven USN, a US Navy scientist the idea of using Bayesian methods to search for a missing US Air Force hydrogen bomb lost near PalomaresPalomares, AlmeríaPalomares is an agricultural, fishing and tourist village on the Mediterranean Sea in the Almería province of Andalusia, Spain. It is about 20 meters above sea level...
, Spain in the 1966 Palomares B-52 crash. Craven used the same methods again in the search for the lost submarine USS ScorpionUSS Scorpion (SS-278)USS Scorpion — a Gato-class submarine — was the fifth ship of the United States Navy to be named for the scorpion, an arachnid having an elongated body and a narrow segmented tail bearing a venomous sting at the tip....
in 1968. Raiffa has analysed situations involving the use of subjective probability and argues that subjective probabilities should follow the same rules (the Kolmogorov axioms) as objective, frequency-based probabilities.
Consider a situation in which you are required to gamble and are given two possible gambles.
Gamble A, in which you bet on the outcome of a fight between the world's greatest boxer and the world's greatest wrestler in a ring fight. (Assume you are fairly ignorant about martial arts and would have great difficulty making a choice of who to bet on.) If your chosen champion wins you win $500 otherwise you get nothing. You place your choice in a sealed envelope, which is opened after the game.
Gamble B. Draw a ball from an opaque urn known to contain 50 orange and 50 blue balls. You will receive $500 if you draw an orange ball and nothing for a blue ball. The balls have been thoroughly mixed and you should assume that all balls are equally likely to be drawn. The draw takes place after the ring match is over.
Many people would feel more unsure about taking Gamble A in which the probabilities are unknown, rather than Gamble B, in which the probabilities are easily seen to be one half for each outcome.
Raiffa argues that a decision-maker should in fact assign a subjective probability of one-half to each outcome of Gamble A, provided that no information was available that makes one outcome more likely than the other.
Raiffa argues as follows. Suppose someone has the following preferences. If forced to take Gamble A they would bet on the boxer, but if given a free choice between the gambles they would prefer Gamble B. Presumably, such a person when allowed to choose Gamble A would prefer to simply bet on the boxer rather than toss a coin to decide the matter of whether they should bet on the boxer or the wrestler. But this randomised approach is equivalent to Gamble B. So, by the axioms of substitutability and transitivity
Transitive relation
In mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b, and b is in turn related to an element c, then a is also related to c....
for utilities
Utility
In economics, utility is a measure of customer satisfaction, referring to the total satisfaction received by a consumer from consuming a good or service....
, they should also prefer to bet on the boxer than on Gamble B. A similar argument can be used to show that when the player has no preference between the boxer and the wrestler he should also have no preference between Gamble A and Gamble B.
(The axiom of substitutability says that if someone is indifferent between outcomes A and B and indifferent between outcomes A and C, they should be indifferent between B and C. The axiom of transitivity says that if someone prefers outcome A to B and also prefers B to C, then they should prefer A to C.)
Others, such as Daniel Ellsberg
Daniel Ellsberg
Daniel Ellsberg, PhD, is a former United States military analyst who, while employed by the RAND Corporation, precipitated a national political controversy in 1971 when he released the Pentagon Papers, a top-secret Pentagon study of U.S. government decision-making in relation to the Vietnam War,...
disagree with Raiffa's reasoning and have devised alternative interpretations of decision theory. One of the most radical departures is Dempster-Shafer theory
Dempster-Shafer theory
The Dempster–Shafer theory is a mathematical theory of evidence. It allows one to combine evidence from different sources and arrive at a degree of belief that takes into account all the available evidence. The theory was first developed by Arthur P...
, which rejects the use of probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
completely, in favour of a theory of belief functions, which do not satisfy the axioms of probability.
Books
- Hammond, J. S., Keeney, R. L. and Raiffa, H. (1998). Smart Choices. Harvard Business School Press, Boston.
- Keeney, R. L. and Raiffa, H. (1976). Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Wiley,New York. Reprinted, Cambridge Univ. Press, New York (1993). MR0449476
- Luce, R. D. and Raiffa, H. (1957). Games and Decisions: Introduction and Critical Survey. Wiley, New York. Paperback reprint, Dover, New York. MR0087572
- Pratt, J. W., Raiffa, H. and Schaifer, R. (1995). Introduction to Statistical Decision Theory. MIT Press, Cambridge,MA. MR1326829
- Raiffa, H. (1968). Decision Analysis: Introductory Lectures on Choices Under Uncertainty. Addison-Wesley, Reading,MA.
- Raiffa, H. (1982). The Art and Science of Negotiation. Harvard Univ. Press, Cambridge, MA.
- Raiffa, H. (2002). Negotiation Analysis. Harvard Univ. Press, Cambridge, MA.
- Raiffa, H., Richardson, J. and Metcalfe, D. (2003). Negotiation Analysis: The Science and Art of Collaborative Decision. Harvard Univ. Press, Cambridge, MA.
- Raiffa, H. and Schaifer, R. (1961). Applied Statistical Decision Theory. Division of Research, Harvard Business School, Boston. 1968 paperback edition, MIT Press, Press, Cambridge, MA. Wiley Classics Library edition (2000)
External links
- Howard Raiffa page at Harvard