# Jeffrey, Richard Carl

# JEFFREY, RICHARD CARL

(*b*. Boston, Massachusetts, 5 August 1926; *d*. Princeton, New Jersey, 9 November 2002),

*rational choice theory, probabilism, epistemology*.

Jeffrey was perhaps the leading philosophical proponent of Bayesian methods in decision theory, epistemology, and philosophy of science.

**Early Years and Career Path** . Richard Carl Jeffrey was born in Boston, Massachusetts, on 5 August 1926. He entered Boston University at age sixteen, where he became interested in philosophy and logic as a result of reading Rudolf Carnap’s *Philosophy and Logical Syntax*. As Jeffrey would later declare, the exposure to Carnap’s work made him into “a teenage logical positivist” (1998). During World War II Jeffrey was drafted out of college and into the U.S. Navy, where he served from 1944 to 1946. After the war, Jeffrey went to the University of Chicago, where he worked closely with Carnap on the foundations of probability and statistics, topics that remained central to his research throughout his career.

After earning his MA in philosophy at Chicago in 1952, he went to work on the design of computers at the Massachusetts Institute of Technology’s (MIT) Digital Computer Laboratory and the Lincoln Laboratory. While in Boston he met Edie Kelman. They married in 1955. In that same year Jeffrey went to Princeton to study under the great philosopher of science Carl Gustav Hempel. Upon completing the PhD under Hempel in 1957, Jeffrey spent a year as a Fulbright Scholar at Oxford, after which he returned to MIT for a year as an assistant professor of electrical engineering. He then held a position as an assistant professor of philosophy at Stanford from 1959 to 1963. At the invitation of Kurt Gödel, Jeffrey spent 1963–1964 at the Institute for Advanced Study at Princeton. During this period he completed *The Logic of Decision*, his first book. Jeffrey went on to hold appointments in the philosophy departments at the City College of New York (1964–1967), the University of Pennsylvania (1967–1974), and finally Princeton (1974–1999), where he spent the bulk of his career. He wrote two books during this period—*Formal Logic: Its Scope and Limits* (1967) and *Computability and Logic* (1974, with George Boolos)—and many important papers, the best known of which are collected in *Probability and the Art of Judgment* (1992). After retiring from Princeton, Jeffrey held a visiting distinguished professorship of social science at the University of California, Irvine.

**Contributions to Rational Choice Theory** . Most of Jeffrey’s research focused on rational choice theory, and on the application of probabilistic thinking to epistemology and the philosophy of science. Jeffrey’s main contribution to rational choice theory, *The Logic of Decision*, was written while he was at the Institute for Advanced Study in Princeton. Combining new insights about decision making, and benefiting from the mathematics of Ethan Bolker (1966), Jeffrey developed a version of expected utility theory that differs from earlier versions, such as that of Leonard J. Savage (1954), in three important respects. First, whereas Savage distinguished among acts, states of the world, and consequences, Jeffrey formulated his theory using a single underlying algebra of propositions, leaving distinctions between acts, states, and consequences to be drawn at the level of application rather than theory.

Second, whereas most decision theories require the maximization of unconditional expected utility, Jeffrey advocated maximizing *conditional* expected utility, thereby allowing for the possibility that acts might influence the states used to frame decisions. This is achieved by replacing the standard formula for expected utility, *Exp*(*A*) = Σ_{S}*P* (*S*) × *u* (*A, S*) (where the probabilities *P*(*S*) do not depend on the choice of an act), by a new formula, *des(A)* = Σ_{S}*P*(S \ A) × des(A & S). The resulting function is such that:

- the choice of state partition does not matter, becauseΣ
_{S}P(S | A) × des(A & S) = Σ_{S*}P(S* | A) × des(A & S*) whatever partitions*S*and*S** range over; - no “state-dependent” utilities are required, because, in any application, consequences are act/state conjunctions;
- potential influences of choices on acts are reflected by the conditional probabilities
*P*(*S*|*A*); and - no explicitly or implicitly causal notions are invoked anywhere in the theory.

Jeffrey’s theory is often referred to as “evidentialist,” because it is natural to interpret *des*(*A*) as expressing the value of *A* as an indicator or sign of desirable or undesirable results.

Third, the framework prevents preferences from uniquely determining subjective probabilities. In Jeffrey’s theory, even if one fixes a zero and a unit for utility, a complete set of preferences can always be represented as maximizing expected utility relative to any of a family of probability/utility pairs (*P*_{λ}, des), where λ satisfies –1/sup{des(X) } ≤ λ ≤ –1/inf{des(X) }. Except in the rare case where the preference ranking requires an unbounded utility, which makes λ = 0 the only option, this family will contain an infinity of members defined by the identities. Pλ(X) = P_{0}(X)[1 + λ × des_{0}(X)] and desλ(X) = des_{0}(X)[(1 + λ)/(1 + λ × des_{0}(X))]. Jeffrey saw this indeterminacy as an advantage of his theory, and argued that the uniqueness of the representation offered by other decision theories was spurious. Beliefs and desires, he maintained, are mostly imprecise and incomplete, and should be represented, in just the way his theory suggests, by sets of probability and utility functions. This was “Bayesianism with a Human Face” (1983). Jeffrey, together with Isaac Levi, Henry Kyburg, Bas van Fraassen, Teddy Seidenfeld, and others, did much to illuminate such “imprecise attitudes.” However, unlike other defenders of this position, Jeffrey thought it impossible to detach probabilities from utilities. A complete representation of a rational agent’s mental state will be a set of probability/utility pairs that typically cannot be decomposed into a Cartesian product of a set of probabilities with a set of utilities.

**Ratificationism** . An additional contribution to decision theory, which appeared with the second edition of *The Logic of Decision*, is the doctrine of ratificationism. This arose as a result of challenges raised by “causal” decision theorists. As noted, Jeffrey’s utilities measure the degree to which news of an act indicates that desirable results will ensue. This can lead to flawed recommendations in decisions whose acts indicate desirable outcomes without doing anything to causally promote those outcomes. Causal decision theorists see such “Newcomb problems” as counterexamples to Jeffrey’s theory, and use them as a rationale for including explicitly causal or counterfactual notions in the formulation of decision theory. This was anathema to Jeffrey, who saw the absence of causal notions as one of the main virtues of his theory. His response, which owes much to Ellery Eells (1982), was to argue that, when properly amended, his system does not recommend auspicious but inefficacious acts. The required amendment is the *maxim of ratification: one should choose**for the person one expects to be once one has chosen*. Decision making is then a two-stage process in which one first eliminates all “unratifiable” acts, those for which *des*(*A | A* is chosen) < *des* (*B | A* is chosen) for some *B*, and then maximizes expected utility among the remaining “ratifiable” options. Jeffrey assumed that an agent’s knowledge that she will choose *A* is sufficient to screen off any spurious evidentiary relationships that hold between *A* and states of the world. When combined with the requirement to choose only ratifiable options, this assumption eliminates auspicious but inefficacious acts from consideration in Newcomb problems.

Ratificationism has had a complicated history. In the face of strong criticism of the screening-off assumption, Jeffrey was forced to repudiate ratificationism as a solution to Newcomb problems. Yet, many causal decision theorists found ratificationism plausible and incorporated it into their theories. It also became clear that the ratificationist idea is built into the concept of a game-theoretic equilibrium. Recently, the idea of a ratifiable decision has reappeared in the work of the economists Michael Rabin and Botond Koszegi (2006) under the title of “personal equilibrium.” All this suggests that the importance of ratifiability to decision theory goes far beyond the role for which it was initially introduced.

After giving up on ratificationism as a solution to Newcomb problems, Jeffrey shifted tactics in *Subjective Probability* (2004) and argued that these problems are not genuine decisions because agents who face them possess so much evidence about correlations between their acts and states of the world that they cannot properly see their choices as causes of outcomes. Jeffrey based this conclusion on a model of rational deliberation that requires conditional probabilities of the form *P*(*outcome*| *act*) to remain constant during deliberation. Some, for example, James M. Joyce (2007), have rejected this claim, and so remain convinced that Newcomb problems cause trouble for Jeffrey’s theory.

**Contributions to Epistemology and Philosophy of Science** . Jeffrey’s central contribution to epistemology was his thoroughgoing defense of radical probabilism, the idea that, “in principle, all knowledge might be merely probable” (1988, p. 135). Radical probabilism opposes “dogmatic” epistemologies that make states of “full belief” the core ingredients of the theory of knowledge, and that presuppose foundationalist conceptions of learning. For a radical probabilist, all information acquisition and processing is described probabilistically.

In a famous exchange with Isaac Levi, Jeffrey (1970) argued that the concept of full belief is largely irrelevant to epistemology because choices among actions are governed by subjective probabilities, and such probabilistic attitudes are appropriate in light of the ambiguous and inherently uncertain data we typically receive. The correct way to model epistemic states, according to Jeffrey, is not with a set of known propositions, but by a family of probability functions that best reflect uncertainty in light of evidence.

Jeffrey was particularly concerned to show that an adequate theory of learning did not require a concept of full belief. He often quoted Clarence Irving Lewis’s remark “if anything is to be probable, then something must be certain” (1946, p. 186), using it as a foil. On Lewis’s dogmatist picture, learning involves becoming certain of some proposition. This is represented probabilistically as simple Bayesian conditioning in which a person who undergoes a learning experience becomes certain of some proposition *e* and updates her “prior” subjective probability function *P* by moving to the “posterior” *P _{e}*(•) =

*P*(• |

*e*). Jeffrey’s rejection of this picture is based on a model that allows experiences to increase probabilities without raising them to certainty. Consider a beer drinker who starts out confident that he is being served lager but who, after taking a sip, suspects that he has mistakenly been given ale. The gustatory experience might have moved his degrees of confidence from the priors

*P*(

*lager*) = 0.95 and

*P*(

*ale*) = 0.05 to the posteriors Q(

*lager*) = 0.45 and

*Q*(

*ale*) = 0.55. More generally, if 〈

*e*〉 = 〈

_{j}*e*〉is a set of mutually exclusive, collectively exhaustive propositions, Jeffrey allows for experiences that fix posteriors

_{1},e_{2}, …,e*p*

_{q}(•) = Σ

_{i}q

_{i}×p(·|

*e*

_{i}) If this is the experience’s only immediate effect, then ratios of probabilities within each cell of the partition remain static, so that

*p*(·|

_{i}*e*) for all

_{i}*i*. This “sufficiency condition” ensures that the posterior is given by

*p*(•) = Σ

_{q}_{i}

*q*

_{i}×

*p*(• |

*e*) Jeffrey called this form of belief revision “probability kinematics,” though most philosophers refer to it as “Jeffrey conditioning.” It describes the sort of nonfoundationalist learning that underwrites radical probabilism.

_{i}Unlike standard conditioning, Jeffrey’s operation is not commutative. If experience ** q** sets probabilities 〈q

_{i}〉 for 〈e

_{i}〉 and experience

**sets probabilities 〈r**

*r*_{j}〉 for 〈f

_{j}〉, and if the sufficiency condition holds at each stage, then it can happen that

*P*

_{q, r }≠

*P*

_{r, q }, so that

**followed by**

*q***is not evidentially equivalent to**

*r***followed by**

*r***. Some have objected to this on the grounds that the order in which data is received should not affect conclusions drawn from it. This principle, however, is dubious in just those cases where Jeffrey conditioning fails to commute. Jeffrey shifts can occur in two ways, depending on whether experience fixes posterior probabilities for events in a way that depends on their priors. If the posterior probability that experience**

*q***sets for each e**

*q*_{i}is independent of its prior probability, then

**obliterates information about the prior probabilities of the e**

*q*_{i}themselves: any two priors with for all

*P*(• | e

_{i}) =

*p**(• |

*e*

_{i})are mapped to same posterior

*P*

_{q }=

*P**

_{q }. The “order makes no difference” principle is bogus for experiences of this type. For, if

**conveys information about the e**

*r*_{i,}, so that for some

*i*, then it

*should*matter whether

**precedes or follows**

*r***. When**

*q***precedes**

*r***, the information it provides about the e**

*q*_{i}is destroyed by

**and so does not show up in**

*q**P*

_{r,q }. This information is, of course, reflected in

*P*

_{q,r }. Thus, when the posterior probabilities for the e

_{i}(or f

_{j}) do not depend on their prior probabilities, one should expect Jeffrey conditioning to commute only when the experiences that generate them are “Jeffrey independent” in the sense that

*P*

_{r }(e

_{i}) =

*P*(e

_{i}) and

*P*

_{q }(f

_{j}) =

*P*(f

_{j}) for all

*i*and

*j*. As shown in Persi Diaconois and Sandy Zabell (1982), this is necessary and sufficient for

*P*

_{q,r }=

*P*

_{r,q }.

As Hartry Field (1978) showed, the “order makes no difference” principle is plausible in some cases where experiences preserve information from earlier shifts. Imagine that, instead of directly determining posteriors, an experience ** q** only fixes ratios of posterior to prior probabilities for cells in a partition, so that

**’s immediate effect is to fix a Bayes factor α**

*q*_{i}=

*P*

_{q }(

*e*)/

_{i}i*P*(

*e*) for each e

_{i}_{i}. When sufficiency holds, the shift from

*P*to

*P*

_{q }is then fully characterized by Bayes factors and priors:

*p*

_{q}(•) =

*p*(•) × Σ

_{i}α

_{i}×

*p*(

*e*

_{i}•)When such shifts occur in succession—one fixing Bayes factors α

_{i}for the e

_{i,}, the other fixing Bayes factors B

_{j}

*f*for the f

_{j}—the result is

*p*

_{q}(•) ×

_{i,j}α

_{i}×

*p*(

*e*

_{i}) & f

_{i}| ·) Since this equation is symmetric in

*i*and

*j*, Jeffrey conditioning can commute when subsequent experiences preserve the information from previous experiences, which is exactly as it should be.

**Lasting Influence** . Jeffrey made contributions in many other areas of philosophy, among them an early and influential account of higher-order preferences (1974), a theory of conditionals (with Robert Stalnaker) that assigned indicative conditionals partially probabilistic semantic values (1994), an important paper on preference aggregation (with Matthias Hild and Mathias Risse), and a number of influential papers on the general philosophy of science (1956, 1969, 1975, and 1993).

Jeffrey had great influence within and outside of philosophy, both for the depth and inventiveness of his philosophical work and for the kindness and generosity with which he dealt with colleagues, students, and friends. Among his many academic honors, Jeffrey served as president of the Philosophy of Science Association and was a member of the American Academy of Arts and Sciences. The impact of his contributions can be seen directly in the work of the philosophers Abner Shimony, Brian Skyrms, William Harper, Stalnaker, van Fraassen, Alan Hájek, Brad Armendt, Joyce, Cristina Bicchieri, and Risse (his last PhD student), as well as the statisticians Diaconis and

Zabell, the physician Michael Hendrickson, and the mathematician Carl G. Wagner.

Richard Jeffrey died on 9 November 2002 in Princeton at the age of seventy-six. He spent his last days putting the finishing touches on his last book, *Subjective Probability: The Real Thing!*, an elegant final expression of his thinking.

## BIBLIOGRAPHY

### WORKS BY JEFFREY

“Valuation and Acceptance of Scientific Hypotheses.” *Philosophy of Science* 23 (1956): 237–246.

*The Logic of Decision*. New York: McGraw-Hill, 1965. Rev. 2nd ed., Chicago: University of Chicago Press, 1983.

*Formal Logic: Its Scope and Limits*. New York: McGraw-Hill, 1967.

“Statistical Explanation vs. Statistical Inference.” In *Essays in Honor of Carl G. Hempel: A Tribute on the Occasion of His Sixty-Fifth Birthday*, edited by Nicholas Rescher. Dordrecht: Reidel, 1969.

“Dracula Meets Wolfman: Acceptance vs. Partial Belief.” In *Induction, Acceptance, and Rational Belief*, edited by Marshall Swain. Dordrecht: Reidel, 1970.

“On Interpersonal Utility Theory.” *Journal of Philosophy* 68 (1971): 647–657.

With George Boolos. *Computability and Logic*. Cambridge, U.K.: Cambridge University Press, 1974.

Rev. 2nd ed., 1980. “Preference among Preferences.” *Journal of Philosophy* 71 (1974):377–391.

“Probability and Falsification: Critique of the Popper Program.” *Synthese* 30 (1975): 95–117 and 149–157.

“Bayesianism with a Human Face.” In *Testing Scientific Theories*, edited by John Earman. Minnesota Studies in the Philosophy of Science 10. Minneapolis: University of Minnesota Press, 1983.

“Conditioning, Kinematics, and Exchangeability.” In *Causation, Chance, and Credence*, vol. 1, edited by Brian Skyrms and William Harper. Boston: Kluwer Academic, 1988.

*Probability and the Art of Judgment*. Cambridge, U.K.:

Cambridge University Press, 1992.

“Take Back the Day! Jon Dorling’s Bayesian Solution to the Duhem Problem.” In *Science and Knowledge*, edited by Enrique Villanueva. Atascadero, CA: Ridgeview, 1993.

With Robert Stalnaker. “Conditionals as Random Variables.” In *Probability and Conditionals: Belief Revision and Rational Decision*, edited by Ellery Eells and Brian Skyrms. Cambridge, U.K.: Cambridge University Press, 1994.

“I was a Teenage Logical Positivist (Now a Septuagenarian Radical Probabilist).” PSA Presidential Address. Delivered Kansas City, 23 October 1998. Revised 10 April 2000.

Available online from http://www.princeton.edu/~bayesway/KC.tex.pdf.

With Matthias Hild and Mathias Risse. “Preference Aggregation after Harsanyi.” In *Justice, Political Liberalism, and Utilitarianism: Themes from Harsanyi and Rawls*, edited by Maurice Salles and John A. Weymark. Cambridge, U.K.: Cambridge University Press, 2004.

*Subjective Probability: The Real Thing*. Cambridge, U.K.:

Cambridge University Press, 2008.

### OTHER SOURCES

Bolker, Ethan. “Functions Resembling Quotients of Measures.” *Transactions of the American Mathematical Society* 124 (1966): 292–312.

Diaconis, Persi, and Sandy Zabell. “Updating Subjective Probability.” *Journal of the American Statistical Association* 77 (1982): 822–830.

Eells, Ellery. *Rational Decision and Causality*. Cambridge, U.K.:

Cambridge University Press, 1982.

Field, Hartry. “A Note on Jeffrey Conditionalization.” *Philosophy of Science* 45 (1978): 361–367.

Joyce, James M. “Are Newcomb Problems Really Decisions.”

*Synthese* 156, no. 3 (2007): 537–562.

Koszegi, Botond, and Matthew Rabin. “A Model of Reference-Dependent Preferences.” *Quarterly Journal of Economics* 121, no. 4 (2006): 1133–1166.

Levi, Isaac. “Probability and Evidence.” In *Induction, Acceptance, and Rational Belief*, edited by Marshall Swain. Dordrecht: Reidel, 1970.

Lewis, Clarence Irving. *An Analysis of Knowledge and Valuation*.

La Salle, IL: Open Court, 1946.

Savage, Leonard J. *The Foundations of Statistics*. New York:

Wiley, 1954.

*James M. Joyce*

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