What Are Preferences?
An informal presentation of Jeffrey (1983, p. chapter 3)
on how decision theory enables us
to think of subjective probabilities and preferences as
simultaneously derivable from patterns of action.
We have relied on notions of belief and desire in considering
both philosophical (in Philosophical Theories of Action)
and psychological theories (in Goal-Directed and Habitual Processes)
of instrumental action and joint action.
But what anchors our understanding, as researchers, of these notions?
While some of us might use these words in everyday life,
there is probably enough diversity between individuals with
different cognitive styles (e.g. Perner & Leekam, 2008),
different upbringings (e.g. Morgan et al., 2014)
or different cultural backgrounds (e.g. Dixson, Komugabe-Dixson, Dixson, & Low, 2018)
that whatever understandings you and I have in everyday life may not
And invoking a philosophical theory does not seem likely to help given
the level of agreement that has been reached in this regard over
the last 2000 or so years.
An attractive alternative is suggested by Jeffrey:
This book has ‘a philosophical end: elucidation of the notions of
subjective probability and subjective desirability or utility.’
(Jeffrey, 1983, p. xi)
In this section we explore how, following Jeffrey, subjective probabilities
and preferences can be identified as constructs of decision theory.
Decision theory therefore promises to be an ideal anchor for a shared
understanding of these notions.
Inspired by Jeffery (and Davidson, 1990), we might therefore
attempt to substitute the informal, poorly understood notions of belief
and desire with the theoretical constructs of subjective probabilty and
‘A binary relation ⪰ on a set A is complete if a⪰b
or b⪰a for every a ∈ A and b ∈ A,
reflexive if a⪰a
for every a ∈ A, and
transitive if a⪰c whenever a⪰b
A preference relation is a complete reflexive transitive
binary relation’ (Osborne & Rubinstein, 1994, p. 7).
The Continuity Axiom states that if c⪰b⪰a then there is some
probability p such that you are indifferent between (i) b happening with certainty
and (ii) a happening with probability p and c happening with probability (1-p).
‘Continuity implies that no outcome A is so bad that you would not be willing to take
some gamble that might result in you ending up with that outcome, but might otherwise
result in you ending up with an outcome (C) that you find to be a marginal improvement
on your status quo (B), provided that the chance of A is small enough.’
(Steele & Stefánsson, 2020)
The Independence Axiom states that if b⪰a then for any probability p,
Put roughly, if you prefer a to b then you should prefer a and c to b and c.
‘Intuitively, this means that preferences between lotteries should be governed only by
the features of the lotteries that differ; the commonalities between the lotteries should be effectively
(Steele & Stefánsson, 2020)
A preference relation is independent of irrelevant alternatives
exactly if ‘no change in the set of candidates (addition to or subtraction from)
[can] change the rankings of the unaffected candidates’
(Dixit, Skeath, & Reiley, 2014, p. 600).
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: A theory, fact or other thing that is used by a group of researchers to ensure
that they have a shared understanding of a phenomenon.
An anchor is needed when it is unclear whether different researchers are offering
incompatible claims about a single phenomenon or compatible claims about distinct phenomena.
For example, we might take decision theory
to anchor a shared understanding of belief and desire.
: I use ‘decision theory’ for the theory elaborated by Jeffrey (1983). Variants are variously called ‘expected utility theory’ (Hargreaves-Heap & Varoufakis, 2004), ‘revealed preference theory’ (Sen, 1973) and ‘the theory of rational choice’ (Sugden, 1991). As the differences between variants are not important for our purposes, the term can be used for any of core formal parts of the standard approaches based on Ramsey (1931) and Savage (1972).
ethically neutral condition
: ‘A condition is ethically neutral in relation to a particular agent and a particular consequence if the agent is indifferent between having that consequence when the condition holds and when it fails’ (Jeffrey, 1983, p. 46).
: An action is instrumental if it happens in
order to bring about an outcome,
as when you press a lever in order to obtain food. (In this case,
obtaining food is the outcome, lever pressing is the action, and the
action is instrumental because it occurs in order to bring it about
that you obtain food.)
You may encounter variations on this definition of instrumental in the literature.
For instance, Dickinson (2016, p. 177)
characterises instrumental actions differently: in place of the teleological
‘in order to bring about an outcome’, he stipulates that an instrumental
action is one that is ‘controlled by the contingency between’ the action
and an outcome. And de Wit & Dickinson (2009, p. 464) stipulate that
‘instrumental actions are learned’.
Burge, T. (2009). Primitive Agency and Natural Norms. Philosophy and Phenomenological Research
(2), 251–278. https://doi.org/10.1111/j.1933-1592.2009.00278.x
Chater, N. (2014). Cognitive Science as an Interface Between Rational and Mechanistic Explanation. Topics in Cognitive Science
(2), 331–337. https://doi.org/10.1111/tops.12087
Davidson, D. (1974). Belief and the basis of meaning. In Inquiries into truth and interpretation
(pp. 141–154). Oxford: Oxford University Press.
Davidson, D. (1987). Problems in the explanation of action. In P. Pettit, R. Sylvan, & J. Norman (Eds.), Metaphysics and morality: Essays in honour of j. J. C. smart
(pp. 35–49). Oxford: Blackwell.
Davidson, D. (1990). The structure and content of truth. The Journal of Philosophy
de Wit, S., & Dickinson, A. (2009). Associative theories of goal-directed behaviour: A case for animalhuman translational models. Psychological Research PRPF
(4), 463–476. https://doi.org/10.1007/s00426-009-0230-6
Dickinson, A. (2016). Instrumental conditioning revisited: Updating dual-process theory. In J. B. Trobalon & V. D. Chamizo (Eds.), Associative learning and cognition
(Vol. 51, pp. 177–195). Edicions Universitat Barcelona.
Dixit, A., Skeath, S., & Reiley, D. (2014). Games of strategy
. New York: W. W. Norton; Company.
Dixson, H. G. W., Komugabe-Dixson, A. F., Dixson, B. J., & Low, J. (2018). Scaling Theory of Mind in a Small-Scale Society: A Case Study From Vanuatu. Child Development
(6), 2157–2175. https://doi.org/10.1111/cdev.12919
Hargreaves-Heap, S., & Varoufakis, Y. (2004). Game theory: A critical introduction
. London: Routledge. Retrieved from http://webcat.warwick.ac.uk/record=b2587142~S1
Heider, F. (1958). The psychology of interpersonal relations
. Hillsdale, N.J: Lawrence Erlbaum Associates.
Hyman, J. (1999). How knowledge works. Philosophical Quarterly
Jeffrey, R. C. (1983). The logic of decision, second edition
. Chicago: University of Chicago Press.
Kaplan, M. (1985). It’s Not What You Know That Counts. Journal of Philosophy
(7), 350–363. https://doi.org/jphil198582748
Keramati, M., Smittenaar, P., Dolan, R. J., & Dayan, P. (2016). Adaptive integration of habits into depth-limited planning defines a habitual-goaldirected spectrum. Proceedings of the National Academy of Sciences
(45), 12868–12873. https://doi.org/10.1073/pnas.1609094113
Lewis, D. (1972). Psychophysical and theoretical identifications. Australasian Journal of Philosophy
(3), 249–258. https://doi.org/10.1080/00048407212341301
Lewis, D. K. (1996). Elusive Knowledge. Australasian Journal of Philosophy
(4), 549–567. https://doi.org/10.1080/00048409612347521
Morgan, G., Meristo, M., Mann, W., Hjelmquist, E., Surian, L., & Siegal, M. (2014). Mental state language and quality of conversational experience in deaf and hearing children. Cognitive Development
, 41–49. https://doi.org/10.1016/j.cogdev.2013.10.002
Nagel, J. (2012). Intuitions and Experiments: A Defense of the Case Method in Epistemology. Philosophy and Phenomenological Research
Nisbett, R. E., & Wilson, T. D. (1977). Telling more than we can know: Verbal reports on mental processes. Psychological Review
O’Brien, L., & Soteriou, M. (Eds.). (2009). Mental actions
. Oxford: Oxford University Press. Retrieved from http://0-doi.org.pugwash.lib.warwick.ac.uk/10.1093/acprof:oso/9780199225989.001.0001
Osborne, M. J., & Rubinstein, A. (1994). A course in game theory
. MIT press.
Perner, J., & Leekam, S. (2008). The Curious Incident of the Photo that was Accused of Being False: Issues of Domain Specificity in Development, Autism, and Brain Imaging. Quarterly Journal of Experimental Psychology
(1), 76–89. https://doi.org/10.1080/17470210701508756
Radford, C. (1966). Knowledge: By Examples. Analysis
(1), 1–11. https://doi.org/10.2307/3326979
Ramsey, F. (1931). Truth and probability. In R. Braithwaite (Ed.), The foundations of mathematics and other logical essays
. London: Routledge.
Rose, D., & Schaffer, J. (2013). Knowledge entails dispositional belief. Philosophical Studies
(1), 19–50. https://doi.org/10.1007/s11098-012-0052-z
Savage, L. J. (1972). The foundations of statistics
(2nd rev. ed). New York: Dover Publications.
Sen, A. (1973). Behaviour and the Concept of Preference. Economica
(159), 241–259. https://doi.org/10.2307/2552796
Sosa, E. (2007). A virtue epistemology: Apt belief and reflective knowledge. Volume I
. Oxford: Oxford University Press. Retrieved from http://webcat.warwick.ac.uk/record=b3489766~S1
Steele, K., & Stefánsson, H. O. (2020). Decision Theory. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy
(Winter 2020). Metaphysics Research Lab, Stanford University.
Steward, H. (2009). Animal Agency. Inquiry
(3), 217–231. https://doi.org/10.1080/00201740902917119
Sugden, R. (1991). Rational Choice: A Survey of Contributions from Economics and Philosophy. The Economic Journal
(407), 751–785. https://doi.org/10.2307/2233854
Unger, P. K. (1975). Ignorance: A case for scepticism
. Oxford: Clarendon. Retrieved from http://webcat.warwick.ac.uk/record=b2663127~S1
Velleman, D. (2000). The possibility of practical reason
. Oxford: Oxford University Press.
Williamson, T. (2000). Knowledge and its limits
. Oxford: Oxford University Press.