Choice-based cardinal utility: a tribute to Patrick Suppes

Abstract

We reexamine some of the classic problems connected with the use of cardinal utility functions in decision theory, and discuss Patrick Suppes' contributions to this field in light of a reinterpretation we propose for these problems. We analytically decompose the doctrine of ordinalism, which only accepts ordinal utility functions, and distinguish between several doctrines of cardinalism, depending on what components of ordinalism they specifically reject. We identify Suppes' doctrine with the major deviation from ordinalism that conceives of utility functions as representing preference differences, while being nonetheless empirically related to choices. We highlight the originality, promises and limits of this choice-based cardinalism.

Simple preference intensity comparisons

“…It is by no means uncommon for the cardinally unique utility differences between pairs of riskless alternatives that can be obtained by lottery comparisons under the von Neumann and Morgenstern (1947) expected-utility model to be interpreted as indicating differences in preference intensities between those alternatives. Yet, it has been well-known among decision and welfare theorists for a long time that such utility differences confound the individuals' preference intensities over the underlying set of riskless alternatives with their attitudes toward risk (Luce and Raiffa, 1957;Schoemaker, 1982;Hammond, 1991;Ellingsen, 1994;Abdellaoui, Barrios, and Wakker, 2007;Baccelli and Mongin, 2016) or "the tastes of individuals for gambling" (Arrow, 1951;p. 10).…”

“…This difficulty is circumvented by simply assuming it away through the standard Positivity axiom whereby all choice probabilities are strictly positive. But one can then refer to an argument that was put forward in Baccelli and Mongin (2016) and respond that even though such genuine choice stochasticity precludes the possibility of the decision maker behaving like an ordinal utility maximizer, the model in fact portrays her as one whose behaviour is describable by maximization of a utility function that has even more refined uniqueness properties, which is somewhat paradoxical. However, while these arguments challenge the capacity of choice probabilities alone to reliably convey information about a single individual agent's preference intensities, they remain compatible with conventional interpretations whereby aggregate stochastic-choice data can reveal such information about the relative appeal of different alternatives within the group of individuals that generated these data.…”

“…For detailed and complementary accounts of these models, the debates they have been associated with and their implications for economic analysis, the reader is also referred toLuce, Krantz, Suppes, and Tversky (1990),Krantz, Luce, Suppes, and Tversky (1971),Suppes, Krantz, Luce, and Tversky (1989),Hammond (1991),Ellingsen (1994),Mandler (1999),Falmagne (2002),Bossert and Weymark (2004),Fleurbaey and Hammond (2004),Abdellaoui, Barrios, and Wakker (2007),Baccelli and Mongin (2016).…”