An Experimental Test of Event Commutativity in Decision Making under Uncertainty

A fundamental rationality assumption of many models of choices under risk and uncertainty is that the sequencing of events should not matter to a decision maker so long as the consequences arise under the same conditions, ignoring the order of events. Subjective expected utility (SEU) implies this property without exception; however, SEU is known not to be descriptive. The boundary between SEU and potentially more descriptive theories, such as the rank-dependent ones, has been shown to lie at a very simple version of this property called event commutativity. Two previous tests of it have yielded mixed results (Brothers, 1990; Ronen, 1973), but with some evidence from Brothers that it may be sustained if choice-based certainty equivalents are used. The present study tested event commutativity using a version of the sequential choice procedure Brothers employed in his third experiment. Twentyfour gambles representing a scenario of suing versus settling a car-accident dispute were presented to students, and certainty equivalents (settlement amounts) were elicited using a computer-controlled choice procedure. Twenty-two of 25 subjects supported the property of event commutativity; the others violated it in ways similar to those discovered in the earlier studies. Assumptions about rational choices among risky or uncertain alternatives can be classified into two distinct types; (a) preference rationality assumptions, which are assumptions that follow from the general principle that replacing something by something better is always desirable (concepts included in this category are transitivity, consequence Address correspondence to Detlof von Winterfeldt, Institute of Safety and Systems Management, University of Southern California, University Park, Los Angeles, CA 90089. monotonicity, and event monotonicity'); and (b) a universal structural rationality assumption, which asserts that the decision maker should be indifferent among all formally equivalent descriptions of a gamble (e.g,, between its extensive and normal forms).^ In sufficiently rich contexts of alternatives, preference and universal structural rationality can be shown to be equivalent to some version of the subjective expected utility (SEU) representation (Fishburn, 1982; Savage, 1954). Such a representation entails constructing a utility function over consequences and a (subjective) probability measure over events such that the expectation of the utility of an alternative relative to the constructed measure faithfully reflects the preference ordering. Note the direction of this assertion; The preference ordering is reflected by SEU; SEU is not the source of the ordering. Considerable empirical evidence (Kahneman & Tversky, 1979; Luce, 1992; Schoemaker, 1982, 1990) makes clear that, whatever its normative status may be, the SEU model fails to be descriptive of human decision making. In particular, event monotonicity was rejected early on (EUsberg, 1961), whereas in the absence of universal structural rationality, consequence monotonicity appears to be sustained (Kahneman & Tversky, 1979; von Winterfeldt, Chung, Luce, & Cho, 1994). So, one problem is to decide whether some rather more 1. Precise definitions of these three concepts can be found In, for example. Luce (1990). 2. Luce (1990) referred to these as accounting equivalences. In the context of known probabilities (risk), the probability calculation called the reduction of compound gambles is an example of structural rationality. Indeed, if risky money gambles are treated as random variables, which is common in economics, universal structural rationality is built into the formulation of the problem. restrained version of structural rationality obtains and to discover what sorts of descriptive representations are possible within that framework. The purpose of this report is to localize in terms of structural rationality assumptions the dividing line between SEU and other more descriptive theories (Luce, 1990), Let xo^y denote the binary gamble that yields the pure consequence x when some event E occurs and y viihen it fails to occur.' Second-order gambles can be created by applying the operation OE to all first-order gambles and pure consequences, and higher order gambles can be defined recursively," If ~ denotes indifference, the three simplest structural rationality properties are