Testing Critical Properties of Decision Making on the Internet

This article reviews recent findings that violate a broad class of descriptive theories of decision making. A new study compared 1,224 participants tested via the Internet and 124 undergraduates tested in the laboratory. Both samples confirmed systematic violations of stochastic dominance and cumulative independence; new tests also found violations of coalescing. The Internet sample was older, more highly educated, more likely male, and also more demographically diverse than the lab sample. Internet participants were more likely than undergraduates to choose the gamble with higher expected value, but no one conformed exactly to expected value. Violations of stochastic dominance decreased as education increased, but violations of stochastic dominance and coalescing were still substantial in persons with doctoral degrees who had read a scientific work on decision making. In their implications, Internet research and lab findings agree: Descriptive decision theories cannot assume that identical consequences can be coalesced. Some people say that psychological science is based on research with rats, the mentally disturbed, and college students. We study rats because they can be controlled, the disturbed because they need help, and college students because they are available. The Internet now makes available a worldwide population. This new medium not only provides new research opportunities, but also raises new questions about sampling and experimental control (Krantz, Ballard, & Scher, 1997; Krantz & Dalal, in press). How do results from the Internet compare with those obtained in the laboratory? This study explores this question with new tests that refute descriptive theories of decision making. Reviews of modern theories, including rank-dependent utility (RDU), rankand sign-dependent utility (RSDU), and cumulative prospect theory (CPT), can be found in Quiggin (1993); Luce (1990, 1998); Luce and Fishburn (1991, 1995); Stevenson, Busemeyer, and Naylor (1991); Tversky and Kahneman (1992); Wakker and Tversky (1993); Weber (1994); and Wu and Gonzalez (1998). These modern theories account for phenomena that were not explained by earlier theories of Edwards (1954), Karmarkar (1979), and Kahneman and Tversky (1979). However, even these modern theories are now challenged by evidence with newly devised tests. STOCHASTIC DOMINANCE Not only is stochastic dominance considered rational, but it is also implied by many descriptive theories, including RSDU, RDU, CPT, and others (Becker & Sarin, 1987; Machina, 1982). A test of stochastic dominance is illustrated in Choice 5 of Table 1 (first row). Birnbaum (1997) proposed this choice as a test between theories that satisfy stochastic dominance and models that violate it. Two configural-weight models, the rank-affected multiplicative (RAM) and transfer-of-attention-exchange (TAX) models (with parameters estimated in previous studies), imply violation of stochastic dominance in this choice (Birnbaum, 1997, 1999; see the appendix).1 Birnbaum and Navarrete (1998) found that 70% of undergraduates violated stochastic dominance by choosing J = G– over I = G+, even though G+ dominates G–. COALESCING AND EVENT SPLITTING Coalescing also distinguishes decision theories (Birnbaum & Navarrete, 1998; Luce, 1998). Coalescing (see Table 2) assumes that branches with identical consequences can be combined (adding their probabilities), without affecting preference. Coalescing was assumed as an editing principle of prospect theory (Kahneman & Tversky, 1979), but it also follows from RSDU, RDU, CPT, and other theories (Luce, 1998). Because stochastic dominance can be deduced from transitivity, consequence monotonicity, and coalescing (see Table 2), Birnbaum and Navarrete (1998) and Birnbaum, Patton, and Lott (1999) argued that violations of coalescing might cause violations of stochastic dominance, but these studies did not test coalescing directly. Starmer and Sugden (1993) and Humphrey (1995) reported event-splitting effects (violations of coalescing combined with transitivity); however, Luce (1998) described that evidence as “decidedly weak” (p. 91). The present study used strong, within-subjects tests to determine if event splitting can reverse violations of stochastic dominance. According to coalescing, Choice 11 in Table 1 is the same as Choice 5, because GS+ (U in Table 1) is simply the split version of G+ (I) and GS– (V) is the split version of G– (J). Any theory assuming coalescing and transitivity implies G+ f G– if and only if GS+ f GS–, where f represents preference. The configural-weight RAM and TAX models with previously estimated parameters predict that people should prefer G– over G+ in Choice 5 and GS+ over GS– in Choice 11. LOWER AND UPPER CUMULATIVE INDEPENDENCE Birnbaum (1997) also devised two cumulative-independence conditions that test modern theories. Any theory that assumes comonotonic branch independence, consequence monotonicity, transitivity, and coalescing implies both lower and upper cumulative independence (see Table 2). Whereas RDU, RSDU, and CPT must satisfy these properties, RAM and TAX models violate them. VOL. 10, NO. 5, SEPTEMBER 1999 Copyright © 1999 American Psychological Society 399 Address correspondence to Michael H. Birnbaum, Department of Psychology H-830M, California State University, Fullerton, P.O. Box 6846, Fullerton, CA 92834-6846; e-mail: [email protected]; Internet: http://psych. fullerton.edu/mbirnbaum/home.htm. 1. To compute predictions for CPT and the configural-weight TAX models, use Netscape to load the on-line calculator at URL http://psych.fullerton. edu/mbirnbaum/taxcalculator.htm. Additional information on model fitting (including source listings of computer programs) is available from this Web site. PSYCHOLOGICAL SCIENCE Testing Decision Theories on the World Wide Web Choices 6 and 8 of Table 1 test lower cumulative independence. Suppose S f R in Choice 6. By comonotonic independence, we can increase the common branch in both gambles from $2 to $10, implying ($10, .8; $40, .1; $44, .1) f ($10, .8; $10, .1; $98, .1). Increasing $40 to $44 should make S even better. Therefore, ($10, .8; $44, .1; $44, .1) f ($10, .8; $10, .1; $98, .1); by coalescing, ($10, .8; $44, .2) f ($10, .9; $98, .1); that is, S'' f R'' in Choice 8. Upper cumulative independence is illustrated with Choices 10 and 9 of Table 1. Suppose S' = ($40, .1; $44, .1, $110, .8) p R' = ($10, .1; $98, .1; $110, .8) in Choice 10. Reduce the (common) prize from $110 to $98 in both gambles. Reducing $44 to $40 makes S' even worse, so S''' p R''' in Choice 9, by coalescing.