Example, on Dow Jones & Nikkei indexes today: Peter P. Wakker & Enrico Diecidue & Marcel Zeelenberg Domain: Individual Decisions under Ambiguity (events with unknown prob s ; Keynes 1921, Knight 1921) Question:How do people perceive of these uncertainties? How do they decide w.r.t. these? Measuring Decision Weights for Unknown Probabilities by Means of Prospect Theory U: both go Up (  ) D: both go Down (  ) R: Rest event (  =; one up other down, or at least one constant) Until 1990s, only DUR. More important: DUU. Studied since 1990s. Only then PT for uncertainty.

Knight (1921): Such uncertainties are “unmeasurable.” 2 Famous result by de Finetti (1931): showed how to measure them after all.

de Finetti’s (1931) book making: 3 People have to take subjective probabilities  U of U  D of D  R of R, (nonnegative,  U +  D +  R = 1) and evaluate U D R U D R $7$5$9 () Obtains expected value = subj. exp. utility with linear utility. Linear utility is reasonable for moderate stakes! No book making (  no arbitrage)   U 7 +  D 5 +  R 9 by For moderate stakes, other factors than utility curvature are more important for understanding risk attitudes. Impressive! Philosophers filled libraries …

In classical model, an easy way to elicit subj. prob s : through betting odds on events. 4 then  U = . However, Subj. Exp. Ut ty has descriptive problems (Ellsberg 1961). Constructive alternative: Cumulative prospect theory (Tversky & Kahneman 1992). Merges - original prospect theory (Kahneman & Tversky 1979) & - rank-dependent utility (Quiggin 1981, Schmeidler 1989). UDRUDR      () = , UDRUDR () ~ If

UDRUDR () U D R U U UU U U () ~ 1 Yes, still holds, need not change  U ! U U UU U U U D R () PT brings in “loss aversion.” Not relevant for our data. Also brings in rank-dependence through nonadditive prob s. Consider w w w and b b b ~ UDRUDR () de Finetti: different!  U   U w PT: So let us write:  U =  U b 5 ? After de Finetti click PT then don’t click on, but explain thatt side payment matters through optimism/pessimism, let certainty effect come in casually as by-product of pessimism. Speak in terms of subtracting some from U and increasing somewhat the other payments. For pessimist, U has more effect if worst so bigger  U is needed. After de Finetti click PT then don’t click on, but explain thatt side payment matters through optimism/pessimism, let certainty effect come in casually as by-product of pessimism. Speak in terms of subtracting some from U and increasing somewhat the other payments. For pessimist, U has more effect if worst so bigger  U is needed. Use term side payment.

Traditional measurements did not distinguish. Usually considered Same for other events D,R,. Likewise: + 1 U D R () UU m,D ~ UDRUDR 1 00 () UU m,D UU + 1 U D R () UU m,R ~ UDRUDR () UU m,R UU This leads to four decision weights: UU m,D UU m,R,,, UU b UU w 6 1 1, m,U DD … b, DD UU b DD b RR b ++  1 may be! Nonadditivity`as found empirically! UU b DD b RR b,,. First say that D surely has the best ranking position, referring to right prospect. Then that R has the worst ranking position, referring to the left prospect. So, U must be middle position.thr Before bringing up b-decision weights, say that traditionally through betting-on and, hence, b- decision weights.

Consider evaluation of a single gamble UDRUDR ()  m,U  U 9 +  D 7 +  R 5 b w Here still UU b m,U DD + + RR w = 1. Our empirical predictions: 1. The decision weights depend on the ranking position. 2. Decision weights for single gamble sum to one. 3. The nature of rank-dependence: 7 UU w > UU b > m,R UU m,D UU {, }

8 Pessimism: UU w > m,R UU m,D UU {, } UU b > (overweighting of bad outcomes ) Optimism: UU w < m,R UU m,D UU {, } UU b < (overweighting of good outcomes ) (Likelihood) insensitivity: UU w > m,R UU m,D UU {, } UU b > m,R UU m,D UU {, } (overweighting of extreme outcomes ) Empirical findings: UU w > UU b > m,R UU m,D UU {, } (Primarily insensitivity; also pessimism; Gonzalez & Wu 1999 ) p  Uncertainty aversion Economists usually want pessimism for equilibria etc.

9 Well known phenomenon is certainty effect: A general tendency to prefer riskless outcomes to risky prospects. Risk aversion/concave utility, as in expected utility, enhances this effect. Allais paradox demonstrated that: Expected utility/concave utility alone cannot explain all of it. Hence, prospect theory: Also pessimism/insensitivity contribute to certainty effect. Other factors beyond prospect theory: “Event-splitting” effect, “collapse” effect, etc. etc. Explained later. We will test for some of those also. No clear prior anticipation about whether they will reinforce or weaken the certainty effect. (Btw., prospect theories and insensitivity can go against certainty effect in specific situations, and generate risk seeking.)

– Many studies in “probability triangle.” Unclear results; triangle is unsuited for testing PT. –Other qualitative studies with three outcomes: Wakker, Erev, & Weber (‘94, JRU) Fennema & Wakker (‘96, JRU) Birnbaum & McIntosh (‘96, OBHDP) Birnbaum & Navarrete (‘98, JRU) Gonzalez & Wu (in preparation) –Lopes et al. on many outcomes, neg. results –confusing situation! 10 Many quantitative empirical studies of PT. Encouraging results. Always for two outcomes. Three outcomes:

Our experiment: 11 ? UD R ( ) UD R ( ) What would you choose? –Critically tests the novelty of PT –by measuring decision weights of events in varying ranking positions –through choices between three-outcome prospects –that are transparent to the subjects by appealing to de Finetti’s betting-odds system (through stating “reference prospects).”

However, we want, say, U in the worst ranking, i.e., we want. We then check if, e.g., U U w 12 UDR 1000 () U D R ().).  Imagine that we want to check if  U > UDR 1000 ()  U D R () i.e., UDR ()  U D R () reference gamble Classical method: w Call audience’s attention to superscript w to be added above.

13 ¹· =   p p Choice U D R Choice   ¹· = p p Choice   ¹· = p p …

14 The Experiment Stimuli: explained before. N = 186 participants. Tilburg-students, NOT economics or medical. Classroom sessions, paper-&-pencil questionnaires; one of every 10 students got one random choice for real. Written instructions –graph of performance of stocks during last two months –brief verbal comment on likelihood of increases/decreases of Dow Jones & Nikkei.

Order of questions –2 learning questions –questions about difficulty etc. –2 experimental questions –1 filler –6 experimental questions –1 filler –10 experimental questions –questions about emotions, e.g. regret order completely randomized 15

.44 (.18) * worst collapse.41 (.18).43 (.17) best middle worst collapse.51 (.20).49 (.20) Rest-event: RR.52 (.18).50 (.19).50 (.18) noncoll..53 (.20).50 (.20) Results 16 * best middle worst.35 (.20).35 (.19) suggests insensitivity DD.34 (.18).31 (.17).34 (.17) collapse noncoll..33 (.18).33 (.19) * * Up-event: best middle UU.48 (.20).46 (.18) noncoll..46 (.22).51 (.23) * * *** Down-event: suggests pessimism suggests optimism collapse: say that this is factor beyond prospect theory that will be explained on next slide Main effect is likelihood and is justfine. Bigger overestimation of unlikely events suggests insensitivity.

17 Empirical prediction 2 was: Decision weights for single gamble sum to one. W ell, they sum to, on average, 1.3 > 1. So, more risk seeking in our data! May be due to response mode effects.

  ¹· = p p Choice Choice   ¹· = p p Choice ¹· =   p p U D R …   ¹· = p p Choice Choice   ¹· = p p ¹· =   p p Choice U D R … With collapse, we find earlier switches than without. It suggests that the factors beyond prospect theory weaken the certainty effect here. What those factors are, we do not know at present. 18 UU w,n UU w,c

regret correlations between regret and decision weights UU b,c p =.019 UU w,c p =.023 DD w,c p =.015 Regret correlates positively with almost all decision weights: The more regret, the more risk seeking. It correlates especially strongly in presence of collapsing. Strange finding for revealed preference approach! 19