Does the Order of Potential Outcomes Influence Economic Decision Making?
Joanne Lee Department of Psychology Wilfrid Laurier University 75 University Avenue West, Waterloo, ON Canada N2L 3C5
Eric Terry* Department of Finance Ryerson University 350 Victoria St., Toronto, ON Canada M5B 2K3
This version: June 10, 2009
*Corresponding author. E-mail address:
[email protected]. Fax: 416-979-5266. We thank participants at the 2008 Midwest Decision Sciences Institute conference, the 2009 Association for Psychological Science annual convention, and a seminar at Ryerson University for their comments on a previous version of the paper.
Does the Order of Potential Outcomes Influence Economic Decision Making? Abstract This study examines whether the order of potential outcomes influences risky decision-making. It is found that individuals select riskier alternatives much more frequently when the outcomes for each alternative gamble are specified from worst to best than when they are given from best to worst. This observed outcome order effect is more consistent with a change in the shape of the probability weighting function of the students rather than a shift in their level of risk aversion. These results suggest the existence of a recency effect in which individuals overemphasize the potential outcomes that are presented last relative to those listed earlier when making risky decisions. Several implications of our findings are discussed. Keywords: recency, order effects, decision-making, probability weighting function, cumulative prospect theory JEL classification: C91, D81
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Does the Order of Potential Outcomes Influence Economic Decision Making? A number of economic theories have been developed to explain decision-making under uncertainty, including Expected Utility Theory (von Neumann & Morgenstern, 1944) and Cumulative Prospect Theory (Tversky & Kahneman, 1992). Responses to forced choices between hypothetical gambles are commonly used to estimate the parameters (e.g., coefficient of relative risk aversion), to determine the appropriate functional forms (e.g., power vs. exponential utility), and to test the underlying premises (e.g., the cancellation principle) of these theories. They are also used to compare the relative performance of these theories in explaining decisionmaking behavior and to identify general patterns in decision-making, such as the conditions under which individuals tend to be more risk-averse or more risk-seeking. This experimental procedure assumes that there is no systematic bias in the choices to these hypothetical gambles. One potential source of bias is the order in which information about the gambles is provided. Although empirical studies of risky decision making often randomize the order in which the alternative gambles appear, very few of these studies control for the order in which the potential outcomes of each alternative are presented. The vast majority of published papers list the potential outcomes of each alternative from best to worst for gambles that involve either gains or mixed outcomes and from worst to best (i.e., most negative to least negative) for gambles that involve losses. Serial order effects have been observed in a variety of situations. Asch (1946) found that personality traits (such as “intelligent” or “critical”) at the beginning of a listing of observed traits for an individual influenced respondents’ impressions about that individual more strongly than ones that appeared later. Miller and Campbell (1959) found that judgments regarding a mock civil trial could be influenced by manipulating the order in which facts were presented and
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the interval between the presentation of the facts of the case and the decision as to fair damages. Studies of memory have typically found a U-shaped curve, with more items at the beginning and end of the list recalled than items from the middle portion of the list (Atkinson & Shiffrin, 1968; Craik & Lockhart, 1972). Levy and Levy (2005) found that subjects tended to overweight recent returns in portfolio decisions despite being informed that generated returns for the assets were i.i.d. through time. Finally, in a closely related paper to the current study, Lee, Lohrey, MacDonald, and Terry (2008) found that observed framing effects were sensitive to the order in which the potential outcomes of the alternatives were presented, with respondents choosing riskier alternatives more frequently in both frames when outcomes are listed from worst to best than when they were listed from best to worst. In this paper, we investigate the extent to which the order of and alternatives impact economic decision making using the decision-making experiment of Wu and Gonzalez (1996). Their experimental procedure was chosen because it allows for simple visual interpretation of the results in addition to formal parametric tests. Based on the findings of our previous study, we hypothesize that: H1: Respondents will choose riskier alternatives more often when potential outcomes are listed from worst to best than when they are listed from best to worst. This expected result would be consistent with a recency effect in which individuals tend to overemphasize potential outcomes that are presented last relative to those listed earlier. Consequently, we would expect that: H2: Any observed outcome order effect will be caused by a shift in the probability weights of respondents when outcome order is changed rather than by a shift in their level of risk aversion.
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In the experiment, we randomize the order of the riskier and safer alternatives. This procedure allows us to examine whether the order of the alternative gambles influences the preferred choices between them and/or interacts with any outcome order effect that we observe. Thus, a final hypothesis is that: H3: The order of the alternatives has no impact on preferences between these gambles. This hypothesis reflects the fact that we were unable to find any previous study that concluded that the order in which the alternatives are listed has a significant impact on risky decisionmaking. Method Participants and materials The participants were 324 undergraduates who were taking an introductory psychology course at the University of Connecticut and received extra credit for their participation. The students were given questionnaires containing 50 decision problems in which they had to choose between two gambles. Ten of these decision problems were filler questions; the remaining 40 decision problems were adapted from the experimental study by Wu and Gonzalez (1996). Design and procedure Each decision problem belongs to one of five families of related problems, which Wu and Gonzalez (1996) refer to as concavity/convexity ladders for reasons that will be clear below. The five concavity/ convexity ladders are outlined in Table 1. Consider the decision problem that forms the first “rung” for Ladder 1: Choose between •
A 5% chance to gain $240 and a 95% chance to gain $0
•
A 7% chance to gain $200 and a 93% chance to gain $0
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The common consequence of a 10% chance of gaining $200 was added to both alternatives in this decision problem in order to create the decision problem forming the second rung of this ladder: Choose between •
A 5% chance to gain $240, a 10% chance to gain $200, and an 85% chance to gain $0
•
A 17% chance to gain $200 and an 83% chance to gain $0
This procedure of adding a common consequence was repeated in order to form eight rungs for each of the five ladders. Wu and Gonzalez (1996) prove that systematic preference shifts across the rungs of a particular ladder reflect concavity/convexity in the probability weighting function of the participants. This property allows the results to be interpreted graphically. Consider the hypothetical results for one of the ladders given in Figure 1. The right intercept of the preference curve is determined by the median level of risk aversion for the respondents and the amount of curvature in these preferences reflects the median curvature in the probability weighting functions of these participants. Thus, a shift upwards in the preference function would indicate a reduction in risk aversion, while increased curvature in this function would reflect greater curvature in the probability weighting function. Whereas Wu and Gonzalez (1996) only considered gambles involving gambles, we also considered gambles involving losses by rewording the decision problems in terms of losses instead of gains. On each questionnaire, four of the rungs belonging to each ladder were presented as choices between potential gains and the other four rungs were given as choices between potential losses. Additionally, each decision problem was ordered in one of four possible ways: (i) the safer alternative first and payoffs ordered from best to worst, (ii) the safer alternative first and payoffs ordered from worst to best, (iii) the riskier alternative first and payoffs ordered from best to worst, and (iv) the riskier alternative first and payoffs ordered from
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worst to best. Finally, the 50 decision problems were presented in a random order on each questionnaire in order to prevent any potential question order effect from confounding the results (cf. Schuman & Presser, 1981). Results The results for the decision problems involving gains are shown in Figure 2. For 32 out of the 40 decision problems, respondents chose the riskier alternative more often when outcomes were ordered from lowest to highest instead of from highest to lowest. Using a non-parametric binomial test, this result is significantly different than chance (p < .001) and so confirms our first hypothesis. Interestingly, this result did not obtain in all four of cases in which the safer payoff was certain. This suggests that the impact of outcome order may be stronger when choosing between two risky alternatives than when the alternatives involve a risky and a safe one. Additionally, because these cases correspond to the right intercept of the preference function, this finding suggests that the observed outcome order effect is driven primarily by a shift in the probability weights of the respondents when outcome order is changed rather than by a shift in their level of risk aversion. This result is consistent with our second hypothesis. Finally, in accord with our third hypothesis, the order in which the two alternatives were presented had no significant impact on respondent’s decisions. Corresponding results were obtained for the decision problems when they involved losses instead of gains. These are shown in Figure 3. For 29 out of the 40 decision problems, respondents chose the safer alternative more often when potential outcomes were ordered from highest to lowest instead of from lowest to highest. This result was again significantly different than chance (p = .001). This general result of individuals choosing riskier alternatives more frequently when outcomes are ordered from lowest to highest instead of from highest to lowest
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held in only two of the four cases in which the safer payoff was certain. As before, this suggests that: (i) the impact of outcome order is stronger when choosing between two risky alternatives than when choosing between a risky alternative and a safe one and (ii) the influence of outcome is caused by a shift in probability weighting rather than in risk aversion levels. The order in which the two alternatives were listed again had no significant impact on respondent’s decisions. We also conducted parametric tests on the results using Cumulative Prospect Theory (Tversky & Kahneman, 1992) as the base model. Stott (2006) conducted an experimental test of various forms of Cumulative Prospect Theory (CPT) and found that the best fit was obtained using the power utility function proposed by Tversky and Kahneman (1992) α ⎧ u ( x) = ⎨ x α ⎩ −λ ( − x )
for x ≥ 0 for x < 0
(1)
and the probability weighting function proposed by Preclec (1998)
(
)
w( p) = exp − [ − ln( p)] . γ
(1)
The parameter α measures the coefficient of relative risk aversion over the gains domain (risk seeking over the losses domain), while the parameter λ captures the degree of loss-aversion. Finally, the parameter γ measures the amount of curvature of the probability weighting function, with a lower value of γ implying greater curvature in this function. The following logistic regression equation was used to estimate the values of these parameters from the responses to the ten decision ladders (five involving gains and five involving losses): ⎛ p ⎞ ln ⎜ ⎟ = β [V ( R) − V ( S ) ] + ε , ⎝ 1− p ⎠
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where p is the probability of choosing the riskier alternative and V(R) and V(S) represent the value under CPT of the riskier and safer alternative, respectively. This equation assumes that the log odds ratio of selecting the riskier alternative over the safer one is linear in the difference in value between the two alternatives. The intercept was forced to equal zero in order to ensure that the representative individual is indifferent between the two alternatives (i.e., p = .5) when they have equal value. The logistic regression results are provided in Table 2. The coefficient of relative risk aversion in the power utility function was not significantly influenced by outcome order. In contrast, the estimated value of γ decreased significantly, i.e., the probability weighting function displayed more curvature when payoffs were ordered from low to high instead of high to low. The logistic regression was also estimated using the probability weighting functions of Lattimore, Baker, and Witte (1992) and Tversky and Kahneman (1992) instead of the form given by equation (2); the results were not significantly different from those presented here. Discussion The results in the previous section indicate that risky decision-making is influenced by outcome order. Respondents consistently chose riskier alternatives more often when outcomes are listed from worst to best than when they are listed from best to worst. Furthermore, it was found that a change in outcome order causes a shift in the probability weights of respondents rather than a shift in their level of risk aversion. Together, these results imply the existence of a recency effect in which individuals tend to overemphasize potential outcomes that are presented last relative to those listed earlier. These findings have several important implications. First, they stress the need to control for outcome order in experimental studies of economic decision-making by counterbalancing the order of potential outcomes within each experiment. Moreover, because the vast majority of
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prior studies have not controlled for outcome order, it is possible that published estimates of the parameters and tests of the appropriate functional form and underlying premises of alternative theories of risky decision-making may be biased. Finally, none of the commonly-used economic models of risky decision-making are able to account for the existence of a significant outcome order effect. Our findings suggest that these models may need to be rethought and revised. The results also suggest that outcome order could be used as a tool to influence individual decision-making. For example, lotteries and other forms of gambling could be marketed most successfully by emphasizing the potential winning payoff at the end of any promotion. The same rationale would apply to the marketing of derivatives and other speculative investments. Conversely, those promoting safer investments would want to emphasize the limited downside of the investment relative to more risky types of investment at the end of their promotional materials. Furthermore, it would be optimal for public corporations and investment companies to present more favorable information near the end of public announcements and other news releases if the information being revealed is mixed. It would be instructive to examine the extent to which these strategies have been followed and how successful these strategies have been. Although this paper has demonstrated the existence of a significant outcome order effect for standard risky decision making problems, future work should be done to determine the extent to which outcome order impacts other types of economic decision-making.
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References Asch, S. (1946). Forming impressions of personality, Journal of Abnormal and Social Psychology, 41, 258-290. Atkinson, R. C., & Shiffrin, R. (1968). Human memory: A proposed system and its control processes. In K. W. Spence & J. T. Spence (Eds.), The Psychology of Learning and Motivation: Advances in Research and Theory. Vol. 2 (pp. 89-195). New York: Academic Press. Craik, F. I., & Lockhart, R. S. (1972). Levels of processing: A framework for memory research. Journal of Verbal Learning & Verbal Behavior, 11, 671-684. Lattimore, P. K., Baker, J. R., & and Witte, A. (1992). The influence of probability on risky choice. Journal of Economic Behavior and Organization, 17, 377-400. Lee, J., Lohrey, P. L., MacDonald, J., & Terry, E. (2008). Do you want the good news or the bad news first? Outcome order and framing. Toronto, ON: Ryerson University, Ted Rogers School of Business Management. Levy, H., & Levy, M. (2005) Overweighting recent observations: experimental results and economic implications. In R. Zwick & A. Rapoport (Eds.), Experimental Business Research, Volume III: Marketing, Accounting and Cognitive Perspectives (pp. 155-183). New York: Springer. Miller, N., & Campbell, D. T. (1959). Recency and primacy in persuasion as a function of the timing of speeches and measurements. Journal of Abnormal and Social Psychology, 59, 1-9. von Neumann, J., & Morgenstern, O. (1944). Theory of games and economic behavior. Princeton, NJ: Princeton University Press. Prelec, D. (1998). The probability weighting function. Econometrica, 66, 497-527.
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Schuman, H., & Presser, S. (1981). Questions and Answers in Attitude Survey: Experiments on Question Form, Wording and Context. Orlando: Academic Press. Tversky, A., & Kahneman, D. (1992). Advances in Prospect Theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5, 297–323. Wu, G., & Gonzalez, R. (1996). Curvature of the probability weighting function. Management Science, 42, 1676–1690.
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Footnote 1. Tversky and Kahneman (1992) allow the utility function to have a different degree of curvature over the losses domain than over the gains domain. However, in their empirical analysis, they find that the curvature is identical over gains and losses. As well, if the utility function has more curvature over the losses domain than over the gains domain, the value function will not display loss aversion for large actuarially fair gambles, which goes against empirical evidence. For these reasons, the curvature of the utility function is usually assumed in practice to be the same over gains and losses.
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Table 1 Concavity/Convexity Ladders Probability of Payoff Option Payoff
Rung 1
Rung 2
Rung 3
Rung 4
Rung 5
Rung 6
Rung 7
Rung 8
Ladder 1 R
S
$240
.05
.05
.05
.05
.05
.05
.05
.05
$200
.00
.10
.20
.30
.45
.60
.75
.90
$200
.07
.17
.27
.37
.52
.67
.82
.97
Ladder 2 R
S
$100
.05
.05
.05
.05
.05
.05
.05
.05
$50
.00
.10
.20
.30
.45
.60
.75
.90
$50
.10
.20
.30
.40
.55
.70
.85
1.00
Ladder 3 R
S
$300
.01
.01
.01
.01
.01
.01
.01
.01
$150
.00
.10
.20
.30
.45
.60
.80
.98
$150
.02
.12
.22
.32
.47
.62
.82
1.00
Ladder 4 R
S
$320
.03
.03
.03
.03
.03
.03
.03
.03
$200
.00
.10
.20
.30
.45
.65
.85
.95
$200
.05
.15
.25
.35
.50
.70
.90
1.00
Ladder 5 R
S
$500
.01
.01
.01
.01
.01
.01
.01
.01
$100
.00
.10
.20
.30
.45
.65
.80
.95
$100
.05
.15
.25
.35
.50
.70
.85
1.00
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Table 2 Parameter Estimates for Cumulative Prospect Theory
Outcomes ordered high to lowa
Outcomes ordered low to high
a
Standard errors in parentheses.
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α
γ
.771
.856
(.019)
(.009)
.741
.642
(.014)
(.014)
% choosing riskier gamble
Original preferences Increased curvature in PWF Decreased risk aversion 0
1
Probability of safer gamble
Figure 1. Hypothetical impact of changing the order of potential outcomes from the highest to lowest outcome to the lowest to highest outcome.
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(a)
(b)
(c)
(d)
(e) Figure 2. Percentage of respondents choosing the riskier alternative for: (a) Ladder 1, (b) Ladder 2, (c) Ladder 3, (d) Ladder 4, and (e) Ladder 5.
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(a)
(b)
(c)
(d)
(e) Figure 3. Percentage of respondents choosing the safer alternative for the negatives of: (a) Ladder 1, (b) Ladder 2, (c) Ladder 3, (d) Ladder 4, and (e) Ladder 5.
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