The Influence of Present and Prior Alternatives on Risk Aversion
Adelson Piñón and Martin Weber*
Abstract
In a series of decision problems the influence of present and past options involving potential
gains and potential losses was tested. This was done in two financial contexts (lottery vs.
portfolio) eliciting individual preferences by means of several mixed gambles. No reduction of
risk aversion was found when an option with higher expected value was included in a high
probability of loosing set. Nevertheless, it was found such reduction when the probability of
winning was high mediated by frame. In the lottery treatment, the higher the probability of
winning the higher the anchor effect of the added option. In the between-trial condition, when
subjects focused on gains (losses) they were less risk averse after a high risk background with
high probability of winning (loosing). In the portfolio treatment, neither within-trial nor betweentrial effects were found, showing that a small frame manipulation was successful in making
individuals context-independent. Activation and salience may explain how particular information
tend to induce predictable patterns of choice under risk.
Keywords: Behavioral Finance, Decision Making, Risk Aversion, Frame, Anchoring.
*Adelson Piñón is from the Lehrstuhl für Bankbetriebslehre, Universität Mannheim, L 13, 15 68131 Mannheim, and
Department of Psychology, Madrid Autonomous University. E-Mail: pinon@bank.bwl.uni-mannheim.de. Martin
Weber is from the Lehrstuhl für Bankbetriebslehre, Universität Mannheim, L 5, 2 68131 Mannheim, and CEPR,
London. E-Mail: weber@bank.bwl.uni-mannheim.de. We would like to thank Hilda Gambara, Jens Grunert,
Christoph Heumann, Orfelio León, and Ignacio Montero for assistance on running the experiment, as well as Anders
Anderson, Silvia Elsland, Lars Nordon, Pablo Quintá, Sava Savov, and Frank Welfens for valuable comments.
Financial support from the Marie Curie RTN European Network for the Advancement of Behavioral Economics
(ENABLE) is gratefully acknowledged.
1. Introduction
In classical decision theory, choice was believed to reveal a person’s preference. Individuals
made rational decisions in order to maximize their utility function, which was assumed to be
concave and based on total wealth. Nevertheless, an extensive amount of experimental and
empirical evidence has demonstrated the falsehood of these assumptions. Preference between
options may change under two normatively equivalent conditions when different formulations are
used (Tversky & Kahneman, 1981). For instance, the concept of framing effect has been applied
to financial decisions such as dollar-cost averaging (e.g. Kahneman & Riepe, 1998; Statman
1995). Psychological studies demonstrate that decisions may also be biased in the direction of a
salient comparison value denominated anchor, a notion first introduced to explain preference
reversals (Slovic, 1967; Slovic & Lichtenstein, 1968; Lichtenstein & Slovic, 1971). Anchoring
effects are remarkably robust and have been proposed as an explanation in a multitude of
domains (e.g. Bleichrodt, 2001; Epley & Gilovich, 2005).
The idea that preferences may be elicited by the context is receiving increased attention
(Frederick, 2002; Slovic, 2000; Usher & McClelland, 2004). Although frame and anchor effects
have been initially considered independent, both may be seen as instances of a broader family of
accessibility effects, a conception compatible with more recent theoretical treatments of judgment
and decision making (Kahneman & Frederick, 2005). This conception is worth exploring because
it is consistent with so much psychological evidence, and to our knowledge, it has not been
applied before to analyze how individuals make sequential and non-sequential choices, two
situations by which decision-makers may assess options at any particular point.
We created an experimental setting with hypothetical choices presenting mixed gambles with
asymmetric payoffs in two financial domains: lottery and portfolio. We selected that type of
gambles because there is an abundance of instruments in the financial markets that deliver such
2
payoffs, and there has been little research on their effect on preferences (Taleb, 2004; Wu, Zhang,
& Gonzalez, 2004).
We know that the reliance on hypothetical choices may raise questions about the validity of
the results, but other methods have also limitations. Real choices can be investigated either in the
field, or in the laboratory. Field studies do not allow neither adequate measurements of
probabilities, nor the manipulation of options that decision makers are taking into account.
Laboratory experiments typically involve very small stakes, and large number of repetitions that
bias the results and restrict their generality.
We agree with Kahneman and Tversky (1979) that the method of hypothetical choices
emerges as the simplest procedure to investigate choice behavior. The method relies on the
assumption that people often know how they would choose in actual situations, and on the further
assumption that subjects have no special reason to mask their true preferences. If people are
reasonably accurate in predicting their choices, the presence of particular patterns in hypothetical
problems provides presumptive evidence for actual situations of choice.
Our main results can be summarized as follows. No reduction of risk aversion was found
when an option with higher expected value was included in a high probability of loosing set.
Nevertheless, it was found such reduction when the probability of winning was high mediated by
frame. In the lottery treatment, the higher the probability the higher the anchor effect of the added
option. In the between-trial condition, when subjects focused on gains (losses) they were less risk
averse after a high risk background with high probability of winning (loosing). In the portfolio
treatment, neither within-trial nor between-trial effects were found, showing that a small frame
manipulation was successful in making individuals context-independent. The results are
consistent with our predictions. The activation and salience of certain information tend to induce
differential systematic choices.
3
The rest of the paper is organized as follows. We first briefly summarize the literature on
context dependency in mixed gambles. Section 3 describes the hypotheses. Next we report on the
results of three experiments. The last section discusses the findings and concludes the article.
2. Literature Review
A large body of evidence in decision making has shown that context influences risky choice
behavior. In our view, three theoretical approaches may be suggested to accommodate the
literature about the topic.
A first approach defends the notion that in making their risky choices, subjects focus on
reaching a special outcome called the aspiration level (e.g. Lopes, 1996; Lopes & Oden, 1999;
Marley, 1997; Payne, Laughhunn, & Crum, 1980, 1981). Outcomes below the aspiration level are
perceived as failures, whereas outcomes above that level are perceived as successes. Once a
certain amount (i.e. the aspiration level) has been subtracted from each consequence, the resulting
gambles are evaluated in terms of some classical choice theory. This approach presents one
fundamental problem: aspiration level theories are unable to predict or explain how the aspiration
level is determined (Luce, 2000).
Regret theory models suggested that people take into account the potential regret or elation of
each alternative under consideration (e.g. Bell, 1982, 1985; Loomes, Starmer, & Sugden, 1991;
Loomes & Sugden, 1982; 1986). The influence of other options on the representation of a
particular alternative is explained as violations of monotonicity and transitivity due to anticipated
emotions. Unfortunately, regret cannot be used to predict risk behavior since it can play a role in
dissuading or motivating individuals to decide a particular option. Furthermore, most of the
phenomena argued to be consistent with regret theory models are also claimed as indications for
prospect theory (Yates, 1990).
4
The third approach accommodates the context effects within the heuristics and biases
paradigm (e.g. Fennema & Van Assen, 1998; Fennema & Wakker, 1997; Tversky & Kahneman,
1992). Cumulative prospect theory is an extension of the most prominent descriptive model of
risky choice (Kahneman & Tversky, 1979). It has four important features: (1) the value function
is defined over gains and losses relative to a reference point; (2) the gain function is concave and
the loss function is convex; (3) losses loom larger than gains (i.e. loss aversion), and (4) prospects
include mixed gambles with multiple risk or uncertain outcomes.
Also this model is limited and incomplete (Payne, 2005) given that decision making is
partially driven by factors related with the task. The list of factors includes among others: the
presence of an anchor (e.g. Epley & Gilovich, 2005), the domain in which the task is presented
(e.g. Shafir, Simonson, & Tversky, 1993), or different elicitation procedures (e.g. Hsee,
Loewenstein, Blount, & Bazerman, 1999; Tversky, Slovic, & Kahneman, 1990; Tversky &
Thaler, 1990). Although this influence is also recognized by other approaches (Luce, 2000),
recent treatments within this paradigm provide a unifying theoretical structure, viewing
preference changes as the product of memory representations and memory processes (Kahneman,
2003; Kahneman & Frederick, 2005; Weber & Johnson, 2006). The next section explains the
predictions based on this framework.
3. Hypotheses & Experimental Design
Focusing on the role of memory in decision making suggests several testable predictions. The
attractiveness of current options may be changed when the salience of particular attributes is
manipulated (Shafir & LeBouef, 2005) or due to the influence of background knowledge
(Morrison, 2005; Novick & Bassok, 2005). If individuals focus more on gains (losses), they will
tend to select options with high (low) expected values, and changes of preference (i.e. reduction
5
of risk aversion) are more likely to be observed when the probability of winning is high (low)
because this attribute is more salient and receive more weight in the decision. Risk aversion is
defined as a preference for the prospect with lower expected value. Confronted with the null
hypothesis of no reduction of risk aversion in any condition, we propose,
Hypothesis 1 (Within-trial condition): the addition of an alternative with higher expected
value and higher risk in the choice set will reduce risk aversion when the probability of winning
is high (low) if participants focus on gains (losses).
Hypothesis 2 (Between-trial condition): previous options with high expected value and high
risk will reduce risk aversion when the probability of winning is high (low) if participants focus
on gains (losses).
Given that different frames imply different cognitive representations of the same information
(Piñón & Gambara, 2005), different effects should be observed (Weber & Zuchel, 2005):
Hypothesis 3 (Frame): The size of within-trial and between-trial effects depends on the
frame (lottery vs. portfolio) provided.
The participants in the studies reported in this article were undergraduate students. We
conducted three studies involving 8 groups of mixed gambles in a class setting. We did not
provide any monetary incentives, because allowing subjects to win or lose the amounts of money
involved is not possible. Figure 1 provides a graphic idea of the design used in all the studies.
In the within-trial condition, we compared a group choosing between the gambles (G1, G2)
with a group choosing between the same set plus an additional gamble with high expected value
6
(G1, G2, G3). In the between-trial condition, we compared how the decision in the target set (G1,
G2) was influenced by a previous choice involving higher risk and expected values (BT1, BT2) or
by a previous background involving lower risk and expected values (BT3, BT4).
Individual valuations were elicited using a questionnaire with hypothetical gambles involving
gains and losses. We used four asymmetric payoffs (80%-90% chances of winning or loosing)
and two frames (lottery vs. portfolio).
[Figure 1 about here]
Study 1
A. Objectives & Subjects
We examine within-trial and between-trial conditions with two opposite asymmetric payoffs
(80% chance of winning vs. 80% chance of loosing) in a lottery frame.
Each of the 456 subjects were asked to fill out a questionnaire. The participants were
undergraduate students of business administration from the University of Mannheim. Their mean
age was 21.7 years (SD = 1.7). Two hundred sixty four (61%) were men, 172 women1.
B. Operationalization & Procedure
Table 1 and 2 show the lotteries presented to the subjects. Two probability levels implying
either potential gains or potential losses with the same expected values were used in the
experimental design adopted. All lotteries employed had positive expected values. Comparisons
1
23 participants did not report age. 20 did not report gender.
7
were made in a between-subject basis. The questionnaires were presented to the participants in a
completely randomized order. One example of questionnaire2 is provided as follows:
Which of these lotteries do you prefer?
Lottery 1
0.8
0.2
91€
- 250€
Lottery 2
0.8
0.2
144€
- 355€
High and low probability of winning groups received lotteries that vary in expected value and
risk (i.e. potential loss)3. The dependent variable was aggregated choices in the low risk option
(Lottery 1 in both conditions). Respondents in groups 1-4 (within-trial condition) made one
choice in the set of lotteries presented. Group 1 and 3 chose between two lotteries, whereas
Group 2 and 4 had to choose between the same lotteries plus an additional one with higher
expected value and higher risk.
Respondents in groups 5-8 (between-trial condition) first made one choice between lotteries
in the background set, followed by one choice between lotteries in the target set. All subjects
received the same target set but half of them chose between lotteries with high differences in
expected value and low differences in high risk. The other half chose between lotteries with
lower differences in expected value and higher differences in risk.
[Table 1 and 2 about here]
2
3
Translated from German.
See Appendix A for further details.
8
C. Results & Discussion
Table 3 shows the results obtained in the within-trial condition. Participants exposed to the
high probability of winning lotteries were indifferent between the lotteries presented, and a
within-trial effect was found when an additional option with high expected value was added to
the choice set (z = 1.946; p = 0.0258). When the probabilities of loosing were high, respondents
were risk seeking (z = 3.016; p = 0.0013) and there was no reduction of risk aversion when the
new option was added (z = -0.378; p = 0.6475). Figure 2 illustrates the effects found.
[Table 3 about here]
[Figure 2 about here]
Table 4 and Figure 3 show the results of the between-trial condition. As may be seen, at both
probability levels independently of the background, individuals tend to be risk seeking (p < .05).
In lotteries involving high probability of loosing, there were no significant differences between
choices in the target set (z = -0.960; p = 0.1686). When the lotteries involved a high probability
of winning, 29% of the individuals chose the less risky option in the target set after the high risk
background, whereas 41% of the participants chose the same option in the low risk background (z
= -1.296; p = 0.0975).
[Table 4 about here]
[Figure 3 about here]
Participants in the high probability of winning gambles showed within-trial and between-trial
effects. We interpret these results in terms of accessibility: focusing on gains (i.e. selecting
9
gambles with high expected value, and therefore being more risk seeking) make respondents
more context dependent when potential gains with high probability are available. The addition of
a new option in the choice set as well as previous choices involving high probability of winning
acted as an anchor, inducing individuals to be less risk averse.
This interpretation implies that different anchor effects (i.e. within-trial and between-trial
effects) should be observed if we vary the factors related with the anchor: the quantitative
information provided to participants (i.e. probability levels and outcomes), and the qualitative
information used (i.e. frame). In the next study we vary probability levels and outcomes
maintaining the expected values constant. By increasing the potential losses involved, we are
inducing participants to weight losses more heavily than gains (i.e. be more risk averse). The
manipulation of the frame is addressed in Study 3.
Study 2
A.
Objectives & Subjects
We examine between-trial and within-trial effects under the same frame as the previous study
but with different outcomes involving different probability levels (90% chances of winning vs.
90% chances of loosing).
Each of the 362 subjects were asked to fill out a questionnaire. The participants were
undergraduate students of psychology from Madrid Autonomous University. The mean age was
19.2 (SD = 3.7). Two hundred thirty eight (73%) were women, 86 men4.
B.
Operationalization & Procedure
Table 5 and 6 show the lotteries presented to the subjects. We used the same expected values
as in Study 1. Comparisons were made in a between-subject basis. The questionnaires were
4
38 participants did not report gender. 46 did not report age.
10
presented to the participants in a completely randomized order. For each pair or triad, subjects
had to report they preferred lottery.
[Table 5 and 6 about here]
C. Results & Discussion
We found higher within-trial and between-trial effects. Tables 7-8 and figures 4-5 show the
results. Participants in group 1 are indifferent between the lotteries. Nevertheless, preference for
lottery 1 decreases in group 2 (z = 2.791; p = 0.0026). When the probability of winning is low
individuals are more risk seeking (z = 1.774; p = 0.0381) but the addition of a new option with
high expected value and higher risk does not change risk aversion (z = 0.102; p = 0.4593).
[Table 7 about here]
[Figure 4 about here]
In the between-trial condition, participants had a general tendency to be highly risk averse (in
3 out of 4 groups p < .01). Individuals are influenced by previous decisions when the probability
of loosing is high (z = -1.534; p = 0.0625), but not when this probability is low (z = 0; p = 0.5).
[Table 8 about here]
[Figure 5 about here]
The experimental manipulation was partially successful (it did not induce risk aversion in the
within-trial condition). Participants in the between-trial condition focused on losses (i.e. selected
11
gambles with low expected values), and as predicted by hypothesis 2, they were less risk averse
when the probability of loosing was high. The anchor effect related with prior decisions is now
observed for potential losses as expected. We finally vary the frame of the options in the next
study in order to check how this manipulation may affect choices.
Study 3
A. Objectives & Subjects
We examine between-trial and within-trial conditions under a portfolio frame, with the same
outcomes and probability levels used in Study 1.
Each of the 357 subjects were asked to fill out the questionnaire. The participants were
undergraduate students of business administration of Mannheim University. Their mean age was
21.7 years (SD = 2.4). Two hundred and eight (61%) were men, 131 women5.
B. Operationalization & Procedure
It was presented the same questionnaires as in Study 1, but with the word “portfolio” instead
of “lottery”, as follows:
Which of these portfolios do you prefer?
Portfolio 1
0.8
0.2
91€
- 250€
Portfolio 2
0.8
0.2
144€
- 355€
As in the previous studies, comparisons were made in a between-subject basis. The
questionnaires were presented to the participants in a completely randomized order.
5
29 participants did not report age. 18 did not report gender.
12
C. Results & Discussion
No effects were found under this frame. Neither in the within-trial condition, probability 0.80
(z = -0.498; p = 0.3091), probability 0.20 (z = 0.560; p = 0.2879), nor in the between-trial
condition, probability 0.8 (z = -1.038; p = 0.1498), probability 0.2 (z = 0.442; p = 0.3293).
[Table 9 about here]
[Figure 6 about here]
Tables 9-10, and Figures 6-7 show the findings under this experimental manipulation.
Participants are risk seeking but the portfolio frame seems to reduce the weight attributed to
gains, making them immune to the anchor effects of prior and present alternatives.
[Table 10 about here]
[Figure 7 about here]
3. General Discussion
Several issues have been addressed in this paper: how present and past alternatives available
may modify risk aversion, and what is the impact of outcomes, probability level, and frame in the
different effects observed.
Neither aspiration level, nor regression theory models can adequately explain our results. The
first cannot explain the apparently contradictory finding of reduction of risk aversion after prior
decisions involving potential gains and after prior decisions involving potential losses. The
second assumes that people must be so extremely sensitive that even in hypothetical choices they
take potential regret or disappointment into account.
13
We interpreted the results obtained in terms of accessibility. The activation and salience of
particular information tend to induce predictable choices. It was not found a reduction of risk
aversion when an option with higher expected value was included in a high probability of loosing
set due to a higher weight of gains that made losses less salient. Nevertheless, it was found
within-trial effects when the probability of winning was high mediated by frame. In the lottery
treatment, the higher the probability the higher the anchor effect of the added option. In the
between-trial condition, when subjects focused on gains (losses) they were less risk averse after a
high risk background with high probability of winning (loosing).
It can be argued that our experimental design induced within-trial effects, given that if one
group of participants selected one of two options randomly (i.e. 50%) and another group decide
between three options randomly (i.e. 33%) a reduction of risk aversion should be always
observed. We believe that this is not the case for two reasons. First, we only observed within-trial
effects in 2 of 6 conditions. Second, a higher within-trial effect for higher potential gains was
found in Study 2. These results exclude the alternative explanation of random selection, and
provide support for the expected finding that the addition of a third alternative induce
respondents to focus on gains only in particular frames when the probability of winning is high.
In the portfolio treatment, neither within-trial nor between-trial effects were found. Although
the same cognitive overload (if any) is elicited by both type of frames, participants are more
prone to reduce cognitive effort (i.e. be more context dependent) when a lottery frame is offered.
Given that our respondents in Study 3 are students of business administration, we speculate that a
lottery frame may lead to representations associated with less controllability (“gamble”), whereas
a portfolio frame is associated with more perceived control (“inversion”).
We argue that our results are consistent with other studies. Changes in preferences are
extensively documented and cannot be attributed to lack of motivation, since the same general
14
effects are observed under greater incentives (LeBouef & Shafir, 2005). Our general finding that
risk aversion depends on the size of payoffs, the probability levels, and frame has been reported
by Kühberger, Schulte-Mecklenbeck, and Perner (1999). Higher risk aversion with increasing
payout magnitudes and larger probabilities has been found in several studies (e.g. Hogarth &
Einhorn, 1990; Prelec & Loewenstein, 1991; Weber & Chapman, 2005).
There is a massive amount of literature about the effect of prior outcomes in decision making
(e.g. Arkes & Blumer, 1985; Karlsson, Gärling, & Bonini, 2005; Neilson, 1998; Thaler &
Johnson, 1990). These researchers found reduction of risk aversion after prior losses (i.e. sunk
cost effect, escalation of commitment), and after prior gains (i.e. house money effect). Our results
can be considered as an extension of these previous works, in the sense that risk aversion is not
only affected by prior outcomes, but also by prior decisions involving potential losses or potential
gains.
Our findings are relevant for financial advisors and decision analysts. Financial advisors
normally use lottery formats for eliciting clients’ risk attitudes. We have shown that preferences
may be modified by the particular options and the order they are provided to investors when a
lottery frame is used. We believe that consultants should keep in mind this fact, and take also into
account that a portfolio format does not influence risk aversion and may help people to make
better decisions.
For decision analysts, being able to increase or reduce risk aversion means that we understand
something about its causes. We believe that the heuristic value of the used framework is
undeniable, and has two main advantages. First, focusing on the role of memory representation
and memory processes on decision making provide not only explanations for the observed results
analyzed here, but also other interesting predictions for choices under risk not considered in
previous frameworks (Weber & Johnson, 2006). Second, it is parsimonious to use a unified set of
15
principles that may explain multitude of phenomena in several domains. The famous Ockam’s
razor (do not multiply entities beyond necessity) is one of the golden rules of science, and this
new promising approach may facilitate the search for basic principles that underlie decision
making.
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21
Appendix A
We assigned one arbitrary expected value and risk to a particular gamble. The values assigned to
other gambles were based on this one as reference, using the figures provided by Tversky and
Simonson (1993)6.
Within-trial condition
Gamble 1: EV = 23; R = -50
Gamble 2: EV = 44; R = -71
Gamble 3: EV = 50; R = -92
Between-trial condition
Gamble BT1: EV = 110; R = -130
Gamble BT2: EV = 150; R = -150
Gamble BT3: EV = 35 ; R = -20
Gamble BT4: EV = 55 ; R = -60
Gamble 1: EV = 70 ; R = -80
Gamble 2: EV = 100 ; R = -110
6
Given the results of a pilot study, in the between-trial condition we used lotteries with higher expected values in the
target set.
22
Figure 1
EV
Within-trial Condition
EV
Between-trial Condition
(BT1, BT2)
G3
G2
G2
G1
G1
(BT3, BT4)
Risk
Risk
23
Table 1. Within-trial Condition (Probability 0.80 vs. 0.20)
Group 1
Lottery 1
Lottery 2
0.8
0.2
0.8
0.2
Group 2
91€
- 250€
144€
- 355€
Lottery 1
Lottery 2
Lottery 3
Group 3
Lottery 1
Lottery 2
0.2
0.8
0.2
0.8
0.8
0.2
0.8
0.2
0.8
0.2
91€
- 250€
144€
- 355€
178€
- 460€
Group 4
365€
- 63€
575€
- 89€
Lottery 1
Lottery 2
Lottery 3
24
0.2
0.8
0.2
0.8
0.2
0.8
365€
- 63€
575€
- 89€
710€
- 115€
Table 2. Between-trial Condition (Probability 0.80 vs. 0.20)
Group 5
Lottery BT1
Lottery BT2
Lottery 1
Lottery 2
Group 6
0.8
0.2
0.8
0.2
300€
- 650€
375€
- 750€
Lottery BT3
0.8
0.2
0.8
0.2
188€
- 400€
263€
- 550€
Lottery 1
Lottery BT4
Lottery 2
Group 7
Lottery BT1
Lottery BT2
Lottery 1
Lottery 2
0.8
0.2
0.8
0.2
69€
- 100€
144€
- 300€
0.8
0.2
0.8
0.2
188€
- 400€
263€
- 550€
Group 8
0.2
0.8
0.2
0.8
1200€
- 163€
1500€
- 188€
Lottery BT3
0.2
0.8
0.2
0.8
750€
- 100€
1050€
- 138€
Lottery 1
Lottery BT4
Lottery 2
25
0.2
0.8
0.2
0.8
275€
- 25€
575€
- 75€
0.2
0.8
0.2
0.8
750€
- 100€
1050€
- 138€
Table 3. Choices in Within-trial Condition (Lottery Frame: 0.80 vs. 0.20)
Probability Levels
0.80
Group 1 (n = 60)
Lottery 1
Lottery 2
0.44
0.56
0.20
Group 2 (n = 60)
Lottery 1
Lottery 2
Lottery 3
0.27
0.38
0.35
Group 3 (n = 46)
Lottery 1
Lottery 2
26
0.20
0.80
Group 4 (n = 66)
Lottery 1
Lottery 2
Lottery 3
0.23
0.33
0.44
Figure 2. Within-trial Effect (Lottery Frame: 0.80 vs. 0.20)
0.44
0.27
0.23
0.2
0.8
0.2
27
Table 4. Choices in Between-trial Condition (Lottery Frame: 0.80 vs. 0.20)
Probability Levels
0.80
Group 5 (n = 55)
0.20
Group 6 (n = 51)
Group 7 (n = 67)
Background Set
Lottery BT1
Lottery BT2
0.38
0.62
Lottery BT3
Lottery BT4
Background Set
0.52
0.48
Lottery BT1
Lottery BT2
Target Set
Lottery 1
Lottery 2
0.29
0.71
Lottery 1
Lottery 2
Group 8 (n = 51)
0.15
0.85
Lottery BT3
Lottery BT4
0.44
0.56
Target Set
0.41
0.59
Lottery 1
Lottery 2
28
0.16
0.84
Lottery 1
Lottery 2
0.23
0.77
Figure 3. Between-trial Effect (Lottery Frame: 0.80 vs. 0.20)
0.41
0.29
0.23
0.16
0.8
0.2
29
Table 5. Within-trial Condition (Probability 0.90 vs. 0.10)
Group 1
Lottery 1
Lottery 2
0.9
0.1
0.9
0.1
Group 2
81€
- 500€
117€
- 710€
Lottery 1
Lottery 2
Lottery 3
Group 3
Lottery 1
Lottery 2
0.1
0.9
0.1
0.9
0.9
0.1
0.9
0.1
0.9
0.1
81€
- 500€
117€
- 710€
158€
- 920€
Group 4
730€
- 56€
1050€
- 79€
Lottery 1
Lottery 2
Lottery 3
30
0.1
0.9
0.1
0.9
0.1
0.9
730€
- 56€
1050€
- 79€
1420€
- 102€
Table 6. Between-trial Condition (Probability 0.90 vs. 0.10)
Group 5
Lottery BT1
Lottery BT2
Lottery 1
Lottery 2
Group 6
0.9
0.1
0.9
0.1
267€
- 1300€
333€
- 1500€
Lottery BT3
0.9
0.1
0.9
0.1
167€
- 800€
233€
- 1100€
Lottery 1
Lottery BT4
Lottery 2
Group 7
Lottery BT1
Lottery BT2
Lottery 1
Lottery 2
0.9
0.1
0.9
0.1
61€
- 200€
117€
- 600€
0.9
0.1
0.9
0.1
167€
- 800€
233€
- 1100€
Group 8
0.1
0.9
0.1
0.9
2400€
- 144€
3000€
- 167€
Lottery BT3
0.1
0.9
0.1
0.9
1500€
- 89€
2100€
- 122€
Lottery 1
Lottery BT4
Lottery 2
31
0.1
0.9
0.1
0.9
550€
- 22€
1050€
- 67€
0.1
0.9
0.1
0.9
1500€
- 89€
2100€
- 122€
Table 7. Choices in Within-trial Condition (Lottery Frame: 0.90 vs. 0.10)
Probability Levels
0.90
Group 1 (n = 44)
Lottery 1
Lottery 2
0.52
0.48
0.10
Group 2 (n = 43)
Lottery 1
Lottery 2
Lottery 3
0.23
0.54
0.23
Group 3 (n = 42)
Lottery 1
Lottery 2
32
0.31
0.69
Group 4 (n = 47)
Lottery 1
Lottery 2
Lottery 3
0.30
0.40
0.30
Figure 4. Within-trial Effect (Lottery Frame: 0.90 vs. 0.10)
0.52
0.31
0.3
0.23
0.9
0.1
33
Table 8. Choices in Between-trial Condition (Lottery Frame: 0.90 vs. 0.10)
Probability Levels
0.90
Group 5 (n = 49)
0.10
Group 6 (n = 49)
Group 7 (n = 48)
Background Set
Lottery BT1
Lottery BT2
0.51
0.49
Lottery BT3
Lottery BT4
Background Set
0.51 Lottery BT1
0.49 Lottery BT2
Target Set
Lottery 1
Lottery 2
0.65
0.35
Lottery 1
Lottery 2
Group 8 (n = 40)
0.44
0.56
Lottery BT3
Lottery BT4
0.60
0.40
Target Set
0.65
0.35
Lottery 1
Lottery 2
34
0.54
0.46
Lottery 1
Lottery 2
0.70
0.30
Figure 5. Between-trial Effect (Lottery Frame: 0.90 vs. 0.10)
0.7
0.65
0.65
0.54
0.9
0.1
35
Table 9. Choices in Within-trial Condition (Portfolio Frame)
Probability Levels
0.80
Group 1 (n = 42)
Portfolio 1
Portfolio 2
0.20
Group 2 (n = 47)
0.31 Portfolio 1
0.69 Portfolio 2
Portfolio 3
Group 3 (n = 48)
0.36 Portfolio 1
0.36 Portfolio 2
0.28
36
Group 4 (n = 45)
0.27 Portfolio 1
0.73 Portfolio 2
Portfolio 3
0.22
0.31
0.47
Figure 6. Within-trial Effect (Portfolio Frame)
0.36
0.31
0.27
0.22
0.8
0.2
37
Table 10. Choices in Between-trial Condition (Portfolio Frame)
Probability Levels
0.80
Group 5 (n = 43)
0.20
Group 6 (n = 43)
Group 7 (n = 43)
Background Set
Portfolio BT1 0.28
Portfolio BT2 0.72
Background Set
Portfolio BT3 0.50
Portfolio BT4 0.50
Portfolio BT1 0.19
Portfolio BT2 0.81
Target Set
Portfolio 1
Portfolio 2
0.34 Portfolio 1
0.66 Portfolio 2
Group 8 (n = 46)
Portfolio BT3 0.48
Portfolio BT4 0.52
Target Set
0.45 Portfolio 1
0.55 Portfolio 2
38
0.26 Portfolio 1
0.74 Portfolio 2
0.22
0.78
Figure 7. Between-trial Effect (Portfolio Frame)
0.45
0.34
0.26
0.22
0.8
0.2
39