The present study tries to clarify why some subjects do not change their preference
towards risk when relevant variables concerning decision making theory under
risk are manipulated (for instance feedback and aspiration level as we will
Recently, Lopes (1987) developed a model explaining subjects' altitudes towards
risk. Because our work is related to this model let we briefly summaries it.
Along her paper, Lopes (1987) analysed carefully two different approaches concerning
the psychology of risk: The experimentalists' view and the personologists' view.
Being aware of the advantages and disadvantages of both positions, she proposed
a theory which takes in account dispositional and situational factors to explain
risky choice; factors that generally haven been treated independently for the
The dispositional factor "describes the underlying motives that dispose people
to be generally oriented to achieving security (i.e., risk averse in conventional
terminology) or to exploiting potential (i.e., risk seeking in conventional
terminology). The situational factor describes people’s responses to immediate
needs and opportunities". (topes 1987; p. 275).
The first factor presents two poles: security versus potential. Risk averse
subjects show more preference for security whereas risk seekers seem more motivated
for potential. In other words, the former group values safety and the latter
A consequence of this is that risk averse people weight more heavily the worst
outcomes in a lottery than the best outcomes. Thus they will choose the lotteries
with few zero or low outcomes. On the other hand, risk seekers weight the best
outcomes more heavily.
The second factor corresponds to aspiration level. This factor reflects not
only the opportunities a person has, but also the constraints imposed by the
While these factors are sometimes in conflict other times are in concert. By
mean of the relations among these factors and depending on how the possible
conflicts between them get resolved, one can explain subjects behavior when
facing risky decisions.
The main point for the present work is that risk avoiders value safety and
risk seekers value opportunity. We think that this aspect is reflected, for
instance, in the subjects' choices between lotteries.
The experimental paradigm used to test this model is based on a set of lotteries
with different levels of risk. Lopes (1984) developed a set of lotteries with
the same expected value but with unequal distributions of outcomes which show
the differences in preferences towards risk, depending on the subjects' attitudes
towards risk (see figure 1). As Lopes (1984) and Schneider and topes (1986)
found, a risk averse person typically prefers the lotteries in the following
order: Riskless > Short Shot > Peaked > Rectangular > Bimodal >
Long Shot. (See figure 1).
Each of the lotteries has 100 lottery tickets (represented by tally marks)
and each has an expected value of approximately 100$ (1,000 pts; Spanish currency),
but they differ in how the prizes are distributed.
The lottery named Long Shot (LS) is the one that best represents the attitude
towards risk. As we can see in fig. 1, the LS lottery is one with high variance
and is positively skewed; although it has a lot of tickets with zero prizes,
it has very good outcomes with 4,390 pts being the maximun prize. Although people
are usually risk averse while considering gains, there are subjects who seem
to be risk seekers.
Those subjects tend to choose this lottery more frequently than risk averses,
the Long Shot lottery (i.e., León and Lopes, 1988). Risk seekers know
that playing the LS lottery can lead to zero or low outcomes, but they also
know that they can make a large amount of mondy with this lottery so they "prefer
to open the door to opportunity" whereas risk averses "would rather have a medium
amount with some certainty than run the risk of nothing or a small amount" (Lopes,
In two different studies using this model subjects' preference patterns have
been studied as a function of relevant variables. León and Lopes (1988)
investigated the effect of feedback, and Lopes and Schneider (1987) manipulated
the subjects' aspiration level. Both studies used the set of lotteries mentioned
above. In the next paragraphs we analyse these studies.
Concerning feedback, there are several studies that stressed the importance
of the information derived from the consequences of decisions, either to make
the next decision or to build a general pattern of behavior. Crozier (1978),
analizing the task's characteristics, concludes that the absence of feedback
may produce ad hoc strategies to the specific task. Einhorn and Hogarth (1981)
pointed out that feedback is a relevant variable to include in behavioral decision
Other studies used feedback as a source to predict changes in the gambling
behavior of subjects when they were either winning or lossing (Edwards, 1954;
Greenberg & Winwer, 1966; Leopard, 1978; McGlothin, 1956; Morgan, 1983).
The main conclusion is that people prefer riskier gambles when they are losing.
Because the above studies do not distinguish between the impact of experience
per se and the outcomes of experience, nor do they differentiate between baseline
preferences and preferences in the first block of trials, León and Lopes
(1988), developed a research in order to resolve these points, using the experimental
paradigm refered above.
León and Lopes (1988) measured the number of times a subject chose each
of Lopes's lotteries before and after a feedback phase (this feedback phase
was similar to the one that we have developed in our experiment and it is described
in the method section). The pre-feedback task required from subjects to judge
and to show their preferences between pairs of stimuli. In that way the task
was similar to these used, between others, by Tversky and Kahneman (p.e. 1979)
(for a general review see Slovic, Lichtenstein and Fischhoff, 1988). In the
feedback phase, the same stimuli were presented, but, after each trial subjects
knew the consequences of their choices. In addition and in order to increase
subjects' involvement in the experiment, a 10$ prize was offered to the subject
who got the largest outcome. The above experimental manipulations correspond
to situational changes in the task, thus, under the two factor model, concretely
concerning aspiration level factor, some changes in subjects' behavior were
expected. Most of the subjects showed a risk averse pattern in the prefeedback
assesment. After feedback, a group of subjects reversed their preferences and
became risk seeking but another group did not change their preferences towards
risk (about half of them). Those subjects maintained and even, in some cases,
increased their risk aversion. The reasons why some people change preferences
and others do not change are not clear, although this result seems to be similar
to these found previously by Lopes & Casey (1987) and Lopes & Schneider
(1987). Our present studie will try to clarify this question.
In Lopes and Schneider's (1987) experiment the same set of stimuli (lotteries)
was used. The authors manipulated the aspiration level conditions in order to
find out whether or not the subjects changed their risk preferences under different
aspiration situations (high, low and neutral). They found a group of subjects
who clearly responded to the experimental manipulation. In Lopes and Schneider
words, only some of the subjects were 'responsive' while some were not maintaining
their risk aversion in all conditions. Here again, it was possible to explain
subject changes in preferences, but it could not be explained completely why
some individuals did not modify their preferences towards risk.
What are the reasons for mainteining preferences regardless of experimental
manipulations? In order to answer this question let us refer to the self fulfilling
prophecy as a cognitive frame explaining why some people stay with their original
preferences towards risk.
The self fulfilling prophecy has been studied mainly from a social approach
(i.e.: Brophy and Good, 1974; Brophy, 1983; Darley, 1983; Jussim, 1986). This
prophecy is related to a false definition of a situation that leads people to
behave in such a way that makes that situation true. In that way, this prophecy
would be related to a set of well known biases concerning judgment and choice,
for instance, verification bias, overconfidence and the basic biases related
to judgment of covariation (see, i.e., Hogarth, 1980). In that sense, feedback
could not affect decision making, because subjects will have information derived
from only the way they behave. If people behave in such a way that tends to
use only confirmatory instantes, they will have no motives for changing their
performance. Hogarth (1980) discusses several cases where outcome feedback can
be irrelevant for correcting poor heuristics, above all if there is a lack of
knowledge about task structure. It is also well known (Wason, 1960) that there
is a tendency towards not testing hypotheses by disconfirmatory evidence (although
this tendency is context dependent). Therefore and in Hogarth words, "...large
amounts of positive feedback can lead to reinforcement of a nonvalid rule" (Hogarth,
1980; p. 12). Moreover, "when judgments are made for the purpose of deciding
between actions, outcome information may be irrelevant for providing self-correcting
feedback" (Hogarth, 1980; p. 17).
Considering risky tasks, people could "treat" information derived from outcome
feedback in a manner that making them maintain their previous strategies when
facing risky situations. In our case (and considering the LS lottery, just because
is the one that best represent risky attitudes, as we have said before), if
a risk seeker choose this lottery because s/he considers it to be the best way
of making a large amount of money when several draws are possible, this lottery
will fullfill his/her prophecy within a set of reasonably lucky draws. In the
same way, if a risk averse individual does not choose this lottery because s/he
thinks it is the wordt one to obtain prizes, s/he will not get any disconfirmatory
In general terms, we hypothesize that, in some cases, subjects' attitudes/strategies
should lead them to behave in such a way that they will obtain data confirming
their previous attitudes/strategies. We will develop our hypothesis considering
the LS lottery, because as we have said before it is the one that best differentiates
people with regard to attitudes towards risk.
More concretely, if subjects, when facing the Long Shot lottery, pay more attention
to some outcomes and ignore others, they would find reasons to confirm/verify
their previous attitudes towards risk. We
propose that, in that lottery, the outcomes having received the most attention
will be the highest ones (specifically we will consider prizes aboye 1,950 pts
of LS lottery1). We suppose that when the LS lottery is chosen it
is because subjects look forward to winning the high prizes of the lottery (see
figure 1). That was supported by previous verbal reports and it seems very reasonable.
In that way, both groups of subjects will choose the LS lottery hoping to obtain
the high possible outcomes, in other words, they prefer "to open the door to
opportunity" as Lopes says. Obviously, the difference between risk averses and
risk seekers is the number of times each group choose this lottery.
Futhermore, if high prizes are overweighted and the rest are underweighted
(in the LS lottery) subjects will obtain data confirming their previous altitudes;
in particular, and if we consider subjects with extreme patterns in preferences
towards risk, we hypothesize that:
Because risk averse subjects choose the LS lottery more infrequently most of
them will obtain a distribution of good outcomes which would fit with their
attitudes (few high prizes). Hence, most risk averse individuals will not change
their patterns towards the lotteries.
In the same way and concerning risk seeking subjects, the number of times that
the LS lottery is chosen should be higher than for risk aversive subjects as
this would give them a greater probability to find some case confirming their
previous ideas about the good prizes which could be obtained in this lottery.
Therefore, the riskiest subjects will obtain data leading them to keep on playing
in a risky way. Being more concrete, risk seekers will obtain a higher number
of "good outcomes" than risk averse subjects and, this faet, will lead subjects
to a maintenance of their attitudes.
Variance is considered to be a good statistical moment of risk. Prospects with
high amount of variance will be perceived riskier than those with a low amount.
That is the point of view of risk preference theories (i.e., Allais, 1953; Coombs,
1975; Hagen, 1969; Markowitz, 1959). In addition to our previous reasoning,
if the variance of prizes gained by risk avoiders is larger than the one related
to risk seekers, then the risk perceived by the former subjects will be higher
than the risk perceived by the last ones.
We can predict that risk avoiders, who choose the LS lottery less frequently,
perceive it as riskier than risk seekers do. Though it is reasonable to think
that the variance of prizes gained with this lottery will be higher for risk
averse subjects than for risk seekers.
Subjects were students of Psychology of the Universidad Autónoma de
Madrid; 110 subjects for the pre feedback and 27 subjects for the following
The stimuli were six multi-outcomes lotteries (adapted from Lopes' lotteries).
Each lottery had an expected value of 1,000 pts, and each had 100 tickets. Each
of those tickets was equal in value to the pts amount listed at the left of
We used the same names of the lotteries as in Lopes' experiments: RL or Riskless
lottery, SS or Short Shot lottery, PK or Peaked, RC or Rectangular lottery,
BM or Bimodal and LS or Long Shot lottery.
Design and Procedure
Independent variables: (1) The lotteries (six different lotteries as we specified
above), (2) risk seeking and risk averse subjects and (3) treatment (pre-Feedback,
Feedback and post Feedback). Subjects'classification concerning risk, was made
in a similar way than in previous studies (i.e., Lopes and Schneider, 1987,
León and Lopes, 1988)
Dependent variable: the number of times subjects choose each of the lotteries
in a complete pair-comparision design. Lotteries were combined in all possible
pairs so 15 pairs were obtained. Each pair of lotteries were presented to the
subjects before and after Feedback.
Basically, the procedure consisted in a pre-test (which served in selecting
a subset of subjects), a Feedback phase and a post-test.
Pre-test or Pre feedback
In a psychology classroom we presented to the students (110 subjects) the 15
possible pairs of lotteries using transparencies. We showed the transparencies
on a screen, one after another and with enough time to respond about preferences.
The pair of lotteries were printed vertically, one above the other.
Subjects should indicate, in their correspondent response sheet their preferences
for each pair by circling either S (for top, "superior") or I (for bottom, "inferior").
At he beginning of the session we told to the subjects that the task was about
their preferences for different kinds of lotteries. We instructed them to indicate
on their response sheet which of the lotteries in a pair they would choose if
they were allowed to play either of the lotteries once. We also told them that
each play of the lotteries was completely independent of the other plays, as
after each play the ticket would be replaced and could be drawn again from the
set of 100 tickets2.
This phase lasted approximately 15 minutes.
As in previous studies, most subjects were risk averse according to the prefeedback
assesment, so we could only select a group of 13 risk seekers. A group of risk
averses (14 subjects) was also selected. We have to stress that we chose the
most extreme subjects according to their preferences for the BM and LS lotteries.
The criteria of classification were as follow. Risk seeking: Subjects choose
the most risky lotteries equal or more than 5 times (LS + BM >= 5). Risk
averse: Subjects choose the most risky lotteries equal or less than 4 times
(LS + BM <= 4) and the LS lottery no more than 2 times.
Once the subjects were classified we called them in to perform the feedback
phase individually. We ran this phase using an Apple II computer to display
the choice pairs and to record the subjects' preferences. After each choice
between the lotteries the computer gave the subjects the outcome of their draws
We displayed the lotteries on a poster positioned near the screen. Each lottery
was labeled with a single letter code (from "A" to "F"). The computer program
was designed to present each pair of lotteries (pair of letters) ten different
times. The presentation was at random. Subjects indicated their preferences
by pressing the keybord letter corresponding to their choice. In all, 150 choices
were necessary to complete this phase, with a feedback trial after each choice.
Once the subject chose a lottery, numbers between 1 and 100 were displayed
at random at the center of the computer screen and on the same spot. The numbers
appeared successively and rapidly. Whenever the subject was ready, s/he pushed
the space bar to stop the number display. Then the number was translated into
a prize amount.
After the subject finished reading the prize amount, s/he pressed another key
and the next pair was presented.
Subjects were told that the person who obtained the greatest amount of theoretical
prize money with the lotteries during the Feedback phase, would have the opportunity
of making 3.000 pts (this was to assure the involvement of subjects).
The feedback phase lasted about 45 minutes.
From this phase the following data were obtained per each subject: (a) Number
of times subjects chose each of the six lotteries; (b) Cumulative outcomes from
all lotteries: (c) Number of times each of the LS lottery outcomes were obtained.
In this last phase we measured subjects preferences towards the pairs of lotteries
again. We used booklets which contained the stimulus pairs. The instructions
were similar to the pre-test phase. The booklets presented the lotteries in
a random order (4 different bookIets).
The post-feedback phase took about 5 minutes. After all subjects were run,
the winner was contacted and was notified about how to pick up his/her prize.
Since we classified our subjects depending on the number of times they choose
the BM and the LS lotteries in the prefeedback phase, we present a general result
in Table 1, the number of times subjects chose BM+LS lotteries during pre Feedback,
Feedback and post Feedback for both groups.
We test wether or not subjects changed their patterns after the feedback phase.
We found more subjects who did not change their preferences pattern than people
who changed after feedback. (table 2).
Analysing the overall results, concerning the number of times LS + BM lotteries
were chosen (considering risk seekers and risk avoiders together), during the
pre and post feedback phase, we found no change, Fl’25=0.72. That
result is understable because people who change and people who do not change
are considered together. This fact produces a large MCE and thus the effect
of changing is hidden.
We were also interested in analysing the difference between variances of prizes obtained for both groups in LS lot, due to the special significance of this lot in the present work. The variances were calculated from the total amount of prizes obtained by each group of subjects over the total amount of LS elections. (risk avoiders, S2= 168510.25; risk seekers, S2 = 34328.68). 14 prizes were obtained by risk avoiders and 13 by risk seekers.
The test of homogenity of variance analysis was also significant, F13,12 = 4.9087, p<0,01; Thus, playing the LS lottery involved more risk for risk avoiders than for risk seekers, from the point of view of outcomes variance.
Discussion and Conclusions
As stated previuosly, there are subjects who maintain their preferences towards
risk regardless of experimental manipulation, and it is for these individuals
that we have proposed our working hypothesis. In contrast with the previous
study about feedback with Lopes' lotteries, most of our subjects did not reverse
their preferences. We can explain this maintenance of preferences for risk averses
from the criteria of classification. As our subjects were more extreme in their
patterns of preferences, they were also more reluctant to abandon their risk
attitudes regardless of possible disconfirmatory data. For risk averse subjects
in León and Lopes's experiment, the mean score of LS+BM lotteries was
2.22 and in the present work it was 1.43. Note also that only one risk averse
subject obtained a score of LS+BM=3, the rest of them obtained a lower score.
(As a matter of fact we had to eliminate 9 risk averse subjects because during
the feedback phase, they did not chose the LS lottery even one time, so we could
not calculate any proportion of good outcomes for them). Because in León
and Lopes's research there were only 2 subjects out of 30 who could be considered
as risk seekers with the criteria we have applied here, it is quite difficult
to compare them with our subjects.
Is it possible to explain why some subjects change their preferences under
the same hypothesis? Although it is not possible to obtain a clear conclusion
with so few subjects, let us focus on the subjects who changed after feedback
On one hand, subject "12" (according table 2) become a risk seeker. This subject
picked the LS and BM lotteries a great number of times (43 times) during the
feedback phase (more than the average of this group, X=25.58). On the other
hand, risk seekers who changed their preferences were those subjects who chose
the LS and the BM lotteries fewer times, during the feedback phase, in comparision
with the rest of the group (mean of LS+BM of subjects who changed was 25.5;
mean score of the whole group was 56.23). In some sense, then, the subjects
who changed were those whose choice in the feedback phase were more like the
other group. What are the reasons they changed their minds during the feedback
phase? We think the answer is the interaction between feedback and their previous
ideas, but from this study we cannot explain how the interaction takes place;
further research is necessary within this point.
What it seems clear, according to our hypothesis, is that both groups of subjects
found reasons for maintaining their preferences towards risk. We think, that
the fact that risk seekers obtained a big proportion of high prizes playing
the LS lottery, made them to keep on being risk seekers afterwards. In the same
way, risk averse subjects did not find any motive to change their preferences
because, the few number of times that they decided to play LS, they did not
gain so much as the other group. In both cases, subjects did not had any motive
to abandon their previous hypothesis concerning the risk involved in the lotteries.
The above is consistent with Lopes' two factor model concerning the fact that
risk averse subjects would pay primary attention to worst outcomes while risk
seekers would pay primary attention to bestcase outcomes.
Such conclusion is confirmed with the variance of prizes for both groups. During
the feedback phase, the variance of outcomes was higher for risk averses than
for risk seekers, in that way it seems that risk averses look at the LS lottery
as riskier than the other group, in consequence they play less times that lottery,
obtaining less high prizes and thus, they maintain their previous preferences
towards the lotteries. On the contrary, risk seekers perceive LS lottery no
so risky, so they play it a great number of times gaining more high outcomes
and thus, they did keep on being risk seekers. In any case, the fullfilling
prophecy seems to play an important role in the performance of the subjects;
both groups may find data to reinforce their attitudes towards risk because
they behave in such a way that they fullfill their previous ideas about risky
The present work opens the door to a future research where subjects' attitudes
towards risk would be changed through experimental manipulation, forcing the
subjects to choose a different number of times the riskiest lotteries. In this
way, both group of subjects would receive the same information. Of course, we
are not saying that people (specially those with more extreme preferences) will
switch their attitudes, only that some of them, would have the chance to modify
their previous ideas, in a kind of situation where there is not any advantage
in any of the patterns.
Finally, we would like to stress the following points:
(a) Assuming that subjects could be considered as different in their attitudes
towards risk and furthermore, that these altitudes would be explained under
the two factor model of Lopes (1987) we have tried to propose a hyphothesis
to explain why some subjects, who are not responsive to the manipulations of
aspiration level (Lopes and Schneider, 1987) or why some individuals do not
shift their preferences when they receive feedback and, therefore, the opportunity
to change (León and Lopes, 1988).
(b) Our explanation has been formulated from the general idea of the self fulfilling
prophecy (which had a clear application to decision making and feedback in the
work of Hogarth -1980-). Hogarth proposed that individuals tend to confirm their
heuristics looking at the data in such a way that if only a part of that data
is considered, and the rest of them are ignored, then feedback will be irrelevant.
We have developed a similar hypothesis about why people do not change their
preferences towards a set of lotteries.
1. In fig. 1, we can see that 1.950 prize is the closest LS prize to the best
outcomes in other lotteries. This is the reason why we will consider prizes
above that one.
2. Instructions given to the subjects along the different phases are showed
in the appendix.