Motivation and Emotion, VoL 6, No. 3, 1982

Risk Taking in Achievement-Oriented Situations: Do People Really Maximize Affect or Competence Information? 1

Klaus Schneider 2 and Norbert Posse Philipps University, Marburg

Several studies o f choice behavior (risk taking) in achievement-oriented situations are reanalyzed. The usual ways o f pooling all choices over trials and subjects conceal the series o f subjects" decisions and the dynamics inherent in these decisions. A basic strategy o f subjects in an achievement- oriented choice situation seems to be to start with an easy task, choose a more difficult one whenever you succeed, and stay mostly at the same difficulty level whenever you fail. A computer model, in which such simple assumptions are made, generates preference functions over the order o f difficulty levels that are indistinguishable f rom those found in empirical studies. It is concluded that the study o f choice behavior in achievement- oriented situations shouM be based on the analysis o f the series o f single decisions by one subject. For this we need models that allow the predictions o f such decisions and the prediction o f action-controlling cognitions and emotions.

The study of "risk behavior" in achievement-oriented situations is based on two experimental paradigms: (1) the level of aspiration or goal setting paradigm and (2) the free choice paradigm. Whereas in the former experimental situation subjects are asked to state a performance goal for a coming trial, subjects are free in the latter to choose a task among several

1This is part of a paper presented in a symposium, Attributional Approaches to Human Motivation, W.-U. Meyer & B. Weiner, Center for Interdisciplinary Research, University of Bielefeld, W. Germany, July 1980. Many thanks to Dr. J. NichoUs, Purdue University, and to two anonymous reviewers for helpful comments on earlier drafts of this manuscript.

2Address all correspondence to K. Schneider, Department of Psychology, Philipps- Universit/it Marburg, Gutenberg str 18, D-3550 Marburg, W. Germany.

259

0164-7239/82/0900-0259503.00/0 © 1982 Plenum Publishing Corporation

260 Schneider and Posse

difficulty levels. Typically, subjects prefer intermediate task difficulty levels and state goals that are somewhat higher than what they achieved before.

For more than two decades, research on risk taking and goal setting has been guided by Lewin's (Lewin, Dembo, Festinger, & Sears, 1944) and Atkinson's (1957) models based on the expected value principle (cf. Atkinson & Feather, 1966; Atkinson & Raynor, 1974). In Atkinson's model, the assumptions are made that individuals try to maximize positive affect as a consequence of success and/or try to minimize negative affect as a consequence of failure. Atkinson followed Escalona's (1940) and Festinger's (1942) intuitive notion that more positive affect ("pride" and "joy") is experienced when a person succeeds at a difficult task than at an easy one, and that more negative affect is experienced when a person fails at an easy task tnan at a difficult one. Therefore, linear relationships between the subjective difficultly of a series of task difficulty levels, reflected ~n subjective probability estimates, and incentive values of success and failure, i.e., anticipated affects after success and failure, were assumed.

On the basis of these assumptions, the model predicts expected anticipated affects of success and failure to be maximal at intermediate difficulty levels, exactly at a difficulty level where subjective success probability (Ps) is .50. Consequently, success-oriented subjects should prefer this difficulty in goal setting and choice behavior, whereas anxious individuals should avoid it. The model asserts that success-oriented individuals try to maximize positive affect in such situations, whereas failure-oriented individuals try to minimize negative affect.

As stated earlier, this model stimulated much research. However, it became apparent very soon that certain aspects of success- and failure- oriented risk preference were not explained by the model (cf. Heckhausen, 1968; Schneider, 1973). Besides minor revisions of the model, an alternative "cognitive" explanation was proposed: it was assumed that subjects would prefer intermediate task difficulty levels in order to get information about their competence (Meyer, 1973; Schneider, 1973; Weiner, Frieze, Kukla, Reed, Rest, & Rosenbaum, 1971).

Anticipated competence information was assumed to be maximal at intermediate difficulty levels because subjects seemed to attribute success and failure at intermediate difficulty levels predominantly to internal factors (Meyer, 1973; Weiner et al., 1971). Success and failure experiences attributed to external factors such as luck and task ease and difficulty, however, provide no information in respect to one's own competence.

In a similar way, Schneider (1973) assumed anticipated competence information to be maximal at intermediate task difficuty levels, because he had found that subjective uncertainty in respect to task outcome is maximal here. Thus, with each try of an intermediate difficult task a maximum of

Risk Taking 261

uncertainty was reduced and, with that, a maximum amount of information was received (Schneider, 1974; Schneider & Heckhausen, 1981).

Subjective uncertainty was assessed in these studies by measuring the decision time subjects needed in predicting a success or failure and by asking their confidence for that prediction.

According to Raynor (1982), it is the search for competence information pertinent to socially and personally valued abilities that arouses achievement motivation. Such information has instrumental values for the attainment of importance future goals. We think that this is an important qualification of the competence assessment hypothesis.

However, the original model and these cognitive revisions predict the same preference function over subjective task difficuty levels in a "risk- taking" situation. No experimental proof clearly favoring one of these conceptualization has as yet appeared (cf. Schneider & Heckhausen, 1981). Common belief holds that Trope and Brickman (1975) and Trope (1975) have demonstrated the superiority of the competence assessment hypothesis over Atkinson's affect maximation hypothesis. However, we think that their results demonstrated only that socially defined competence information is another important determinant of choice behavior-a t least when it is made ~rominent by the experimental procedure.

In addition most critical for the original risk preference model, as well as for these cognitive reformulations, seems to be the fact that subjects do not seem to maximize in such a choice or goal-setting si tuation- at least not all the time. Instead of consistently choosing that task difficultly level at which expected affect or information is maximal, they choose all difficulty levels in proportions that match the distribution of expected affect or expected information over those difficulty levels. This means that although the intermediate difficulty level is preferred by success-oriented subjects, all other difficulty levels are chosen too, only less and less frequently the easier or harder the tasks are. On the basis of the expected value principle, one has to predict, however, that the person always chooses the alternative with the highest expected va lue -a t least when the principle is deterministically formulated, as in Atkinson's model, and not supplemented by an error assumption. This fact was pointed out in the early years of achievement motivation research (Simon, 1955), but it has not stimulated any revision of the model until now. However, the "dynamic theory" of achievement- oriented behavior (Atkinson & Birch, 1970, 1974) can explain this fact as a consequence of growing action tendencies for trying nonchosen difficulty levels. We will come back to this in a later section.

As devoted empiricists, we were convinced by the observation of the actual choice behavior of our subjects, in a series of risk taking studies using a psychomotor task, that the principle of affect or information

262 Schneider and Posse

maximization describes only one of the several strategies that guide subjects in risk preference situations. These strategies are not seen when risk preference data are analyzed in the usual way by summing choices over trials and individuals in order to deduce preference functions. In the following, the results of some of our own risk taking studies are therefore reanalyzed to test if they support this proposition.

The task we used in these studies was a psychomotor task. Subjects had to push a steel ball through a gap of nine different widths at the end of a table. They were given 10 practice trials at each width, their objective probabilities being written on a blackboard in front of them. Subjective probability estimates, as well as other experimental variables, were assessed by appropriate scaling procedures. Free choice of difficulty levels was always allowed after the extended practice period with 10 trials at every difficulty level. Thus. subjects knew the task when they made their first choice.

Patterns of goal setting had already been classified in several risk preference studies (Heckhausen & Wagner, 1965; Rotter, 1945; Wagner, 1969; Wasna, 1970). Jopt (1974) analyzed choice behavior in our psychomotor task in a free choice situation in a similar way. He found that a majority of subjects showed a tendency to choose increasingly more difficult tasks, starting with an easy or intermediate difficulty task. Observing the behavior of the subjects in the choice situation gave us the impression that subjects were somehow testing their limits by moving step by step to more and more difficult tasks. It looked as if they followed a heuristic rule by trying more or less all difficulty levels, starting with an easy one.

Figure 1 illustrates a typical sequence of choices of one subject (No. 12) in one of the earlier studies (No. 4), in which subjects estimated their success probability at every chosen task in the free choice situation. Normally, probability estimates were given only postexperimentally. This subject started with an intermediate difficulty level (5), didn't succeed, and went down to the next easier difficulty level (6). There he succeeded, and went up again to difficulty level 5.

Generally, subjects showed the following behavior: They started with an intermediate or easy task, went to higher difficulty levels most of the time when they succeeded (mostly one step only), and stayed at the same difficulty level most of the time when they experienced a failure. However, sometimes they went back to a less difficult level after a failure, especially after a series of failures. Thus, it appeared that, even in this free choice situation, (1) subjects implicitly stated goals so as to have one or more successes at the most difficult levels and not only at the one where expected success affect was maximal, and (2) they were influenced subsequently by success and failure in the very same way as in a typical level of aspiration situation with explicitly stated goals (cf. Lewin et al., 1944).

Risk Taking 263

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264 Schneider and Posse

The individual choice sequence of subject No. 12 (Figure 1) also demonstrates that choosing a less difficult task is not a necessary consequence of a failure experience or even of a series of failures. This subject stays at the same difficulty level in spite of repeated failure-e.g. , at trials 6, 7, and 8. However, his Ps estimates reflect the fact that he "got the message." The subject reacts here by lowering his estimates of success probability. If we pool choices over trials and subjects in the usual way, however, the typical group preference function emerges (Figure lb): Subjects mostly prefer an intermediate difficulty level.

By assuming that the choices of subjects are determined by the sequence of their choices, one can explain a considerable portion of the individual serial choice functions. Kendall rank correlation coefficients were computed for each individual between the sequence of his choices and the chosen difficulty levels. Correlations ought to be negative in the typical case, i.e., in the case that subjects chose higher difficulty levels (smaller numbers) with increasing trial numbers. The respective correlation coefficient for subject No. 12 (Figure la) is - .83. The medians of the distributions of these correlation coefficients, as well as the percentages of significant coefficients of seven independent studies with the same psychomotor task and comparable subjects (high school and college students), are given in Table I.

Table I, Median Kendall Rank Correlation Coef- ficients (Medians of the Distributions of Individual- ly Computed Coefficients) Between the Sequence of Choices of Difficulty Levels and Chosen Dif- ficulty Levels in Seven Studies, and Percentages of Significant Coefficients (p < .05) in Each Studya

Study N K Median % s (< .05)

No. lb 41 I5 - .47 71% No. 3 30 12 - .41 50 % No. 4 26 10 - .04 42 % No. 5 31 15 - .37 58 % No. 6 27 15 - . 52 63 % No. 7 22 15 - .75 64 % No. 8 20 15 - .75 65 %

aSubjects were allowed between 10 and 15 choices (K); the numbers of subjects in each study, for whom rank correlation coeffients could be computed, are given in the second column (N).

b Subjects in Study 1 were male students of eco- nomics; subjects in Study 3 were maIe high school students; subjects in all other studies were male and female first-year psychology students (from Schneider, 1973, chap. 4; 1974; Schneider & Posse, 1978a, 1978b).

Risk Taking 265

The relationship is considerable, especially if we compare the predictive power of this simple rule with the power of the theoretical concepts used so far in risk preference research.

If we summarize percentages of correct predictions over the five studies in Table I, in which probability and confidence estimates were also assessed (Study 4-8, N = 126), only 35% of the individual preference functions over the nine difficulty levels of our task could be predicted significantly (p < .05) with uncertainty estimates (confidence in one's prediction of success or failure at each task difficulty level), and only 32% of all individual preference functions significantly with expected affect, using Atkinson's formula and subjects' probability estimates. For these computations, difficulty levels were rank-ordered for each subject on the basis of her or his confidence estimates (subjective uncertainty) and expected success incentive (see Atkinson, 1957) and correlated with the preference order of difficulty levels. In the same studies, however, the precent- ages of significant coefficients between the individual preference functions and the sequence of choices varies between 42070 and 71070 (Table I). Pooled over these four studies, 58 if'0 of all individual preference functions are predicted significantly by this simple rule-nearly twice as many as the different models achieve.

We assume that "serial" choice behavior is also a rational expression of the wish to learn more about an ongoing task and one's own competence. This assumption is supported by the results of an unpublished study with the same psychomotor task and a comparable sample of subjects (30 first- year psychology students). Students were allowed 50 free choices of task difficulty level before they could practice extensively on the task. In one condition, subjects were told to select tasks in such a way as to learn as much as possible how good they were at the task; in the other conditions, subjects received the standard instruction, just telling them they could play at whatever difficulty level they wanted. In both conditions, subjects showed marked serial choice behavior. However, when learning was stressed, the tendency to start with an easy task and go up stepwise was more pronounced. The median of the distribution of individually computed

'Kendall rank-correlation coefficients between the rank order of trials (1 to 50) and the increasing numbers of task difficulty levels was .52 in the standard situation and .83 in the situation where learning was stressed.

The tendencies to move to higher difficulty levels after a success and to remain at a same difficulty level, most of the times after failure are reflected in the table of transition probabilities of "going down," "staying," and "going up" one or more difficulty levels after o n e success or after o n e failure (Table II). Shifts after success and failure were pooled for these computations over all subjects and all trials in the seven studies listed in Table I (combined number of observations: 2,538).

266 Schneider and Posse

Table II. Transition Probabilities of Staying at the Same Difficulty Level (Main Diagonal) of Shifting Up (from Difficulty Level 9 to 1) or Down (from 1 to 9) After One Success and

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"Probabilities in these matrices were computed from pooled changes (over trials and subjects) of seven studies. Numbers of observations pooled over trials and subjects are given for the first choice of each transition (rows of the table) in the last column (P0. Difficulty level 9 was the most easy gate; subjects could not go down further, as they could not go higher after a success or failure at difficulty level 1.

The proportions for the general classes of behavior, (1) "going up," (2) "staying," and (3) "going down," were 51%, 49%, and 8°70, respectively, after success, and 10%, 73070, and 16070, respectively, after failure. After one success, "going up" is the most probable decision at all difficulty levels but the highest. After one failure, "staying" is the most prevalent reaction at all difficulty levels. Remaining at the same difficulty level after a failure experience is significantly more likely than after success (X 2 = 261, d f = 1, p < .001).

The inferred strategy of going from easy tasks to more difficult ones and the rule of advancing predominantly after a success and staying predominantly at the same level after a failure can be translated easily into

Risk Taking 267

Fortran language. A computer model (SIM l) was formulated with the following simple assumptions.

1. Subjects start randomly at one of the nine difficulty levels.

2. Success and failure are determined by a monotonic and linear probability function of the task difficulty levels starting with a success probability of 20% and in- creasing in equal steps of .075. This function reflects quite accurately the empirical success probabilities at this task.

3. The changes after success and failure are determined by the empirically ascertained changes of "going up," "staying," and "going down" after one success or one failure, pooled over all difficulty levels; i.e., the actual change (one step only) is determined by a random generator for these three categories of behavior on the basis of the empirically ascertained transition probabilities of the changes after success and failure at all nine difficulty levels (cf. Table II). To make the model easier, only the most often observed change of one step up or down is progran~ed.

The computer model generates sequences of choices that look similar to the choices we observed with our subjects. In Figure 2, the sequences of three randomly chosen simulated subjects, who started with the same task difficulty level as three randomly chosen real subjects from Study 5, are

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2 6 8 S c h n e i d e r a n d P o s s e

shown. These three subjects were selected randomly from among those subjects who followed the general rule of a serial choice. Individual sequences, as well as the emerging group preference functions (Figure 2c and 2d), are quite similar. However, actual sequences of chosen difficulty levels are more erratic. The computer model provides only for transitions of one step, whereas real subjects (e.g., No. 1) may skip several difficulty levels.

Even a most simple model, in which the only assumptions made are that subjects go up one step after a success and go down one step after failure (the probabilities of success and failure at the nine difficulty levels being determined again by the same probability function as in SIM I), leads to the emergence of a typical group preference function (Figure 3).

We have to conclude that group preference functions of the kind usually found in risk-taking studies in achievement-oriented situations are not specific enough to allow testing any of the discussed models. The same function can be generated by simple rules deduced from the analysis of goal setting behavior in achievement-oriented situation. The typical finding of an inverted U-relationship between percentages of choice (group preference

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Risk Taking 269

function) and task difficulty with a peak at intermediate difficulty levels is, in addition, partly a product of an inappropriate pooling of individual choice sequences. Such a combination of individual preference functions would be legitimate only when the pooled individuals show a preference for intermediate difficulty levels. In our studies, only about one third of all subjects manifested such a significant preference for intermediate difficulty levels (cf. Schneider & Heckhausen, 1981).

Models of achievement behavior should be evaluated according to their predictive power for individual preference functions. Our observation was that the maximization principle of the prevalent model predicted only a third of all individual preference functions in our studies, whereas 60°-/0 of these functions are significantly predicted by the simple assumption that subjects start with easier tasks and go up to more difficult ones.

In all our studies, subjects still chose difficulty levels in ascending order after extensive practice with the task. In one of the aforementioned studies (Schneider & Posse, 1978c), we had demonstrated that after much less practice with this task (than reported here) success probability estimates were already stabilized. Thus, the ascending order of chosen difficulty levels cannot be explained by the assumption of growing success expectancies.

As mentioned earlier, serial choice behavior can also be predicted on the basis of the new dynamic theory of achievement motivation proposed by Atkinson and Birch (1970, 1974). Kuhl and Btankenship (1979a, 1979b) have shown that even under the assumption of stable success probabilities, success- and failure-oriented subjects should prefer more and more difficult tasks in a series of choices, as the consumatory value of a success is greater for easy than for difficult tasks. Subjects therefore should prefer more and more difficult tasks. However, the choice behavior data that Kuhl and Blankenship (1979b) report might very well be interpreted as an expression of the assumed tendency of subjects to get to know the task better, particularly when stimulated by the instruction to the subjects that "their opinions were being sought concerning the difficulty of the task" (Kuhl & Blankenship, 1979b, p. 555).

In summary, then, we think that students of achievement motivation should study actual achievement-oriented behavior of individuals in the way so brilliantly demonstrated by Lewin and associates in the 1940s. On the basis of a more detailed description of observed behaviors, several different strategies or rules of goal setting and choice behavior may be inferred. In the longer run, testable models of achievement-oriented behavior are needed to guide future research. However, such models must involve not only individual sequences of behavior (the stream of behavior), in the way the dynamic theory of motivation does, but also behavior-controlling thoughts (strategies) and emotions.

270 Schneider and Posse

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Risk Taking 271

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