A class of stochastic models is presented which assume that binary choice among multidimensional alternatives is accomplished by sequential accumulation of dimensional value differences until enough evidence is accumulated. The models purpose not only to predict individual choices or choice probabilities from dimensional evaluations of the alternatives but also to map the cognitive processes taking place. The latter conjecture is tested by an analysis of choice latencies.

There are two equivalent modes for presenting a simple two-outcome gamble. In the final outcomes presentation, a player is offered a gamble (x, p, y, 1p) in which x might be won with probability p, and otherwise y might be lost with probability 1 -p. In the stake presentation (y, p, x + y) the player has to pay the stake, y, in advance if wanting to play the gamble. One might then win x + y with probability p and nothing otherwise. Coombs and Avrunin's theory of conflict and single-peaked preferences is interpreted in terms of such gambles. It is shown that the theory allows different predictions of subjects' choices for the two presentation modes. The theory predicts that for certain sets of stake gambles, subjects' preferences will be single-peaked functions of the stake. If, however, the gambles are transformed into the equivalent final outcome gambles, the theory does not predict single-peaked preferences. Thus, this mathematical theory of preference implies that formally irrelevant aspects of presentation greatly influence subjects' choices. This prediction was empirically supported.When choosing among risky options, people in general do not follow the principles of rational behavior stated in the theory of subjectively expected utility. Portfolio theory (Coombs, 1975) was an attempt to explain such behavior by assuming that people may like to seek some risk. Portfolio theory assumed that preferences for risky options were determined by two dimensions, expected value and perceived risk. For each expected value an individual is supposed to This research was conducted at the Sonderforschungsbereich 24 "Wirtschafts-und Sozialpsychologische Entscheidungsforschung" at the Universitat Mannheim with financial support from the Deutsche Forschungsgemeinschaft and the Land Baden-Wurttemberg. Parts of this study were presented at the European Mathematical Psychology meeting, Saarbriicken, West-Germany, August 30-September 2, 1977. I wish to thank Giinther Wurm for his help as experimenter, and David A. Seaver and Michael Zaus for helpful comments and suggestions.Requests for reprints should be sent to K. Michael Aschenbrenner, Sonderforschungsbereich 24 der

While previous research has shown that human decision processes adjust to the characteristics of choice situations and task demands, the present study examined whether information processing would even adapt to the characteristics of an individual choice pair. By a process tracing method it was found that the amount of inspected information systematically depended upon the particular choice pair. In order to specify the selective and adaptive information processing, criterion-dependent choice models were introduced. These models postulate that information processing continues until the accumulated amount by which one alternative is better than the other reaches or exceeds a certain criterion. These models are strongly supported by the empirical data of the present study. Deviations between model predictions and observed data are explained in terms of fluctuating feature values of the choice alternatives.

Fishbein and Ajzerfs (1975) theory of reasoned action is currently the most successful and much discussed theory in attitude-behavior research. Although the theory is well established for predicting behavior in various contexts, its central assumption of a static attitude-behavior intention relation appears questionable when recent results of cognitively oriented decision research are considered. This assumption is dynamically reformulated in order to model the cognitive processes in binary choice. The resulting criterion-dependent choice models assume a sequential evaluative processing of the alternatives' attributes until enough evidence in favor of one alternative is accumulated. Within this general framework, specific models distinguish between internally (memory) and externally (display) available information about the alternatives. The models and a series of experimental studies, which were specifically designed to investigate various aspects of the models, are comprehensively presented. Relations to other theories and consequences for attitude-behavior research are discussed.

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