Two very different paradigms have been used to experimentally study decision making: in the descriptive paradigm, all the information concerning available options and their possible outcomes is described to the decision maker; in the experiential paradigm, the distribution of payoffs from each option is learned by experience. A result of these distinct paradigms is that different results requiring different theories emerged. On one hand, Tversky (1972) proved that all simple scalable models adhere to principles systematically violated by individuals. For example, simple scalable models predict identical behavior when payoffs between options are positively correlated relative to when they are negatively correlated, in contrast to empirical observations (Diederich & Busemeyer, 1999). Consequently, decision theorists working within the description-based paradigm developed more sophisticated models of choice behavior; however, they ignored the issue of learning.
On the other hand, choice models within the experiential paradigm require both learning and choice mechanisms, the most prominent of which utilizes the very simple scalable models of choice known to be inadequate (see Sutton & Barto, 1998). Interestingly, comparisons between choices in the descriptive paradigm and experiential paradigm reveal that the effects of learning can produce dramatically different choice behavior between the paradigms, occasionally making theories derived using the descriptive paradigm completely wrong when applied to the experiential paradigm (Barron & Erev, 2003; Jessup, Bishara, & Busemeyer, 2008)!
Thus, we have recently developed a version of decision field theory (DFT; Busemeyer & Townsend, 1993) that incorporates learning (DFT-L) in order to bridge the two paradigms. Here we present the results of two studies designed to test between competing models from the different paradigms.
Method
In study one, 20 participants completed 150 choices each from two conditions consisting of two options and three outcomes. The outcomes were provided but their probabilities needed to be learned via experience. In study two, 32 participants needed to learn both the outcomes and their relative probabilities. Participants were compensated according to their choices.
In the tasks, one option stochastically dominated the other and outcomes were either positively correlated between the two options or negatively correlated. The expected values of the dominated options were equal between conditions and the dominant option was identical between conditions. Simple scalable models such as the softmax or Luce choice rule predict no difference between payoff conditions, in contrast to DFT which predicts that individuals can detect the dominance more easily when payoffs are positively rather than negatively correlated.
For both studies, choices were analyzed using a 2×2 repeated measures ANOVA, with condition (positive or negative) and 30-trial block (first or last) as the factors. A significant main effect of payoff condition indicates support for DFT models, a significant main effect of block indicates support for models that contain learning. Two significant main effects or a significant interaction support only DFT-L.
Results
Separate repeated measures analyses for both studies yielded significant main effects for payoff condition and significant interactions between payoff condition and block. The observed pattern was consistent with the predictions of DFT-L, suggesting learning when payoffs were positively but not when negatively correlated.
We further conducted a model comparison by minimizing the negative log likelihood of four competing models: the softmax choice function, DFT, softmax with reinforcement learning, and DFT-L. Using the BIC which adjusts for differences in the numbers of free parameters, DFT-L provided the best fit of the data, consistent with ANOVA results.
Conclusions
The results indicate that neither DFT without learning nor traditional reinforcement learning models sufficiently capture this pattern of choice behavior. Only DFT-L is able to account for the full complement of observed effects. Further theoretical implications will be discussed.