Dynamic-stochastic decision models for multiple alternatives with multiple attributes
Final Report Abstract
The project focused on the mathematical development of models for decision making. The underlying processes are stochastic processes, in particular, the Wiener process and the Ornstein-Uhlenbeck process. Both processes have been developed in physics/mathematics but enjoy high popularity in psychology and neuroscience to simultaneously account for choice responses (choice probabilities and choice response times). Here we considered choice situations with binary and multiple (>2) choice options, each option characterized by several attributes (multiattribute). For binary choice problems, the multi-stage decision model (one stochastic process for each attribute considered) was extended to include a) different attention-time distributions (i.e. how long the decision maker spent thinking about one attribute before switching to the next attribute); b) attribute orders (i.e in which order the decision makers considers the attributes; c) finite and infinite time horizon (i.e. is the time in which the decision maker has to make a decision limited or not (no answer is made until then); d) fixed and variables boundaries (i.e. the decision criterion is fixed and constant throughout the trials or not e.g. declining as time goes on. For multi-choice options we developed a model – the cube model – based on Wiener processes in higher dimensions. The specialty of the model is that is assumes acceptance and rejection boundaries. Furthermore, correlated noise allows to model processes as dependent race models. That is, the preferences for several choice alternatives compete over time and the winner determines the choice. However, unlike other race models in this area, it assumes a stochastic dependency between the accumulated preferences.
Publications
- (2016). Multi-stage sequential sampling models with finite or infinite time horizon and variable boundaries. Journal of Mathematical Psychology, 74, 128–145
Diederich, A. & Oswald, P.
(See online at https://doi.org/10.1016/j.jmp.2016.02.010) - (2018). A dynamic dual process model of risky decision making. Psychological Review, 125(2), 270 – 292
Diederich, A. & Trueblood, J.T.
(See online at https://doi.org/10.1037/rev0000087) - (2018). Stochastic Methods for Modeling Decision-Making. In: Batchelder, W., Colonius, H., and E. N. Dzhafarov (Eds). New Handbook of Mathematical Psychology Vol. II Modeling and Measurement. Cambridge University Press
Diederich, A. & Mallahi-Karai, K.
(See online at https://doi.org/10.1017/9781139245906.002) - (2019) Decision with multiple alternatives: geometric models in higher dimensions – Cube Model. Journal of Mathematical Psychology, 93
Mallahi-Karai, K., & Diederich, A.
(See online at https://doi.org/10.1016/j.jmp.2019.102294)
