Foundations Of Cognitive Science

Probabilistic Contrast Model

The probabilistic contrast model (Cheng & Holyoak, 1995; Cheng & Novick, 1990, 1992) is a formal, normative model of contingencies between causes and outcomes. Early models that were based on 2X2 contingency tables were able to define contingency as a difference between conditional probabilities, but were only able to do so for a single cue. The probabilistic contrast model extends this idea to multiple cues. For example, it preserves the same notion of contingency as older theories, where contingency is the difference between the probability of an outcome occurring when a cue i is present versus the conditional probability when cue i is absent (P(O|i) - P(O|~i)). However, higher order interactions can also formulated when multiple cues (i and j, for instance) can be considered (e.g. P(O|ij) - P(O|~ij) versus P(O|i~j) - P(O|~i~j)). Shanks (1995) has suggested that the probabilistic contrast model provides a general enough notion of contingency that this model can be viewed as providing a computational account of associative learning.


  1. Cheng, P. W., & Holyoak, K. J. (1995). Complex adaptive systems as intuitive statisticians: Causality, contingency, and prediction. In H. L. Roitblat & J.-A. Meyer (Eds.), Comparative Approaches To Cognitive Science (pp. 271-302). Cambridge, MA: MIT Press
  2. Cheng, P. W., & Novick, L. R. (1990). A probabilistic contrast model of causal induction. Journal of Personality and Social Psychology, 58(4), 545-567.
  3. Cheng, P. W., & Novick, L. R. (1992). Covariation in natural causal induction. Psychological Review, 99(2), 365-382.
  4. Shanks, D. R. (1995). The Psychology Of Associative Learning. Cambridge, UK: Cambridge University Press.

(Added March 2010)