Conditioning and Contingency

Question

I've learned, that spatiotemporal neighborhood among the conditioned and the unconditioned stimuli is a presupposition of conditioning (classical or operant). A second presupposition is called "contingency" in my notes. The explanation is, that the CS has to predict the US with certainty. But in my opinion the meaning of the word "contingency" is quite the opposite of predictability with certainty (necessity). Why is the second presupposition called "contingency"?

Answer 1

"Contingent" means "dependent upon".

See the first definition of http://dictionary.reference.com/browse/contingent?s=t

The reason the second definition there (which is the one you are thinking of) has the same word is because if B is contingent on A, then B is not for sure going to happen. B will only happen if A does.

Answer 2

The contingency of an event (A) can be expressed as the probability of A given another event (B) less the probability of A in the absence of B. So if the probability of A given B is 100%, then A is certain, given B. i.e., P(A|B) = 1. However if the probability of A given the absence of B (~B) is also 100%, then A is also certain without B. i.e., P(A|~B) = 1. In this case, B would have no detectable impact on the overall probability of A.

Thus the contingency of A is given by P(A|B) – P(A|~B) = ∆P

In the above example, ∆P = 0, since P(A|B) = 1 and P(A|~B) = 1. Zero represents the fact that B has no detectable impact on the occurrence of A.

If however P(A|B) > P(A|~B) then the contingency (∆P) will be positive, that is greater than 0. In this case, A is considered (somewhat) contingent on B. I say somewhat because P(A|B) could be 1 and P(A|~B) could be 0.99 so ∆P = .01, or P(A|~B) could be as low as 0 so ∆P = 1. These cases where ∆P > 0 represent the fact that B has some positive impact on the occurrence of A. That is, B makes A more likely to happen, and even certain when ∆P = 1.

The contingency could also be negative if P(A|B) < P(A|~B). When this happens, ∆P < 0 (i.e., negative) and this represents the case when B lowers (or prevents) the occurrence of A.

Rescorla (1968) Journal of Comparative and Physiological Psychology, 66, p4 was the first to make this connection to animal learning and Pavlovian condiitoning. He found that rats will be afraid of a light if it has a positive contingency with shock (i.e., it predicts that shock is more likely to occur), while rats will feel safe if a light has a negative contingency with shock (i.e., the light predicts that shock is less likely to occur). The implications have been discussed at length for how we (and animals) learn about the causal structure of our environment - see Maier & Seligman (1976) Journal of Experimental Psychology: General, 105, p3-46 for implications for instrumental conditioning, and Rescorla (1988) American Psychologist, 43, p151-160 for a good overview.