Contexts of interference Sample Clauses

Contexts of interference. We turn now to the opposite case: consider a context C˜ where remembering X is detrimental to the agent’s chances of making the correct choice, due to interference effects. Using the same notation (with C replaced by C˜) and assumptions as in the previous section, we can see that again ∆E[u | sX, X, C˜] = N (C˜)[π(sX) − π(0)]. (4.23) threshold κ, such that if the agent’s credence P (X) exceeds κ then she will make the best decision 4A further possible justification is to consider a simple generic decision scenario that could represent X’s context of relevance. In any such setup, decision theory will prescribe some fixed no more information, it is standard to use a uniform prior for κ between zero and one (following P (X), meaning that the agent’s chance of success π(0) = P (X). (P (X) being the key quantity since we are ex hypothesi in a context of relevance of X). With the principle of insufficient reason). In that case, the chance that κ is less than P (X) is exactly { } As before, appreciating that there may be multiple interference contexts C˜j , the second half of eq. (4.12) can be expressed as: j ∆E[ut(w) | sX, X, interferes] f (interferes) = Σ N (C˜j )[πj(sX) − πj(0)] f (C˜j ). ( ) − ( ) (4.24) ( ) < ( ) − ( ) Once again, the challenge now is to determine how πj sX πj 0 scales with sX; once again, we will – for simplicity – consider a single context of interference, and drop the subscript X as implicit. Hence the question revolves around the behaviour of ∆π s π s π 0 in interference contexts . Our reasoning for this can follow an almost identical line to that in the previous section, with one crucial difference. Recall that for contexts of relevance, retrieval of X ensured success – thus if X was retrieved on any attempt, success was guar- anteed. By contrast, in interference contexts, retrieval of X impedes success – if X is retrieved on every attempt then the agent will fail. Since the probability of success in a context of interference if the agent retrieves X on every attempt is zero (since then the interference has been complete), we can express the probability of success in general as just