Lovett, M. C. (1998). Choice. In J. R. Anderson, & C. Lebiere (Eds.). The atomic components of thought, 255-296. Mahwah, NJ: Erlbaum.
In ACT-R theory each production rule is chosen according to the probability that reflects its expected gain E(i) relative to the competitors expected gains E(j). ACT-R chooses the production with the highest expected gain, but because of the noise in evaluation the production with a highest expected gain is chosen only a certain proportion of time. The presented below Conflict Resolution Equatation describes the probability that the a production with its expected gain E(i) will have the highest noise added expected gain
where t controls the noise of the evaluation. There evaluations of expected gain are computed as the quantity E=PG – C, where P Is estimated probability of achieving the productions goal, G is the value of the goal and C is the cost to be expected in reaching the goal. P is the estimated probability of eventual successes in attaining the goal, it is decomposed into two parts: P=qr, where q is the probability that the production under consideration will achieve intended next state, and t is the probability of achieving the production’s goal given arrival at the intended next state. For practical reasons we can takes q a 1, leaving r as the main quantity to estimate. Under this constraint the r parameter is important for determining the choice among competitive productions. When a production’s parameter r Is low it implies that the production tends not to lead to the goal even when it leads to its intended next state, this r low value will be represented in a low P value, which will lead the production to have a low expected gain. In contrast a production with a high likehood of leading to its goal will have a higher estimated probability of achieving the goal and hence a higher expected gain evaluation.
In ACT-R the value of the production’s r parameter is estimated as:
r = successes/(successes + failures)
The very important improvement made within ACT-R theory of choice is also implementation of decay of successes and failures experiences used in computing expected gain. In other words: more time elapsed from last use of a production rule a r parameter shall be lower.
r(t) = successes (t) /[successes (t) + failures (t)]
where t(j) is defined as how long ago past success of failure was.
The author describes in the article variety of examples proving how much such implementations makes us closer for good description of the human choice.