Departures from optimal stopping in an anagram task

To demonstrate the feasibility of defining impulsiveness (or its opposite, overcautiousness) as a departure from an optimum amount of time, we gave subjects a specified number of points (e.g., 100) for a correct answer to an anagram problem, a specified cost per second for working on each problem (e.g., 4 points), and a specified probability that each problem was insoluble (e.g., 0.25). At any point in time after each problem was presented, the subject could give up working on it. To find the optimum stopping point, we fit a curve representing the probability of solving an as-yet-unsolved, soluble problem as a function of time spent working on the problem. From this curve, under certain assumptions, we could calculate (for each condition) each subject's optimum stopping point, the time at which the subject should give up. Subjects' optimum stopping points, calculated in this way, dit not correlate with their actual mean stopping points (for giving up without a solution). Although subjects spent more time than their respective optima in some conditions, they were insensitive to increases in the optimum that resulted from decreases in the probability of the problem being insoluble, decreased cost of time, or increased payoff resulting from repetition of a problem later under conditions of high payoff and high cost. Hence, in these conditions with longer optima, subjects tended to spend too little time. Subjects' stopping points did not approach their respective optima over trials, but subjects were sensitive to false feedback about whether problems were insoluble when they gave up. Individual differences in mean stopping point were predicted by ability to solve problems in the first few seconds but not by ability to continue to solve problems with further effort after the first few seconds. Individual differences in departures from optimum were not related to individual differences in confidence.