• Optimal stopping
• Heuristics
• Threshold
• Learning
• Intelligence

Optimal stopping theory concerns problems of timing to take an action. The “secretary problem” is a classic example of this type of problem.
In its traditional formulation the decision maker can choose whether to accept or refuse the current option, given a finite number of alternatives shown sequentially. The only information available for each element is its relative quality and the decision maker’s goal is to maximize the probability of picking the best one.

We modify two of the main assumptions in order to obtain a problem more similar to real choice situations. First, we use cardinal values instead of rankings for the applicants. The values are randomly drawn from normal distributions with different means and variances. The parameters are unknown and change between sequences, but they can be estimated within each trial. Second, we remove the 0-1 utility function: in this way the goal is to maximize the expected gain of the sequence instead of the probability of picking the highest value.
This new problem is solved using a computational demanding "dynamic threshold model", whereas previously studied rules perform significantly worse.
We compare the performances with two new simplified rules: a “maximum-threshold rule” that uses extreme values as proxy of variance, and a “cutoff-threshold rule” that includes features of both cutoff rule and threshold model.

In the experiment 120 subjects do their choices with 30 different sequences and run various tests (measuring intelligence, memory and risk aversion). The cutoff-threshold rule, that performs slightly worse than the optimal strategy, fits behavioural data better than all the others, showing a trade-off between the optimal policy and the already identified heuristic.
Additionally we study the learning process during the task and the role of intelligence of participants. Results confirm previous studies on the role of intelligence as major predictor of performance, both as value earned and precision of the model adopted.