Decision-Making on the Full Information Secretary Problem

Abstract

The secretary problem is a recreational mathematics problem, suited to laboratory experimentation, that nevertheless is representative of a class of real world sequential decision-making tasks. In the ‘full information’ version, an observer is presented with a sequence of values from a known distribution, and is required to choose the maximum value. The difficulties are that a value can only be chosen at the time it is presented, that the last value in the sequence is a forced choice if none is chosen earlier, and that any value that is not the maximum is scored as completely wrong. We report a study of human performance on full information secretary problems with 10, 20 and 50 values in the sequence, and considers three different heuristics as models of human decision-making. It is found that some people achieve near-optimal levels of accuracy, but that there are individual differences in human performance. A quantitative evaluation of the three heuristics, using the Minimum Description Length criterion, shows inter-individual differences, but intra-individual consistency, in the use of the heuristics. In particular, people seem to use the heuristics that involve choosing a value when it exceeds an internal threshold, but differ in how they set thresholds. On the basis of these findings, a more general threshold-based family of heuristic models is developed.