On the magnification of small biases in decision-making

Shaun William Davies, Edward Dickersin Van Wesep, Brian Waters

December 5, 2019

Abstract
We analyze a setting in which an actor chooses between N ex ante identical options. She can exert effort to learn about the quality of each option, but can ultimately choose only one. Under quite general conditions, optimal effort is asymmetric: a large amount of effort is expended learning about one arbitrarily chosen option, less on another, even less on a third, etc. This implies asymmetric likelihoods of each item being chosen. If the actor has an infinitesimal bias in favor of one option, then the actor selects an effort vector that maximizes the likelihood of her favored option being chosen. Small biases are magnified, sometimes enormously. We also show that a glass ceiling can arise, in which favored types are increasingly prevalent as one ascends the corporate ladder. These results have implications for portfolio selection (e.g., home bias, socially responsible investment funds), hiring (e.g., CEO choice, the glass ceiling), start-up funding, and a variety of other applications. The results also have implications for the optimal design of randomized experiments: different numbers of subjects should be assigned to each treatment. This applies to advertisers running focus groups to decide on an ad campaign or an ending for a movie, or to credit card lenders sending mailers to determine the optimal card to offer.