A One-Third Advice Rule Based on a Control-Theoretic Opinion Dynamics Model

We commonly seek advice in making decisions. However, multiple empirical studies report that, on average, we shift our own initial decision by only 30% toward external advice after advice is provided. This “egocentric advice discounting” is particularly counterintuitive because we do care a lot about the opinion of our peers. There is significant literature that attempts to explain the egocentric advice discounting and factors that influence this phenomenon; however, this literature is unable to explain why the numerical value of 30% is robust across a number of experimental settings. In this paper, we employ a control-theoretic opinion dynamics model to show that the one-third advice rule-adjusting one's decision about 33.3% toward advice-is in fact distributionally robust for a crowd of decision-makers whose decisions also serve as advice for others. Our results imply that the observed egocentric advice discounting might not be a coincidence; instead, when an individual is faced with insufficient information, the distributionally robust optimal decision is to combine one-third of advice with two-thirds of his/her initial decision. Our theory also suggests that knowing the dispersion of decisions can further help decision-makers optimize advice taking.