📝 SummarXiv

Abstract

In business, politics and life, folk wisdom encourages people to aim for above-average results, but to not let the perfect be the enemy of the good. Here, we mathematically formalize and extend this folk wisdom. We model a time-limited search for strategies having uncertain rewards. At each time step, the searcher either is satisfied with their current reward or continues searching. We prove that the optimal satisfaction threshold is both finite and strictly larger than the mean of available rewards -- matching the folk wisdom. This result is robust to search costs, unless they are high enough to prohibit all search. We show that being too ambitious has a higher expected cost than being too cautious. We show that the optimal satisfaction threshold increases if the search time is longer, or if the reward distribution is rugged (i.e., has low autocorrelation) or left-skewed. The skewness result reveals counterintuitive contrasts between optimal ambition and optimal risk taking. We show that using upward social comparison to assess the reward landscape substantially harms expected performance. We show how these insights can be applied qualitatively to real-world settings, using examples from entrepreneurship, economic policy, political campaigns, online dating and college admissions. We discuss implications of several possible extensions of our model, including intelligent search, reward landscape uncertainty and risk aversion.