The Dating Problem and Optimal Ordering of Sequential Opportunities

TL;DR

This paper studies a stochastic decision problem of optimally ordering opportunities to maximize uncertain rewards, revealing that solutions can be derived from simple ordering of real numbers, applicable to various real-world scenarios.

Contribution

It introduces a novel approach to the sequential opportunity ordering problem, showing that optimal solutions can be obtained through simple numerical ordering, despite its combinatorial appearance.

Findings

Optimal solutions can be found by ordering real numbers.

Applicable to dating, journal submissions, and similar decision problems.

Simplifies complex combinatorial problems into numerical ordering.

Abstract

In this paper, we discuss a stochastic decision problem of optimally selecting the order in which to try $n$ opportunities that may yield an uncertain reward in the future. The motivation came out from pure curiosity, after an informal conversation about what could be the best way to date friends. The problem structure turned out to be suitable also for other situations, such as the problem of optimally selecting the order of submission of a paper to journals. Despite the seemingly combinatorial nature of the problem, we show that optimal-tradeoff solutions can be found by simply ordering a sequence of $n$ real numbers.