Citizen Strategies in School Choice: How Strategic Agents Influence Rank-Minimizing Matchings

We consider one-sided matching problems in citizen-facing allocation systems such as school choice. In these settings, agents are allocated items based on their stated preferences. Posing this as an as- signment problem, the average rank of obtained matchings can be min- imized using the Rank Minimization (RM) mechanism. RM matchings can lead to significantly better rank distributions than matchings ob- tained by random-priority mechanisms such as Random Serial Dictator- ship (RSD). However, these matchings are also vulnerable to strategic behavior, where agents manipulate their reported preferences to achieve better outcomes. In this work, we derive a best response strategy for a scenario where agents aim to be matched to their top-n preferred items using the RM mechanism under a simplified cost function. This strategy is then extended to a first-order heuristic strategy for being matched to the top-n items in a setup that minimizes the average rank. Based on this finding, an empirical study is conducted examining the impact of the first-order heuristic strategy. The study utilizes data from both simulated markets and real-world matching markets in Amsterdam, taking into ac- count variations in item popularity, fractions of strategic agents, and the preferences for the n most favored items. For most scenarios, RM yields more rank efficient matches than Random Serial Dictatorship, even when agents apply the first-order heuristic strategy. In competitive markets, the matching performance can become worse when 50% of agents or more want to be matched to their top-1 or top-2 preferred items and apply the first-order heuristic strategy to achieve this. These findings contribute to the design of matching systems, showing how agents might manipulate preferences and how this manipulation can impact allocation efficiency.