Beyond Strategy-Proofness: How Biased Beliefs and Information Fuel Justified Envy
Meisner, Süer, Tolksdorf & Tominaj: "Confidence and Information in Strategy-Proof School Choice" CRC Discussion Paper No. 546
Strategy-proof mechanisms are a key tool to design markets without money. For example, in school districts all over the world, students submit a preference ranking over schools to a centralized clearinghouse that then assigns them according to strategy-proof assignment rules. Such mechanisms are powerful and desirable because a student’s knowledge or belief about their priority ranking should be irrelevant, as ranking schools based on true preference is a dominant strategy. However, Vincent Meisner (HU Berlin, Project A04), Müge Süer (IWH Halle), Michel Tolksdorf (TU Berlin, Project A04), and Sokol Tominaj (TU Berlin) demonstrate in a recent discussion paper that students’ submissions are significantly impacted, first when beliefs are biased and second when additional information is provided.
The researchers conducted a laboratory school-choice experiment, in which “students”—the participants in the experiment—were assigned to hypothetical schools according to a serial dictatorship rule. To shock participants’ beliefs, they used the “hard-easy gap” method to exogenously vary students’ beliefs about their relative position in the central priority ranking that was determined by their performance in a test: in one treatment condition this test was hard and in another one it was easy. It is well-known (and verified in the experiment) that harder tests trigger more pessimistic beliefs about relative rankings (underconfidence) compared to easier tests (overconfidence). Since subjects were randomly assigned to treatment conditions, this method can be used to establish a causal link between priority beliefs and misallocations.
The researchers mainly study justified envy, a specific indicator for undesirable allocations. In their setting, a student x has justified envy towards another student y when y has a worse test score (meaning lower priority), but was assigned to a school that x prefers over their own assignment. Such a situation is not only considered unfair, it is also a defining feature of unstable allocations which individual schools and students may want to upset. A core finding in the experiment is that underconfidence systematically induces significantly higher rates of justified envy than overconfidence among participants that were not informed about their own priority.
Having established that biased beliefs distort students’ submissions, the researchers then turned to the question of whether additional information could correct these biases. When the authors provided information to the students, the effects were heterogeneous and revealed a more complex pattern than previous literature has identified. While informing top-scoring students about their rank significantly reduced their justified envy in the initially underconfident group, this same priority information significantly increased justified envy among non-top students in the initially overconfident condition. Correcting overconfidence among lower-ranked non-top students often triggered more dominated non-truthful play.
A further implementation involved a dynamic design where participants sequentially submitted rankings while observing remaining school capacities, an environment where the dominant strategy is considered “obvious.” Though combining priority and capacity information reduced justified envy compared to priority information alone, justified envy did not entirely vanish. This persistent instability challenges not only the classical strategy-proofness, but also more recent behavioral notions of this property.
These results reveal that systematic, belief-based deviations are critical factors in the real-life performance of otherwise strategy-proof mechanisms. That is, participants seem to rely on strategic heuristics based on provided information, although the system is specifically designed to render non-strategic play the most profitable, both for individuals and for society.
Link (pdf): Confidence and Information in Strategy-Proof School Choice
