The Impossibility of Strategy-Proof Clustering

Clustering methods group individuals or objects based on information about their similarity or proximity. When the raw information to generate the clusters cannot be easily observed or verified, the clusters designer must rely on information reported on individuals behind the observations. When individuals receive utility from a public decision taken with aggregated data within each own's cluster and have single-peaked preferences, we prove that there do not exist cluster methods such that truth-revealing behavior is always a dominant strategy.