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 clusters cannot be easily observed or verified, the cluster designer must rely on information reported by individuals behind the observations. When these 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 clustering methods such that truth-revealing behavior is always a dominant strategy