Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized

The Gibbard-Satterthwaite Theorem on the manipulability of social-choice ru les assumes resoluteness: there are no ties,no multi-member choice sets. Ge neralizations based on a familiar lottery idea allow ties but assume perfec tly shared probabilistic beliefs about their resolution. We prove a more st raightforward generalization that assumes almost no limit on ties or belief s about them.