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

The Gibbard-Satterthwaite Theorem on the manipulability of socialchoice rules assumes resoluteness: there are no ties, no multi-member choice sets. Generalizations based on a familiar lottery idea allow ties but assume perfectly shared probabilistic beliefs about their resolution. We prove a more straightforward generalization that assumes almost no limit on ties or beliefs about them.