We prove a “General Manipulability Theorem” for general one-to-one two-sided matching markets with money. This theorem … implies two folk theorems, the Manipulability Theorem and the General Impossibility Theorem, and provides a sort of converse … of the Non-Manipulability Theorem (Demange, 1982, Leonard, 1983, Demange and Gale, 1985). …

We propose a simple criterion to compare generalized median voter schemes according to their manipulability. We …