We propose a simple criterion to compare generalized median voter schemes according to their manipulability. We identify three necessary and sufficient conditions for the comparability of two generalized median voter schemes in terms of their vulnerability to manipulation. The three conditions are stated using the two associated families of monotonic fixed ballots and depend very much on the power each agent has to unilaterally change the outcomes of the two generalized median voter schemes. We perform a specific analysis of all median voter schemes, the anonymous subfamily of generalized median voter schemes.