One-dimensionality and stability in legislative voting

Abstract

The widespread use in legislative studies of the one-dimensional model and its median-stability consequence raises a question: Do stability and one-dimensionality rest on evidence drawn from observed votes? They do not and cannot. I prove that every possible legislative history is compatible with a transitive majority preference (hence stability), and except in very special circumstances with a cyclic majority preference (hence instability) as well: observed votes can never refute and almost never confirm stability. One-dimensionality fares worse: any legislative history is compatible with the one-dimensional model if it includes no two votes with overlapping pairs of alternatives, but otherwise, I show, it is almost certainly incompatible with the model, even in those rare cases that ensure transitivity. Voting evidence aside, the one-dimensional model is unduly restrictive, and arguments in its defense do not survive scrutiny. © 2010 The Author(s).