Order Independence in Sequential, Issue-by-Issue Voting.

This article investigates the conditions under which the outcome of sequential, issue-by-issue voting in a multidimensional spatial voting model is independent of the order in which issues are voted upon. Voters have norm-based preferences measuring distance from their ideal points, with norms possibly generated by inner products (e.g., Euclidean norm) or more general norms. The main findings establish that for inner-product norms, order independence holds if and only if the voting issues form an orthogonal basis. For general norms, order independence and strategy-proofness require the basis to satisfy a stronger property called left-additive mutual orthogonality (LAMO), defined via Birkhoff–James orthogonality, a generalization of orthogonality for normed spaces. While LAMO bases exist in two-dimensional spaces and certain lp-normed spaces, the authors prove that in higher dimensions, the existence of such bases is not generic, implying that order independence and strategy-proofness of sequential voting are fragile and often unattainable. These results highlight the endogenous nature of issue decomposition in multidimensional voting and its critical impact on the robustness and manipulability of collective decisions.