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Order Independence in Sequential, Issue-by-Issue Voting

Author

Listed:
  • Alex Gershkov
  • Benny Moldovanu
  • Xianwen Shi

Abstract

We study when the voting outcome is independent of the order of issues put up for vote in a spacial multi-dimensional voting model. Agents equipped with norm- based preferences that use a norm to measure the distance from their ideal policy vote sequentially and issue-by-issue via simple majority. If the underlying norm is generated by an inner-product – such as the Euclidean norm – then the voting outcome is order independent if and only if the issues are orthogonal. If the underlying norm is a general one, then the outcome is order independent if the basis defining the issues to be voted upon satisfies the following property: for any vector in the basis, any linear combination of the other vectors is Birkhoff-James orthogonal to it. We prove a partial converse in the case of two dimensions: if the underlying basis fails the above property then the voting order matters. Finally, despite existence results for the two-dimensional case and for the general lp case, we show that non-existence of bases with the above property is generic.

Suggested Citation

  • Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2023. "Order Independence in Sequential, Issue-by-Issue Voting," CRC TR 224 Discussion Paper Series crctr224_2023_413, University of Bonn and University of Mannheim, Germany.
    • Handle: RePEc:bon:boncrc:crctr224_2023_413
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    File URL: https://www.crctr224.de/research/discussion-papers/archive/dp413
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    More about this item

    Keywords

    Sequential voting; order independence; norm-based preferences;
    All these keywords.

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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