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The core in Participatory Budgeting can be empty

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  • Maly, Jan

Abstract

The core is a strong fairness notion in multi-winner voting and participatory budgeting (PB). It is known that the core can be empty if we consider cardinal utilities, but it is not known whether it is always satisfiable with approval ballots. In this short note, I show that in approval-based PB the core can be empty for nearly all satisfaction functions that are based on the cost of a project. In particular, I show that the core can be empty for the cost satisfaction function, satisfaction functions based on diminishing marginal returns, and the share. However, it remains open whether the core can be empty for the cardinality satisfaction function.

Suggested Citation

  • Maly, Jan, 2025. "The core in Participatory Budgeting can be empty," Economics Letters, Elsevier, vol. 254(C).
    • Handle: RePEc:eee:ecolet:v:254:y:2025:i:c:s016517652500309x
    DOI: 10.1016/j.econlet.2025.112472
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    References listed on IDEAS

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    1. Haris Aziz & Markus Brill & Vincent Conitzer & Edith Elkind & Rupert Freeman & Toby Walsh, 2017. "Justified representation in approval-based committee voting," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 461-485, February.
    2. Steven Brams & Richard Potthoff, 2015. "The paradox of grading systems," Public Choice, Springer, vol. 165(3), pages 193-210, December.
    3. Yves Sintomer & Carsten Herzberg & Anja Röcke, 2008. "Participatory Budgeting in Europe: Potentials and Challenges," International Journal of Urban and Regional Research, Wiley Blackwell, vol. 32(1), pages 164-178, March.
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