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The replacement principle for the provision of multiple public goods on tree networks

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Abstract

This article considers the provision of two public goods on tree networks where each agent has a single-peaked preference. We show that if there are at least four agents, then no social choice rule exists that satisfies efficiency and replacement-domination. In fact, these properties are incompatible, even if agents’ preferences are restricted to a smaller domain of symmetric single-peaked preferences. However, for rules on an interval, we prove that Miyagawa’s (Soc Choice Welf 18:527–541, 2001) characterization that only the left-peaks rule and the right-peaks rule satisfy both of these properties also holds on the domain of symmetric single-peaked preferences. Moreover, if agents’ peak locations are restricted to either the nodes or the endpoints of trees, rules exist on a subclass of trees. We provide a characterization of a family of such rules for this tree subclass.

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Authors and Affiliations

  1. Faculty of Business Administration, Daito Bunka University, 1-9-1 Takashimadaira, Itabashi-ku, Tokyo, 175-8571, Japan

    Masashi Umezawa

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  1. Masashi Umezawa
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Correspondence to Masashi Umezawa.

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Umezawa, M. The replacement principle for the provision of multiple public goods on tree networks. Soc Choice Welf 38, 211–235 (2012). https://doi.org/10.1007/s00355-010-0526-x

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  • DOI: https://doi.org/10.1007/s00355-010-0526-x

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