The replacement principle for the provision of multiple public goods on tree networks |
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Authors: | Masashi Umezawa |
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Institution: | (1) D?partment de Sciences ?conomiques, Universit? de Montr?al, C.P. 6128, succursale Centre-ville, Montr?al, QC, H3C 3J7, Canada |
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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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Keywords: | |
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