On location problem of public facilities by collective choice model

当代理人位于网络上时，考虑提供公共产品。每个代理都有一个单峰偏好。我们证明了，如果树网络上至少有四个代理，那么不存在满足效率和执行支配的社会选择规则。效率是一个公理，意味着帕累托最优。替代-支配是一个公理，与偏好发生变化时代理人之间的团结一致的想法有关。事实上，这些属性被证明是不相容的，即使代理的偏好被限制在一个较小的域的对称单峰的偏好。此外，它被证明，如果代理的峰值位置被限制在节点或端点的树，规则存在于一个子类的树。我们给出了这个树子类的一个家庭这样的规则的表征。

When agents are located on a network, the provision of public goods is considered. Each agent has a single-peaked preference. We showed that if there were at least four agents on a tree network, then no social choice rule existed that satisfied efficiency and replacement-domination. Efficiency is an axiom meaning Pareto optimality. Replacement-domination is an axiom in relation to the idea of solidarity among agents when changes in preferences occur. In fact, these properties were shown to be incompatible, even if agents' preferences were restricted to a smaller domain of symmetric single-peaked preferences.Moreover, it was shown that if agents' peak locations were restricted to either the nodes or the endpoints of trees, rules existed on a subclass of trees. We gave a characterization of a family of such rules for this tree subclass.