We study solutions that choose an interval of alternatives when agents have single-peaked preferences. Similar to Klaus and Storcken (2002), we ordinally extend these preferences over intervals. Loosely speaking, we extend the results of Moulin (1980) to our setting and show that the results of Ching (1997) cannot always be similarly extended. Our main results are the following. First, strategy-proofness and peaks-onliness characterize the class of generalized median solutions. Second, although peaks-onliness cannot be replaced by the "weaker" property of continuity in our first result -as is the case in Ching (1997)- this equivalence is achieved when voter-sovereignty is also required. Finally, if preferences are symmetric and single-peaked, strategy-proofness and voter-sovereignty characterize the class of efficient generalized median solutions.

中文翻译：

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关于策略证明性和单峰性：间隔的中值投票

我们研究了当代理具有单峰偏好时选择一系列备选方案的解决方案。与 Klaus 和 Storcken (2002) 类似，我们通常会在间隔上扩展这些偏好。粗略地说，我们将 Moulin (1980) 的结果扩展到我们的环境中，并表明 Ching (1997) 的结果不能总是类似地扩展。我们的主要结果如下。首先，策略证明性和峰值在线性表征了广义中值解决方案的类别。其次，虽然在我们的第一个结果中不能用连续性的“较弱”属性代替峰值在线性 - 正如 Ching (1997) 的情况一样 - 当还需要选民主权时，就可以实现这种等效性。最后，如果偏好是对称的和单峰的，