论文标题
二维欧几里得偏好
2-Dimensional Euclidean Preferences
论文作者
论文摘要
如果可以将替代方案和选民都放入二维空间，以使每对替代方案都更喜欢欧几里得距离较短的选民。我们研究二维欧几里得偏好曲线如何取决于m和n的值。我们发现，最多有两个选民或最多三个替代方案的任何个人资料都是二维欧几里得人，而对于三名选民来说，我们可以为最多七个替代方案展示该物业。结果在Bogomolnaia和Laslier方面很紧张[2，命题15（1）]。
A preference profile with m alternatives and n voters is 2-dimensional Euclidean if both the alternatives and the voters can be placed into a 2-dimensional space such that for each pair of alternatives, every voter prefers the one which has a shorter Euclidean distance to the voter. We study how 2-dimensional Euclidean preference profiles depend on the values m and n. We find that any profile with at most two voters or at most three alternatives is 2-dimensional Euclidean while for three voters, we can show this property for up to seven alternatives. The results are tight in terms of Bogomolnaia and Laslier [2, Proposition 15(1)].
