论文标题
圆形社会中的刺穿数字
Piercing Numbers in Circular Societies
论文作者
论文摘要
在批准投票系统中，个人投票赞成他们认为可以接受的所有候选人。许多批准的投票情况可以以几何形式进行建模，因此诸如穿孔数字之类的几何概念具有自然的解释。在本文中，我们探讨了在选民偏好可以由一致的圆弧（即在固定长度的圆形社会中）建模的环境中的刺穿数字。鉴于许多选民和选民偏好弧的长度，我们对社会可能的刺耳数量进行了界限。此外，我们探讨了哪些穿孔数字更有可能。具体而言，在假设均匀分布的选民偏好弧的假设下，我们确定了弧形长度足够小的社会刺穿数量的概率分布。我们以模拟为具有较大选民偏好弧的社会刺穿数字的估计概率结束。
In the system of approval voting, individuals vote for all candidates they find acceptable. Many approval voting situations can be modeled geometrically, and thus geometric concepts such as the piercing number have a natural interpretation. In this paper, we explore piercing numbers in the setting where voter preferences can be modeled by congruent arcs on a circle -- i.e., in fixed-length circular societies. Given a number of voters and the length of the voter preference arcs, we give bounds on the possible piercing number of the society. Further, we explore which piercing numbers are more likely. Specifically, under the assumption of uniformly distributed voter preference arcs, we determine the probability distribution of the piercing number of societies in which the length of the arcs is sufficiently small. We end with simulations that give estimated probabilities of piercing number for societies with larger voter preference arcs.
