论文标题
匿名二元社会选择的几何形状，这些选择是防止策略的
Geometry of anonymous binary social choices that are strategy-proof
论文作者
论文摘要
让$ v $成为社会，其成员对两种替代方案表示偏好，包括冷漠。通过二进制函数确定匿名二进制社会选择功能$ f = f（k，m）$在整数三角网格上定义的$通过依次列出G的G片段，GOMETIAL的长度相等（最大）长度，交替地和垂直，代表了确定两种选择之一的集体选择。确实，我们表明，可以用一系列非负整数$ $（q_1，q_2，\ cdots，q_s）$来描述每个匿名和防止策略的功能，这些函数与上述片段的红衣主教相对应。我们还分析了我们目前的代表性与涉及多数配额序列的另一种早期表示之间的联系。 作者可以使用Python代码实施任何此类社交选择功能。
Let $V$ be society whose members express preferences about two alternatives, indifference included. Identifying anonymous binary social choice functions with binary functions $f=f(k,m)$ defined over the integer triangular grid $G=\{(k,m)\in \mathbb{N}_0\times\mathbb{N}_0 : k+m\le |V|\} $, we show that every strategy-proof, anonymous social choice function can be described geometrically by listing, in a sequential manner, groups of segments of G, of equal (maximum possible) length, alternately horizontal and vertical, representative of preference profiles that determine the collective choice of one of the two alternatives. Indeed, we show that every function which is anonymous and strategy-proof can be described in terms of a sequence of nonnegative integers $(q_1, q_2, \cdots, q_s)$ corresponding to the cardinalities of the mentioned groups of segments. We also analyze the connections between our present representation with another of our earlier representations involving sequences of majority quotas. A Python code is available with the authors for the implementation of any such social choice function.
