Let ≽ be a total order on the power set of a finite set [n]. A subset S ⊂ [n] is separable when for any X,Y ⊂ S and any Z ⊂ [n] − S, the ordering of X and Y is the same as the ordering of X ∪ Z and Y ∪ Z. The character of a preference order is the collection of all separable subsets. Motivated by questions in the theories of voting, marketing and social choice, the admissibility problem asks which collections \(\mathcal {C} \subset \mathcal {P}({[n]})\) can arise as characters of preference orders. We introduce a linear algebraic technique to construct preference orders. Each vector in our 2ⁿ-dimensional voter basis induces a simple preference preorder (where ties are allowed) with nice separability properties. Given any collection \(\mathcal {C} \subset \mathcal {P}({[n]})\) that contains both ∅ and [n], and such that all pairs of subsets are either nested or disjoint, we use the voter basis to construct a preference order with character \(\mathcal {C}\).

令≽是有限集[ n ]的幂集的总阶。一个子集小号⊂[ Ñ ]是可分离当对于任何X，ÿ ⊂小号和任何ž ⊂[ Ñ ] -小号，的顺序X和ÿ相同的排序X ∪ Ž和ÿ ∪ ž。优先顺序的特征是所有可分离子集的集合。受投票，市场营销和社会选择理论中的问题所激发，可接纳性问题询问哪个集合\（\ mathcal {C} \ subset \ mathcal {P}（{[n]}）\）可以作为偏好顺序的字符出现。我们引入了线性代数技术来构造偏好顺序。我们的2 ⁿ维投票者基础中的每个向量都诱导出具有良好可分离性的简单偏好预排序（允许平局）。给定任何集合\（\ mathcal {C} \子集\ mathcal {P}（{[N]}）\）同时包含∅和[ Ñ ]，并且使得所有对的子集的要么嵌套的或不相交的，我们使用投票者基础，以使用字符\（\ mathcal {C} \）构造优先顺序。