Automated Search for Impossibility Theorems in Social Choice Theory: Ranking Sets of Objects
Automated Search for Impossibility Theorems in Social Choice Theory: Ranking Sets of Objects
复制标题
自动搜索社会选择理论中的不可能性定理：对对象集进行排名
DOI：
10.1613/jair.3126
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Ulrich Endriss
中科院分区：
文献类型：
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作者：
Christian Geist;Ulrich Endriss
我们提出了一种方法，用于使用可满足性检查的标准技术来自动验证和发现经济理论领域中的定理，称为对象排序集。该领域的关键问题是如何将智能体对许多对象的偏好扩展到对这些对象的非空集合的偏好关系，这在社会选择理论和不确定条件下的决策制定中具有重要应用。这种偏好扩展的某些看似自然的原则组合可能导致逻辑不一致，这导致了许多重要的不可能定理。我们首先证明了一个一般结果，该结果表明，对于以多排序一阶逻辑表达的语法形式为特征的广泛的此类原则，在固定（小）域尺寸上表现出的任何不可能性都必然扩展到一般情况。然后，我们展示了如何在命题逻辑中以固定的域大小制定不可能定理的候选者，这反过来使我们能够使用SAT求解器自动搜索（一般）不可能定理。当应用到一个由20个从文献中熟悉的偏好扩展原则组成的空间时，该方法产生了总共84个不可能定理，包括已知的和重要的新结果。
We present a method for using standard techniques from satisfiability checking to automatically verify and discover theorems in an area of economic theory known as ranking sets of objects. The key question in this area, which has important applications in social choice theory and decision making under uncertainty, is how to extend an agent's preferences over a number of objects to a preference relation over nonempty sets of such objects. Certain combinations of seemingly natural principles for this kind of preference extension can result in logical inconsistencies, which has led to a number of important impossibility theorems. We first prove a general result that shows that for a wide range of such principles, characterised by their syntactic form when expressed in a many-sorted first-order logic, any impossibility exhibited at a fixed (small) domain size will necessarily extend to the general case. We then show how to formulate candidates for impossibility theorems at a fixed domain size in propositional logic, which in turn enables us to automatically search for (general) impossibility theorems using a SAT solver. When applied to a space of 20 principles for preference extension familiar from the literature, this method yields a total of 84 impossibility theorems, including both known and nontrivial new results.
关于判断和偏好聚合的推理
DOI：
10.1145/1329125.1329228
发表时间：
2007
期刊：
--
影响因子：
--
作者：
Ågotnes T
通讯作者：
Ågotnes T