Using the Borda rule for ranking sets of objects
分析了基于单个对象排序来对对象集合进行排序的问题，指出了使用博尔达分数进行集合比较的缺点，并给出了博尔达求和排序的两个特征化结果。
We analyze the problem of ranking sets of objects based on a ranking over the single objects. In recent years various papers used the sum of individual scores for the objects, in particular Borda scores, to make such comparisons. The advantage of this approach lies in providing a complete ranking of sets of objects and therefore can be seen as an alternative to other methods based on best and/or worst objects. The paper contributes in two ways. On the one hand, we highlight certain drawbacks that arise when using Borda scores in such comparisons. On the other hand, we provide two characterization results for Borda-sum rankings, one for the restricted setting of sets of equal cardinality and one for the general setting which allows for comparisons of sets of unequal cardinality.