Strong maximals: Elements with maximal score in partial orders

Abstract

It is usually assumed that maximal elements are the best option for an agent. But there are situations in which we can observe that maximal elements are “different” one from another. This is the case of partial orders, in which one maximal element can be strictly preferred to almost every other element, whereas another maximal is not strictly preferred to any element. As partial orders are an important tool for modelling human behavior, it is interesting to find, for this kind of binary relation, those maximal elements that could be considered the best ones. In so doing, we define a selection inside the maximal set, which we call strong maximals (elements with maximal score), which is proved to be appropriate for choosing among maximals in a partial order.