In discrete mathematics, an interesting problem that has called the attention of many scholars is that of ranking the elements of a given partially ordered set. In this contribution, we propose reasonable properties that a method for ranking the elements of a poset may satisfy and we study the relationships between these properties. Interestingly, it is shown how a plethora of additional properties may be borrowed from the field of social choice theory and, in particular, from the problem of the aggregation of rankings. Finally, we present three prominent methods for ranking the elements of a poset (namely, the averaged rank method, the mutual rank probabilities and the maximal method) and analyse which among the proposed properties each of these three methods satisfies.