The problem of social ranking consists in determining a ranking over elements in a population, based on a ranking over %all coalitions within that population's coalitions, with the objective to rank elements according to their overall influence over coalitions. The lex-cel method, for instance, ranks elements based on the lexicographic comparison of their occurrences in the ranking over coalitions. As the number of coalitions grows exponentially with the size of the population, ranking them may prove cognitively costly for the user. As such, it is interesting to consider a setting of incomplete knowledge over that ranking. In this paper, we introduce two elicitation approaches for the determination of lex-cel necessary winners (i.e., the elements that are ranked highest according to the lex-cel) in a social ranking problem, when the knowledge about preferences over the coalitions is incomplete, and the initially accessible input is a subset of an existing total preorder. The first approach is preorder-driven, and elicitates enough of the underlying total preorder to determine the lex-cel necessary winners. The second approach is element-driven and guides comparisons based on strategically-located coalitions. Finally, we present experimental results and discuss the performance of each approach depending on various parameters and scenarios.