How to Address Multiple Sources of Influence in Group Decision-Making?: From a Nonordering to an Ordering Approach

Abstract

We consider settings of group decisions where agents’ choices/preferences are influenced (and thus changed) by each other. Previous work discussed at length the influence among agents and how to obtain the result of influence resulting choice/preference but mainly considered the influence of one agent at a time or the simultaneous influence of more than one agent but in a nonordering (such as unidimensional utility or belief, binary opinion or choice) context. However, the question regarding how to address multiple influences in an ordering (specifically, ordinal preference) context, particularly with varied strengths (stronger or weaker) and opposite polarities (positive or negative), remains. In this paper, we extend classical social choice functions, such as the Borda count and the Condorcet method, to signed and weighted social influence functions. More importantly, we extend the KSB (Kemeny) distance metric to a matrix influence function. Firstly, we define the rule for transforming each preference ordering into a corresponding matrix (named the ordering matrix) and set a metric to support the computation of the distance between any two ordering matrices (namely, any two preferences). Then, the preference (theoretically existing) that has the smallest weighted sum of distances from all influencing agents’ preferences will be the resulting preference for the influenced agent. As the weight of influencing agents can be either positive or negative (as friends or enemies) in a real-world situation, it will play a role in finding the “closest” possible preference from the positively influencing preferences and finding the “farthest” possible preference from the negatively influencing preferences.