Selecting the Most Conflicting Pair of Candidates

Where a collective decision over a set of options based on a number of opinions has to be reached, conflict is inevitable. Reflected by differences in the opinions, it usually comes from different perspectives of the opinions (e.g., in the case of human opinions, a beginner investor would likely have completely different opinion on various asset classes than their professional counterpart). However, conflict might also be option-based and stem from diverse, sometimes even contradicting, inherent qualities of the options (e.g., potentially high-return assets typically have high risk levels). We are interested in how to identify these conflicting options, based on the preferences. Since the options might represent multiple entities (e.g., sports players, societal issues, or marketing strategies), answering this question has numerous natural applications that include selecting competitors to organize engaging sport events (e.g., boxing matches), controversial topics to organize interesting political debates, disputable issues for socially-relevant deliberations, or conflicting ideas for boosting the creativity with passionate discussions.