Keywords: Malmquist DEA, data envelopment analysis, ranked data, voting data, interval efficiency, minimax regret ranking, candidates, votes, relative measures, voting models, best relative efficiencies, candidate performance, inverted voting, worse performances, MILP, mixed integer linear programming, optimistic viewpoints, pessimistic viewpoints, systems science
Introducing an interval efficiency for each candidate in ranked voting data using data envelopment analysis
Efficiency is a relative measure because it can be measured within different ranges. The traditional voting models measure the efficiencies of candidates within the range of less than or equal to one. The corresponding efficiencies are referred to as the best relative efficiencies, which measure the best performances of candidates. There is another model called 'inverted voting' which measures the worse performances of candidates based on mixed integer linear programming. But, there are no relations essentially between voting model and inverted voting model. Thus, we introduce an interval efficiency which consists of efficiencies obtained from the optimistic and pessimistic viewpoints. A minimax regret-based approach (MRA) is used to compare and rank the efficiency intervals of candidates.