Rank Aggregation Using Scoring Rules

To aggregate rankings into a social ranking, a natural approach is to use scoring systems such as Plurality, Veto, and Borda that assign scores to candidates. We distinguish three types of methods built on scoring systems: ranking by score, ranking by repeatedly choosing a winner, and ranking by repeatedly choosing a loser. The latter method captures the frequently studied voting rules Instant Runoff Voting (IRV), Coombs, and Baldwin. We compare these classes of methods axiomatically, referencing prior results. In an experimental analysis, we show that the three types of methods produce different rankings in practice. We also provide evidence that sequentially selecting winners is most suitable to detect a ground truth ranking of candidates. For different rules in our classes, we then study the (parameterized) computational complexity of deciding in which positions a given candidate can appear in the chosen ranking. As part of our analysis, we also consider the Winner Determination problem for IRV, Coombs, and Baldwin and determine their complexity when there are few voters or candidates.