Rank aggregation

The Kemeny method is a commonly used approach to rank aggregation. It selects an output ranking that minimises the sum of Kendall tau distances to all input rankings. It is considered majoritarian in the sense that if more than 50% of the input rankings are identical, then the method will necessarily return that ranking.

However, in some contexts it may be desirable to aggregate rankings in a more proportional manner that also takes minority rankings into account. A related rule, sometimes referred to as the squared Kemeny method, minimises the sum of squared distances. This approach guarantees an upper bound on the distance between the output ranking and any input ranking, depending on its frequency in the input.^[2]

• Ranked voting – a setting in which the input consists of rankings of candidates, and the goal is to select a single candidate or a subset of candidates rather than produce a full ranking.
• Arrow's impossibility theorem – a fundamental result in social choice theory concerning the limitations of ranked voting systems.
• Social welfare function – a function that takes individual preferences as input and produces a collective ranking of alternatives.