Diversity of Structured Domains via k-Kemeny Scores
This addresses computational complexity in social choice theory for researchers, but it is incremental as it extends known intractability results.
The paper tackled the k-Kemeny problem in structured domains like single-peaked and single-crossing elections, showing it remains intractable even for k=2, and used it to rank these domains by diversity.
In the k-Kemeny problem, we are given an ordinal election, i.e., a collection of votes ranking the candidates from best to worst, and we seek the smallest number of swaps of adjacent candidates that ensure that the election has at most k different rankings. We study this problem for a number of structured domains, including the single-peaked, single-crossing, group-separable, and Euclidean ones. We obtain two kinds of results: (1) We show that k-Kemeny remains intractable under most of these domains, even for k=2, and (2) we use k-Kemeny to rank these domains in terms of their diversity.