Computational Social Choice and Computational Complexity: BFFs?

Abstract

We discuss the connection between computational social choice (comsoc) and computational complexity. We stress the work so far on, and urge continued focus on, two less-recognized aspects of this connection. Firstly, this is very much a two-way street: Everyone knows complexity classification is used in comsoc, but we also highlight benefits to complexity that have arisen from its use in comsoc. Secondly, more subtle, less-known complexity tools often can be very productively used in comsoc.

Consensus halving is PPA-complete

“…By contrast, hitherto the only problems known to be PPA-complete are ones that involve circuits (or equivalently, polynomial-time Turing machines) in their definition, which represented a critique of PPA. Noting that consensus-halving is a kind of social-choice problem, our result can be seen as an example of computational social choice helping to populate "lonely" complexity classes, a phenomenon recently reviewed by Hemaspaandra [24]. The complexity class PPP still suffers from that problem, although the present paper should raise our hope that problems such as Equal Subsets will turn out to be complete for PPP.…”

Computational Social Choice and Computational Complexity: BFFs?

“…Due to space limitations, we will cover each topic but briefly, though we will try to give a sense of how each supports this section's thesis that comsoc has been a fertile ground for complexity techniques and notions, helping comsoc of course, but also in the case of little-used or narrowly used complexity techniques helping establish the value or breadth of the techniques. sion (Hemaspaandra 2017).…”