Introduction to Computational Social Choice

Monotonicity-based consensus states for the monometric rationalisation of ranking rules with application in decision making

“…The subfield of computational social choice is calling the attention of the scientific community to the fact that not only the normative properties of ranking rules are to be studied, but that also the execution time of these ranking rules needs to be taken into account [21]. One of the most prominent examples of ranking rules that are computationally unfriendly is the method of Kemeny [80], which has been extensively analysed from a computational point of view [9].…”

“…), the Kemeny ranking problem (given a profile and two candidates a i 1 and a i 2 , is there a ranking that has minimum score and ranks a i 1 at a better position than a i 2 ?) and the Kemeny rank aggregation problem (given a profile, find a ranking that has minimum score) are proved to be NP-hard (see Chapter 4 of [21]). Obviously, the corresponding adaptation of these problems to the search for monotonicity of a representation of votes is computationally harder.…”

“…The extension of the method of Kemeny to rankings with ties (and to tournaments and to binary relations) is a common problem in social choice [8,21,30,31], usually referred to as the search for 'median orders' or 'median relations'. These extensions are obtained by allowing the relations in the profile to be rankings with ties (or tournaments, or binary relations) or by allowing the winning relations to be rankings with ties (or tournaments, or binary relations).…”

Subset Selection Via Implicit Utilitarian Voting

“…Traditional social choice theory typically takes a normative approach, by specifying desirable axioms that the aggregation method (also known as a voting rule) should satisfy (Arrow, 1951). In contrast, researchers in computational social choice (Brandt, Conitzer, Endriss, Lang, & Procaccia, 2016) often advocate quantitative approaches to the same problem. The high-level idea is to identify a compelling objective function, and design voting rules that optimize this function.…”

Voting on Actions with Uncertain Outcomes

“…This combination of concerns is what we should expect to encounter in a variety of application domains, e.g., when devising mechanisms for teams of autonomous software agents to interact and agree on actions to pursue collectively. However, while social choice theory has, rightly, been argued to be relevant to multiagent systems [17,7], the standard model of social choice only deals with the aggregation of preferences [10]. In this paper we put forward a model for voting on actions with uncertain effects that integrates this standard perspective with a simple notion of uncertainty.…”