Thiele Methods for Comment Selection under Trichotomous Preferences

Abstract

Many online discussion platforms and citizen assemblies provide participants with the ability to react to comments by means of up- and downvotes. Such reactions can be understood as preferential information: upvotes are interpreted as approvals and downvotes as disapprovals of a comment. A natural question is how this information can be used to present such a discussion in a concise manner. In this thesis, we approach this question through the lens of Computational Social Choice.We propose a framework of trichotomous ballots, a three-valued generalisation of approval ballots that distinguishes between approved, disapproved, and unassigned comments. Based on the framework of Approval-Based Committee voting, we define selection methods that map a trichotomous profile and a size bound to selections (i.e. sets of comments). We discuss a number of procedural constraints that such methods may be required to satisfy – exhaustiveness, resoluteness, and monotonicity – and show how they relate to each other as well as to the more familiar presentation of comments as rankings.We then discuss how trichotomous preferences communicated by a ballot can be used to infer a lifted preference over selections. We introduce a number of requirements such that the class of methods satisfying these requirements can be represented by a trichotomous generalisation of Thiele scoring functions. This provides a pragmatic motivation of the class of Thiele selection methods. We give particular attention to the subclass of tally-based methods, which can be computed by solely keeping tallies of up- and downvotes of each comment. We show that these methods are conceptually simple, computationally tractable, and that their behaviour with respect to exhaustiveness and resoluteness on a given profile can be described by numerical degrees.Finally, we conduct a quantitative analysis of real-world data gathered from several deliberations run on the Polis platform. We analyse the distribution of assignments, the distribution of net scores, and the practical degrees of exhaustiveness and resoluteness of the tally-based net support rule. Our findings lend some empirical support to the normative assumptions underlying our framework and illustrate the behaviour of the proposed methods on real-world trichotomous profiles.