Using Database Dependencies to Constrain Approval-Based Committee Voting in the Presence of Context

TL;DR

The paper advances ABC voting by integrating external contextual knowledge through a relational database, formulating legality as $D[B]\models\Gamma$ with TGDs and DCs in an extended schema that includes a virtual committee relation ${\textsc{Com}}$. It provides a general MIP-based implementation that supports arbitrary ABC scoring rules and demonstrates tractable cases (via reductions such as min-cost max-flow) alongside NP-hard instances when constraints are present. An extensive empirical study across political, hospitality, and media domains shows that targeted optimizations reduce MIP size by up to ~90% and generally improve runtimes, while DB constraints can variably impact performance. The work enables constraint-aware, context-rich multi-winner voting with practical tools and highlights future avenues such as more expressive counting constraints and alternative solver paradigms.

Abstract

In Approval-Based Committee (ABC) voting, each voter lists the candidates they approve and then a voting rule aggregates the individual approvals into a committee that represents the collective choice of the voters. An extensively studied class of such rules is the class of ABC scoring rules, where each voter contributes to each possible committee a score based on the voter's approvals. We initiate a study of ABC voting in the presence of constraints about the general context surrounding the candidates. Specifically, we consider a framework in which there is a relational database with information about the candidates together with integrity constraints on the relational database extended with a virtual relation representing the committee. For an ABC scoring rule, the goal is to find a committee of maximum score such that all integrity constraints hold in the extended database. We focus on two well-known types of integrity constraints in relational databases: tuple-generating dependencies (TGDs) and denial constraints (DCs). The former can express, for example, desired representations of groups, while the latter can express conflicts among candidates. ABC voting is known to be computationally hard without integrity constraints, except for the case of approval voting where it is tractable. We show that integrity constraints make the problem NP-hard for approval voting, but we also identify certain tractable cases when key constraints are used. We then present an implementation of the framework via a reduction to Mixed Integer Programming (MIP) that supports arbitrary ABC scoring rules, TGDs and DCs. We devise heuristics for optimizing the resulting MIP, and describe an empirical study that illustrates the effectiveness of the optimized MIP over databases in three different domains.

Figures (5)

• Figure 1: ABC voting with external context.
• Figure 2: From left to right: impact of the optimizations on the number of MIP constraints (first) and runtime (second), impact of varying constraints (third) and voting rules (fourth) on the runtime. G, P, and C refer to the optimizations: Grouping similar voters, Pruning infeasible scores, and Contracting DC constraints.
• Figure 3: Computing time for varying committee size $k$.
• Figure 5: The markings G, P, and C refer to the different optimizations - grouping similar voters, pruning infeasible scores, and contracting DC constraints via hypercliques accordingly.
• Figure 6: Computing time for varying committee size $k$. In the Trip Advisor dataset, the candidate group size is $|C|=1,845$, and we have one TGD, and for the Movies Dataset $|C|=100$ with no constraints.

Theorems & Definitions (10)

• theorem 1
• theorem 2
• lemma 1
• lemma 2
• lemma 3
• lemma 4
• lemma 5
• lemma 6
• lemma 7
• lemma 8