Democratix: A Declarative Approach to Winner Determination

Abstract

Computing the winners of an election is an important subtask in voting and preference aggregation. The declarative nature of answer-set programming (ASP) and the performance of state-of-the-art solvers render ASP very well-suited to tackle this problem. In this work we present a novel, reduction-based approach for a variety of voting rules, ranging from tractable cases to problems harder than NP. In addition, we discuss how encodings of voting rules can be optimized and combined in our approach. The encoded voting rules are put together in the extensible tool DEMOCRATIX, which handles the computation of the winners and is also available as a web application.To learn more about the capabilities and limits of the approach, the encodings are evaluated thoroughly on real-world data as well as on random instances.

Very Hard Electoral Control Problems

“…For E-CCAC, our input consists of a fact for the number of registered candidates, the number of unregistered candidates, the addition limit, the preferred candidate, and facts that describe the voters. For the voters, we follow the approach used in Democratix [13], where each distinct vote (c 1 > i · · · > i c m ) is represented by m atoms of the form p(i, j, c) meaning candidate c is the jth-preferred candidate by vote i. The corresponding count is represented by votecount(i, k), meaning k voters have vote i.…”

“…% Number of votes that disagree on C and D. Figure 1 shows guess part of Kemeny-CCAC that assumes an input as described in Democratix [13], but extended with predicates for the control problem. We start by guessing (with a choice rule) a subset of at most K of the unregistered candidates to add to the election and we update the number of candidates (candnum/1).…”

“…The work on solving hard election-attack problems has been restricted to problems in NP, and such approaches do not work for Σ p 2 -complete problems. Answer set programming (ASP) is an approach that has been recently applied for winner determination in voting, including for systems with hard winner problems [13]. ASP is suited to express Σ p 2 problems.…”

“…• We show for the most commonly-studied election systems with Θ p 2 -complete winner problems, including the Kemeny rule, that control is typically Σ p 2 -complete. • We build upon recent work on combining ASP with voting [13] by encoding our Σ p 2 -complete control problems using advanced ASP techniques.…”

A testbed to enable comparisons between competing approaches for computational social choice

“…Prefmine is not the first system intended to mine preference data, though it fulfills a different niche than other methods. Web-based social choice systems like Pnyx [4], Spliddit [17], Whale 3 [3], Democratix [6] and RoboVote 1 provide user friendly implementations of social choice functions that may be difficult to implement or operate correctly, to assist with popularizing these techniques. Ordinary users can submit preferences to the systems and obtain results from sophisticated Condorcet extensions or other rules that are automatically selected according to expert knowledge, in order to fit the users' problem domain.…”