In this work, we study the metric distortion problem in voting theory under a limited amount of ordinal information. Our primary contribution is threefold. First, we consider mechanisms that perform a sequence of pairwise comparisons between candidates. We show that a popular deterministic mechanism employed in many knockout phases yields distortion O(log m) while eliciting only m − 1 out of the Θ(m2 ) possible pairwise comparisons, where m represents the number of candidates. Our analysis for this mechanism leverages a powerful technical lemma developed by Kempe (AAAI ‘20). We also provide a matching lower bound on its distortion. In contrast, we prove that any mechanism which performs fewer than m−1 pairwise comparisons is destined to have unbounded distortion. Moreover, we study the power of deterministic mechanisms under incomplete rankings. Most notably, when agents provide their k-top preferences we show an upper bound of 6m/k + 1 on the distortion, for any k ∈ {1, 2, . . . , m}. Thus, we substantially improve over the previous bound of 12m/k established by Kempe (AAAI ‘20), and we come closer to matching the best-known lower bound. Finally, we are concerned with the sample complexity required to ensure near-optimal distortion with high probability. Our main contribution is to show that a random sample of Θ(m/ϵ2 ) voters suffices to guarantee distortion 3 + ϵ with high probability, for any sufficiently small ϵ > 0. This result is based on analyzing the sensitivity of the deterministic mechanism introduced by Gkatzelis, Halpern, and Shah (FOCS ‘20). Importantly, all of our sample-complexity bounds are distribution-independent. From an experimental standpoint, we present several empirical findings on real-life voting applications, comparing the scoring systems employed in practice with a mechanism explicitly minimizing (metric) distortion. Interestingly, for our case studies, we find that the winner in the actual competition is typically the candidate who minimizes the distortion.

We study convergence properties of iterative voting procedures. Such procedures are defined by a voting rule and a (restricted) iterative process, where at each step one agent can modify his vote towards a better outcome for himself. It is already known that if the iteration dynamics (the manner in which voters are allowed to modify their votes) are unrestricted, then the voting process may not converge. For most common voting rules this may be observed even under the best response dynamics limitation. It is therefore important to investigate whether and which natural restrictions on the dynamics of iterative voting procedures can guarantee convergence. To this end, we provide two general conditions on the dynamics based on iterative myopic improvements, each of which is sufficient for convergence. We then identify several classes of voting rules (including Positional Scoring Rules, Maximin, Copeland and Bucklin), along with their corresponding iterative processes, for which at least one of these conditions hold.

The paper presents an approach for optimizing the evaluation of SPARQL queries over OWL ontologies using SPARQL's OWL Direct Semantics entailment regime. The approach is based on the computation of lower and upper bounds, but we allow for much more expressive queries than related approaches. In order to optimize the evaluation of possible query answers in the upper but not in the lower bound, we present a query extension approach that uses schema knowledge from the queried ontology to extend the query with additional parts. We show that the resulting query is equivalent to the original one and we use the additional parts that are simple to evaluate for restricting the bounds of subqueries of the initial query. In an empirical evaluation we show that the proposed query extension approach can lead to a significant decrease in the query execution time of up to four orders of magnitude.

Following recent studies of iterative voting and its effects on plurality vote outcomes, we provide characterisations and complexity results for three models of iterative voting under the plurality rule. Our focus is on providing a better understanding regarding the set of equilibria attainable by iterative voting processes. We start with the basic model of plurality voting. We first establish some useful properties of equilibria, reachable by iterative voting, which enable us to show that deciding whether a given profile is an iteratively reachable equilibrium is NP-complete. We then proceed to combine iterative voting with the concept of truth bias, a model where voters prefer to be truthful when they cannot affect the outcome. We fully characterise the set of attainable truth-biased equilibria, and show that it is possible to determine all such equilibria in polynomial time. Finally, we also examine the model of lazy voters, in which a voter may choose to abstain from the election. We establish convergence of the iterative process, albeit not necessarily to a Nash equilibrium. As in the case with truth bias, we also provide a polynomial time algorithm to find all the attainable equilibria.

Rewriting-based approaches for answering queries over an OWL 2 DL ontology have so far been developed mainly for Horn fragments of OWL 2 DL. In this paper, we study the possibilities of answering queries over non-Horn ontologies using datalog rewritings. We prove that this is impossible in general even for very simple ontology languages, and even if PTIME = NP. Furthermore, we present a resolution-based procedure for SHI ontologies that, in case it terminates, produces a datalog rewriting of the ontology. We also show that our procedure necessarily terminates on DL-Lite Bool H,+ ontologies — an extension of OWL 2 QL with transitive roles and Boolean connectives.

Query rewriting is a prominent reasoning technique in ontology-based data access applications. A wide variety of query rewriting algorithms have been proposed in recent years and implemented in highly optimised reasoning systems. Query rewriting systems are complex software programs; even if based on provably correct algorithms, sophisticated optimisations make the systems more complex and errors become more likely to happen. In this paper, we present an algorithm that, given an ontology as input, synthetically generates ``relevant'' test queries. Intuitively, each of these queries can be used to verify whether the system correctly performs a certain set of ``inferences'', each of which can be traced back to axioms in the input ontology. Furthermore, we present techniques that allow us to determine whether a system is unsound and/or incomplete for a given test query and ontology. Our evaluation shows that most publicly available query rewriting systems are unsound and/or incomplete, even on commonly used benchmark ontologies; more importantly, our techniques revealed the precise causes of their correctness issues and the systems were then corrected based on our feedback. Finally, since our evaluation is based on a larger set of test queries than existing benchmarks, which are based on hand-crafted queries, it also provides a better understanding of the scalability behaviour of each system.

In this paper we propose a research agenda on the use of information markets as tools to collect, aggregate and analyze citizens’ opinions, expectations and preferences from social media in order to support public policy design and implementation. We argue that markets are institutional settings able to efficiently allocate scarce resources, aggregate and disseminate information into prices and accommodate hedging against various types of risks. We discuss various types of information markets, as well as address the participation of both human and computational agents in such markets.