Umberto Grandi

Graph Aggregation

Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of situations, e.g., when applying a voting rule (graphs as preference orders), when consolidating conflicting views regarding the relationships between arguments in a debate (graphs as abstract argumentation frameworks), or when computing a consensus between several alternative clusterings of a given dataset (graphs as equivalence relations). Other potential applications include belief merging, data integration, and social network analysis. In this short paper, we review a recently introduced formal framework for graph aggregation that is grounded in social choice theory. Our focus is on understanding which properties shared by the individual input graphs will transfer to the output graph returned by a given aggregation rule. Our main result is a powerful impossibility theorem that generalises Arrows seminal result regarding the aggregation of preference orders to a large collection of different types of graphs. We also provide a discussion of existing and potential applications of graph aggregation.

A Borda count for collective sentiment analysis

Sentiment analysis assigns a positive, negative or neutral polarity to an item or entity, extracting and aggregating individual opinions from their textual expressions by means of natural language processing tools. In this paper we observe that current sentiment analysis techniques are satisfactory in case there is a single entity under consideration, but can lead to inaccurate or wrong results when dealing with a set of multiple items. We argue in favor of importing techniques from voting theory and preference aggregation to provide a more accurate definition of the collective sentiment over a set of multiple items. We propose a notion of Borda count which combines individuals’ sentiment with comparative preference information, we show that this class of rules satisfies a number of properties which have a natural interpretation in the sentiment analysis domain, and we evaluate its behavior when faced with highly incomplete domains.

Goal-Based Collective Decisions: Axiomatics and Computational Complexity

We study agents expressing propositional goals over a set of binary issues to reach a collective decision. We adapt properties and rules from the literature on Social Choice Theory to our setting, providing an axiomatic characterisation of a majority rule for goal-based voting. We study the computational complexity of finding the outcome of our rules (i.e., winner determination), showing that it ranges from Nondeterministic Polynomial Time (NP) to Probabilistic Polynomial Time (PP).

Judgment aggregation in dynamic logic of propositional assignments

Judgment aggregation models a group of agents having to collectively decide over a number of logically interconnected issues starting from their individual opinions. In recent years, a growing literature has focused on the design of logical systems for social choice theory, and for judgment aggregation in particular, making use of logical languages designed ad hoc for this purpose. In this paper we deploy the existing formalism of Dynamic Logic of Propositional Assignments (DL-PA), an instance of Propositional Dynamic Logic where atomic programs affect propositional valuations. We show that DL-PA is a well-suited formalism for modeling the aggregation of binary judgments from multiple agents, by providing logical equivalences in DL-PA for some of the best-known aggregation procedures, desirable axioms coming from the literature on judgment aggregation and properties for the safety of the agenda problem.

Relaxing Exclusive Control in Boolean Games.

In the typical framework for boolean games (BG) each player can change the truth value of some propositional atoms, while attempting to make her goal true. In standard BG goals are propositional formulas, whereas in iterated BG goals are formulas of Linear Temporal Logic. Both notions of BG are characterised by the fact that agents have exclusive control over their set of atoms, meaning that no two agents can control the same atom. In the present contribution we drop the exclusivity assumption and explore structures where an atom can be controlled by multiple agents. We introduce Concurrent Game Structures with Shared Propositional Control (CGS-SPC) and show that they account for several classes of repeated games, including iterated boolean games, influence games, and aggregation games. Our main result shows that, as far as verification is concerned, CGS-SPC can be reduced to concurrent game structures with exclusive control. This result provides a polynomial reduction for the model checking problem of specifications in Alternating-time Temporal Logic on CGS-SPC.

Learning Agents for Iterative Voting

This paper assesses the learning capabilities of agents in a situation of collective choice. Each agent is endowed with a private preference concerning a number of alternative candidates, and participates in an iterated plurality election. Agents get rewards depending on the winner of each election, and adjust their voting strategy using reinforcement learning. By conducting extensive simulations, we show that our agents are capable of learning how to take decisions at the level of well-known voting procedures, and that these decisions maintain good choice-theoretic properties when increasing the number of agents or candidates.