Convergence of Opinion Diffusion is PSPACE-complete

We analyse opinion diffusion in social networks, where a finite set of individuals is connected in a directed graph and each simultaneously changes their opinion to that of the majority of their influencers. We study the algorithmic properties of the fixed-point behaviour of such networks, showing that the problem of establishing whether individuals converge to stable opinions is PSPACE-complete

Binary Voting with Delegable Proxy: An Analysis of Liquid Democracy

The paper provides an analysis of the voting method known as delegable proxy voting, or liquid democracy. The analysis first positions liquid democracy within the theory of binary aggregation. It then focuses on two issues of the system: the occurrence of delegation cycles; and the effect of delegations on individual rationality when voting on logically interdependent propositions. It finally points to proposals on how the system may be modified in order to address the above issues

Iterative social consolidations:Forming beliefs from many-valued evidence and peers' opinions

Recently, several logics modelling evidence have been proposed in the literature. These logics often also feature beliefs. We call the process or function that maps evidence to beliefs consolidation. In this paper, we use a four-valued modal logic of evidence as a basis. In the models for this logic, agents are represented by nodes, peer connections by edges and the private evidence that each agent has by a four-valued valuation. From this basis, we propose methods of consolidating the beliefs of the agents, taking into account both their private evidence as well as their peers' opinions. To this end, beliefs are computed iteratively. The final consolidated beliefs are the ones in the point of stabilization of the model. However, it turns out that some consolidation policies will not stabilize for certain models. Finding the conditions for stabilization is one of the main problems studied here, along with other properties of such consolidations. Our main contributions are twofold: we offer a new dynamic perspective on the process of forming evidence-based beliefs, in the context of evidence logics, and we set up and address some mathematically challenging problems, which are related to graph theory and practical subject areas such as belief/opinion diffusion and contagion in multi-agent networks.</p

Detecting bots with temporal logic

Social bots are computer programs that act like human users on social media platforms. Social bot detection is a rapidly growing field dominated by machine learning approaches. In this paper, we propose a complementary method to machine learning by exploring bot detection as a model checking problem. We introduce Temporal Network Logic (TNL) which we use to specify social networks where agents can post and follow each other. Using this logic, we formalize different types of social bot behavior with formulas that are satisfied in a model of a network with bots. We also consider an extension of the logic where we explore the expressive power of including elements from hybrid logic in our framework. We give model checking algorithms for TNL and its hybrid extension, and show that the complexity of the former is in P and the latter in PSPACE.publishedVersio

Aggregazione di giudizi

L’aggregazione di opinioni individuali per formare una decisione collettiva è l’oggetto di studio di Judgment Aggregation, una disciplina che coinvolge logica, economia, filosofia politica ed informatica. Il problema della presa di decisione collettiva a partire da posizioni individuali è comune nella vita di tutti i giorni e, sebbene la procedura da seguire sembri evidente, i risultati possono nascondere paradossi sorprendenti. La formalizzazione del problema dell’aggregazione di giudizi individuali ha permesso di portare un buon numero di risposte, di evidenziare legami con la teoria della scelta sociale e l’aggregazione di credenze, e di aprire la strada a nuove ricerche che permettono di applicare buona parte dei risultati ad altri paradigmi della decisione collettiva. Obiettivo di questo lavoro è di introdurre il problema dell’aggregazione di giudizi, motivare l’interesse per tali questioni, presentando i risultati principali ottenuti e indicando alcune delle piste di ricerca attuali.The aggregation of individual opinions to form a collective decision is the object of study of Judgment Aggregation, a discipline involving logic, economics, political philosophy and computer science. The problem of collective decision-making from individual positions arises in everyday life and, although the procedure to follow seems evident, the results can hide surprising paradoxes. The formalization of the problem of the aggregation of individual judgements has made it possible to bring a good number of answers, to highlight links with social choice theory and the aggregation of beliefs, and to pave the way to new research that allows to apply most of the results to other paradigms of collective decision-making. The aim of this work is to introduce the problem of judgement aggregation, to motivate interest in such issues, presenting the main results obtained so far and highlighting some of the current research tracks

Evidence-Based Beliefs in Many-Valued Modal Logics

Rational agents, humans or otherwise, build their beliefs from evidence – a process which we call consolidation. But how should this process be carried out? In this thesis, we study a multi-agent logic of evidence and the question how agents should form beliefs in this logic. The main contributions of this thesis are twofold. First, we present and study a many-valued modal logic, and show how it can be suitable for modelling multi-agent scenarios where each agent has access to some evidence, which in turn can be processed into beliefs. This is a technical and practical contribution to many-valued modal logics. Second, we open new paths for research in the field of evidence logics: we show a new approach based on many-valued logics, we highlight the concept of consolidations and the importance of looking at their dynamic nature, and build a methodology based on rationality postulates to evaluate them

An algorithmic analysis of deliberation and representation in collective behaviour

The selection of a nominee by a group of players in the process of selecting a winner is present in many contexts. In sports, it is a major strategic problem to select the best team members. Crucially, in politics, this problem is essential for the process of primaries. There, factions decide which of their candidates should take part in the elections. We study the strategic behaviour of coalitions from the game-theoretic perspective. More precisely, we analyse the existence of a pure Nash equilibrium in the games capturing the strategic nomination problem. First, we adapt the well-known Hotelling-Downs model, capturing the strategic behaviour of political parties in primaries. Subsequently, we explore this problem for tournament-based rules. There, winners are chosen based on the pairwise comparisons between candidates. First, we study the setting of knockout-tournaments. Next, we investigate tournaments, in which participants do not compete in rounds. For each of these mechanisms, we analyse the computational complexity of checking the existence of a pure Nash equilibrium. Nominee selection can also be influenced by the deliberation between the voters. To account for that, we investigate the complexity of checking the convergence of a synchronous, threshold-based protocol. There, in every time step all agents update their opinion if the strict majority of their influencers disagrees with them. Furthermore, we explore computational aspects of majority illusion. This phenomenon occurs when a large number of agents in a network perceives the opinion, which is a minority view, as the one which is held by the majority of agents. We study the problem of checking the possibility of assigning opinions to agents, so that it holds for a large fraction of them. We further address the complexity of checking the possibility of eliminating the majority illusion by changing a small number of edges in a social network