Davide Grossi, Sanjay Modgil
The paper develops a formal theory of the degree of justification of arguments, which relies solely on the structure of an argumentation framework, and which can be successfully interfaced with approaches to instantiated argumentation. The theory is developed in three steps. First, the paper introduces a graded generalization of the two key notions underpinning Dung's semantics: self-defense and conflict-freeness. This leads to a natural generalization of Dung's semantics, whereby standard extensions are weakened or strengthened depending on the level of self-defense and conflict-freeness they meet. The paper investigates the fixpoint theory of these semantics, establishing existence results for them. Second, the paper shows how graded semantics readily provide an approach to argument rankings, offering a novel contribution to the recently growing research programme on ranking-based semantics. Third, this novel approach to argument ranking is applied and studied in the context of instantiated argumentation frameworks, and in so doing is shown to account for a simple form of accrual of arguments within the Dung paradigm. Finally, the theory is compared in detail with existing approaches.
Jonas Stein, Shannon Cruz, Davide Grossi, Martina Testori
A core tenet underpinning the conception of contemporary information networks, such as social media platforms, is that users should not be constrained in the amount of information they can freely and willingly exchange with one another about a given topic. By means of a computational agent-based model, we show how even in groups of truth-seeking and cooperative agents with perfect information-processing abilities, unconstrained information exchange may lead to detrimental effects on the correctness of the group's beliefs. If unconstrained information exchange can be detrimental even among such idealized agents, it is prudent to assume it can also be so in practice. We therefore argue that constraints on information flow should be carefully considered in the design of communication networks with substantial societal impact, such as social media platforms.
Davide Grossi, Ulrike Hahn, Michael Mäs, Andreas Nitsche, Jan Behrens, Niclas Boehmer, Markus Brill, Ulle Endriss, Umberto Grandi, Adrian Haret, Jobst Heitzig, Nicolien Janssens, Catholijn M. Jonker, Marijn A. Keijzer, Axel Kistner, Martin Lackner, Alexandra Lieben, Anna Mikhaylovskaya, Pradeep K. Murukannaiah, Carlo Proietti, Manon Revel, Élise Rouméas, Ehud Shapiro, Gogulapati Sreedurga, Björn Swierczek, Nimrod Talmon, Paolo Turrini, Zoi Terzopoulou, Frederik Van De Putte
This white paper outlines a long-term scientific vision for the development of digital-democracy technology. We contend that if digital democracy is to meet the ambition of enabling a participatory renewal in our societies, then a comprehensive multi-methods research effort is required that could, over the years, support its development in a democratically principled, empirically and computationally informed way. The paper is co-authored by an international and interdisciplinary team of researchers and arose from the Lorentz Center Workshop on ``Algorithmic Technology for Democracy'' (Leiden, October 2022).
Krzysztof R. Apt, Davide Grossi, Wiebe van der Hoek
We provide an in-depth study of the knowledge-theoretic aspects of communication in so-called gossip protocols. Pairs of agents communicate by means of calls in order to spread information---so-called secrets---within the group. Depending on the nature of such calls knowledge spreads in different ways within the group. Systematizing existing literature, we identify 18 different types of communication, and model their epistemic effects through corresponding indistinguishability relations. We then provide a classification of these relations and show its usefulness for an epistemic analysis in presence of different communication types. Finally, we explain how to formalise the assumption that the agents have common knowledge of a distributed epistemic gossip protocol.
Nicolo' Brandizzi, Davide Grossi, Luca Iocchi
This paper focuses on the emergence of communication to support cooperation in environments modeled as social deduction games (SDG), that are games where players communicate freely to deduce each others' hidden intentions. We first state the problem by giving a general formalization of SDG and a possible solution framework based on reinforcement learning. Next, we focus on a specific SDG, known as The Werewolf, and study if and how various forms of communication influence the outcome of the game. Experimental results show that introducing a communication signal greatly increases the winning chances of a class of players. We also study the effect of the signal's length and range on the overall performance showing a non-linear relationship.
Barbera de Mol, Davide Barbieri, Jan Viebahn, Davide Grossi
Power grid operation is becoming more complex due to the increase in generation of renewable energy. The recent series of Learning To Run a Power Network (L2RPN) competitions have encouraged the use of artificial agents to assist human dispatchers in operating power grids. However, the combinatorial nature of the action space poses a challenge to both conventional optimizers and learned controllers. Action space factorization, which breaks down decision-making into smaller sub-tasks, is one approach to tackle the curse of dimensionality. In this study, we propose a centrally coordinated multi-agent (CCMA) architecture for action space factorization. In this approach, regional agents propose actions and subsequently a coordinating agent selects the final action. We investigate several implementations of the CCMA architecture, and benchmark in different experimental settings against various L2RPN baseline approaches. The CCMA architecture exhibits higher sample efficiency and superior final performance than the baseline approaches. The results suggest high potential of the CCMA approach for further application in higher-dimensional L2RPN as well as real-world power grid settings.
Maaike Venema-Los, Zoé Christoff, Davide Grossi
Limited Voting (LV) is an approval-based method for multi-winner elections where all ballots are required to have a same fixed size. While it appears to be used as voting method in corporate governance and has some political applications, to the best of our knowledge, no formal analysis of the rule exists to date. We provide such an analysis here, prompted by a request for advice about this voting rule by a health insurance company in the Netherlands, which uses it to elect its work council. We study conditions under which LV would improve representation over standard approval voting and when it would not. We establish the extent of such an improvement, or lack thereof, both in terms of diversity and proportionality notions. These results help us understand if, and how, LV may be used as a low-effort fix of approval voting in order to enhance representation.
Agneau Belanyek, Davide Grossi, Wiebe van der Hoek
The paper reports on some results concerning Aqvist's dyadic logic known as system G, which is one of the most influential logics for reasoning with dyadic obligations ("it ought to be the case that ... if it is the case that ..."). Although this logic has been known in the literature for a while, many of its properties still await in-depth consideration. In this short paper we show: that any formula in system G including nested modal operators is equivalent to some formula with no nesting; that the universal modality introduced by Aqvist in the first presentation of the system is definable in terms of the deontic modality.
Nicole Orzan, Erman Acar, Davide Grossi, Roxana Rădulescu
Understanding the emergence of cooperation in systems of computational agents is crucial for the development of effective cooperative AI. Interaction among individuals in real-world settings are often sparse and occur within a broad spectrum of incentives, which often are only partially known. In this work, we explore how cooperation can arise among reinforcement learning agents in scenarios characterised by infrequent encounters, and where agents face uncertainty about the alignment of their incentives with those of others. To do so, we train the agents under a wide spectrum of environments ranging from fully competitive, to fully cooperative, to mixed-motives. Under this type of uncertainty we study the effects of mechanisms, such as reputation and intrinsic rewards, that have been proposed in the literature to foster cooperation in mixed-motives environments. Our findings show that uncertainty substantially lowers the agents' ability to engage in cooperative behaviour, when that would be the best course of action. In this scenario, the use of effective reputation mechanisms and intrinsic rewards boosts the agents' capability to act nearly-optimally in cooperative environments, while greatly enhancing cooperation in mixed-motive environments as well.
Yuzhe Zhang, Davide Grossi
The paper develops a theory of power for delegable proxy voting systems. We define a power index able to measure the influence of both voters and delegators. Using this index, which we characterize axiomatically, we extend an earlier game-theoretic model by incorporating power-seeking behavior by agents. We analytically study the existence of pure strategy Nash equilibria in such a model. Finally, by means of simulations, we study the effect of relevant parameters on the emergence of power inequalities in the model.
Ben Abramowitz, Edith Elkind, Davide Grossi, Ehud Shapiro, Nimrod Talmon
Any community in which membership is optional may eventually break apart, or fork. For example, forks may occur in political parties, business partnerships, social groups, cryptocurrencies, and federated governing bodies. Forking is typically the product of informal social processes or the organized action of an aggrieved minority, and it is not always amicable. Forks usually come at a cost, and can be seen as consequences of collective decisions that destabilize the community. Here, we provide a social choice setting in which agents can report preferences not only over a set of alternatives, but also over the possible forks that may occur in the face of disagreement. We study this social choice setting, concentrating on stability issues and concerns of strategic agent behavior.
Edith Elkind, Davide Grossi, Ehud Shapiro, Nimrod Talmon
We study a setting in which a community wishes to identify a strongly supported proposal from a space of alternatives, in order to change the status quo. We describe a deliberation process in which agents dynamically form coalitions around proposals that they prefer over the status quo. We formulate conditions on the space of proposals and on the ways in which coalitions are formed that guarantee deliberation to succeed, that is, to terminate by identifying a proposal with the largest possible support. Our results provide theoretical foundations for the analysis of deliberative processes such as the ones that take place in online systems for democratic deliberation support.
Daan Bloembergen, Davide Grossi, Martin Lackner
Liquid democracy is a proxy voting method where proxies are delegable. We propose and study a game-theoretic model of liquid democracy to address the following question: when is it rational for a voter to delegate her vote? We study the existence of pure-strategy Nash equilibria in this model, and how group accuracy is affected by them. We complement these theoretical results by means of agent-based simulations to study the effects of delegations on group's accuracy on variously structured social networks.
Feline Lindeboom, Martijn Brehm, Davide Grossi, Pradeep Murukannaiah
We study diversity in approval-based committee elections with incomplete or inaccurate information. We define diversity according to the Maximum Coverage problem, which is known to be \textsc{np}-complete, with a best attainable polynomial time approximation ratio of $1-1/\e$. In the incomplete information setting, voters vote only on a small portion of the candidates, and we prove that getting arbitrarily close to the optimal approximation ratio w.h.p. requires $Ω(m^2)$ non-adaptive queries, where $m$ is the number of candidates. This motivates studying adaptive querying algorithms, that can adapt their querying strategy to information obtained from previous query outcomes. In that setting, we lower this bound to only $Ω(m)$ queries. We propose a greedy algorithm to match this lower bound up to log-factors. We prove the same $\tildeΘ(m)$ bound for the generalized problem of Max Cover over a matroid constraint, using a local search algorithm. Specifying a matroid of valid committees lets us implement extra structural requirements on the committee, like quota. In the inaccurate information setting, voters' responses are corrupted with a small probability. We prove $\tildeΘ(nm)$ queries are required to attain a $(1-1/\e)$-approximation with high probability, where $n$ is the number of voters. While the proven bounds show that all our algorithms are viable asymptotically, they also show that some of them would still require large numbers of queries in instances of practical relevance. Using real data from Polis as well as synthetic data, we observe that our algorithms perform well also on smaller instances, both with incomplete and inaccurate information.
Andrea Bracciali, Davide Grossi, Ronald de Haan
Decentralisation is one of the promises introduced by blockchain technologies: fair and secure interaction amongst peers with no dominant positions, single points of failure or censorship. Decentralisation, however, appears difficult to be formally defined, possibly a continuum property of systems that can be more or less decentralised, or can tend to decentralisation in their lifetime. In this paper we focus on decentralisation in quorum-based approaches to open (permissionless) consensus as illustrated in influential protocols such as the Ripple and Stellar protocols. Drawing from game theory and computational complexity, we establish limiting results concerning the decentralisation vs. safety trade-off in Ripple and Stellar, and we propose a novel methodology to formalise and quantitatively analyse decentralisation in this type of blockchains.
Davide Grossi
One of the most innovative aspects of blockchain technology consists in the introduction of an incentive layer to regulate the behavior of distributed protocols. The designer of a blockchain system faces therefore issues that are akin to those relevant for the design of economic mechanisms, and faces them in a computational setting. From this perspective the present paper argues for the importance of computational social choice in blockchain research. It identifies a few challenges at the interface of the two fields that illustrate the strong potential for cross-fertilization between them.
Yuzhe Zhang, Davide Grossi
We study wisdom of the crowd effects in liquid democracy when agents are allowed to apportion weights to proxies by mixing their delegations. We show that in this setting -- unlike in the standard one where votes are always delegated in full to one proxy -- it becomes possible to identify delegation structures that optimize the truth-tracking accuracy of the group. We contrast this centralized solution with the group accuracy obtained in equilibrium when agents interact by greedily trying to maximize their own individual accuracy through mixed delegations, and study the price of anarchy of these games. While equilibria with mixed delegations may be as bad as in the standard delegations setting, they are never worse and may sometimes be better.
Davide Grossi
These lecture notes have been developed for the course Computational Social Choice of the Artificial Intelligence MSc programme at the University of Groningen. They cover mathematical and algorithmic aspects of voting theory.
Zoé Christoff, Davide Grossi
The paper proposes an analysis of liquid democracy (or, delegable proxy voting) from the perspective of binary aggregation and of binary diffusion models. We show how liquid democracy on binary issues can be embedded into the framework of binary aggregation with abstentions, enabling the transfer of known results about the latter---such as impossibility theorems---to the former. This embedding also sheds light on the relation between delegation cycles in liquid democracy and the probability of collective abstentions, as well as the issue of individual rationality in a delegable proxy voting setting. We then show how liquid democracy on binary issues can be modeled and analyzed also as a specific process of dynamics of binary opinions on networks. These processes---called Boolean DeGroot processes---are a special case of the DeGroot stochastic model of opinion diffusion. We establish the convergence conditions of such processes and show they provide some novel insights on how the effects of delegation cycles and individual rationality could be mitigated within liquid democracy. The study is a first attempt to provide theoretical foundations to the delgable proxy features of the liquid democracy voting system. Our analysis suggests recommendations on how the system may be modified to make it more resilient with respect to the handling of delegation cycles and of inconsistent majorities.
Stéphane Airiau, Nicholas Kees Dupuis, Davide Grossi
The paper studies information markets concerning single events from an epistemic social choice perspective. Within the classical Condorcet error model for collective binary decisions, we establish equivalence results between elections and markets, showing that the alternative that would be selected by weighted majority voting (under specific weighting schemes) corresponds to the alternative with highest price in the equilibrium of the market (under specific assumptions on the market type). This makes it possible in principle to implement specific weighted majority elections, which are known to have superior truth-tracking performance, by means of information markets without needing to elicit voters' competences.