arXiv subjects
Publications and source records attributed to Davide Grossi.
We contribute to the programme of lifting proportionality axioms from the multi-winner voting setting to participatory budgeting. We define novel proportionality axioms for participatory budgeting and test them on known proportionality-driven rules such as Phragmén and Rule X. We investigate logical implications among old and new axioms and provide a systematic overview of proportionality criteria in participatory budgeting.
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.
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.
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.
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.
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.
This paper introduces the notion of `commonly knowing whether', a non-standard version of standard common knowledge which is defined on the basis of `knowing whether', instead of standard `knowing that'. After giving five possible definitions of this notion, we explore the logical relations among them in the single-agent and multi-agent cases. We propose a sound and complete axiomatization. We investigate one of the five definitions in terms of expressivity via a strategy of modal comparison games.
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.
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.
The Poison Game is a two-player game played on a graph in which one player can influence which edges the other player is able to traverse. It operationalizes the notion of existence of credulously admissible sets in an argumentation framework or, in graph-theoretic terminology, the existence of non-trivial semi-kernels. We develop a modal logic (poison modal logic, PML) tailored to represent winning positions in such a game, thereby identifying the precise modal reasoning that underlies the notion of credulous admissibility in argumentation. We study model-theoretic and decidability properties of PML, and position it with respect to recently studied logics at the cross-road of modal logic, argumentation, and graph games.
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.
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.
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.
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.
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.
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.
We study voting games on binary issues, where voters hold an objective over the outcome of the collective decision and are allowed, before the vote takes place, to negotiate their voting strategy with the other participants. We analyse the voters' rational behaviour in the resulting two-phase game, showing under what conditions undesirable equilibria can be removed and desirable ones sustained as a consequence of the pre-vote phase.
Gossip protocols aim at arriving, by means of point-to-point or group communications, at a situation in which all the agents know each other's secrets. We consider distributed gossip protocols which are expressed by means of epistemic logic. We provide an operational semantics of such protocols and set up an appropriate framework to argue about their correctness. Then we analyze specific protocols for complete graphs and for directed rings.