Umberto Grandi

Umberto Grandi, Emiliano Lorini, Timothy Parker et al.

In this paper we propose a framework for ethical decision making in the context of planning, with intended application to robotics. We put forward a compact but highly expressive language for ethical planning that combines linear temporal logic with lexicographic preference modelling. This original combination allows us to assess plans both with respect to an agent's values and their desires, introducing the novel concept of the morality level of an agent and moving towards multigoal, multivalue planning. We initiate the study of computational complexity of planning tasks in our setting, and we discuss potential applications to robotics.

Timothy Parker, Umberto Grandi, Emiliano Lorini

Responsibility anticipation is the process of determining if the actions of an individual agent may cause it to be responsible for a particular outcome. This can be used in a multi-agent planning setting to allow agents to anticipate responsibility in the plans they consider. The planning setting in this paper includes partial information regarding the initial state and considers formulas in linear temporal logic as positive or negative outcomes to be attained or avoided. We firstly define attribution for notions of active, passive and contributive responsibility, and consider their agentive variants. We then use these to define the notion of responsibility anticipation. We prove that our notions of anticipated responsibility can be used to coordinate agents in a planning setting and give complexity results for our model, discussing equivalence with classical planning. We also present an outline for solving some of our attribution and anticipation problems using PDDL solvers.

Rachael Colley, Umberto Grandi, César Hidalgo et al.

In rank aggregation, members of a population rank issues to decide which are collectively preferred. We focus instead on identifying divisive issues that express disagreements among the preferences of individuals. We analyse the properties of our divisiveness measures and their relation to existing notions of polarisation. We also study their robustness under incomplete preferences and algorithms for control and manipulation of divisiveness. Our results advance our understanding of how to quantify disagreements in collective decision-making.

Clément Contet, Umberto Grandi, Jérôme Mengin

We view voting rules as classifiers that assign a winner (a class) to a profile of voters' preferences (an instance). We propose to apply techniques from formal explainability, most notably abductive and contrastive explanations, to identify minimal subsets of a preference profile that either imply the current winner or explain why a different candidate was not elected. Formal explanations turn out to have strong connections with classical problems studied in computational social choice such as bribery, possible and necessary winner identification, and preference learning. We design algorithms for computing abductive and contrastive explanations for scoring rules. For the Borda rule, we find a lower bound on the size of the smallest abductive explanations, and we conduct simulations to identify correlations between properties of preference profiles and the size of their smallest abductive explanations.

Mohamed Ouaguenouni, Felipe Garrido-Lucero, Umberto Grandi et al.

We analyze the structure of the disagreement among a population of voters over a set of alternatives. Surveys typically ask either for pairwise comparisons, simple and intuitive for participants, or full rankings over alternatives, eliciting the entire voters' preferences. Building on the observation that pairwise comparisons cannot distinguish structural disagreement from noise, we propose a stratified framework to identify the minimal aggregated preference information needed to compute a number of disagreement measures from the literature. Specifically, we introduce the plurality matrix, a generalization of pairwise comparisons that records, for every subset $S$ of alternatives, the probability that each $a \in S$ ranks first in $S$. We define the level of a disagreement measure as the smallest subset size needed to express it, showing that many existing notions, including rank-variance and divisiveness, sit at level $3$, proving that pairwise comparisons are not enough. In addition, we demonstrate the interest of going beyond level $3$ both theoretically and experimentally. To make these results actionable, we design two elicitation protocols to estimate the plurality matrix, exploring the trade-off between the number of required participants and the cognitive load requested to each of them.

Emile Martinez, Felipe Garrido-Lucero, Umberto Grandi et al.

We introduce the \textit{prophet inequality with uncertain acceptance} model, in which a decision maker sequentially observes a sequence of independent options, each characterized by a value $x_i$ and an acceptance probability $p_i$, both sampled from a known joint distribution. At time $i$, the decision maker observes the value $x_i$ and must irrevocably and immediately decide whether to attempt to select it or to continue to the next time step. If the option is selected, the process terminates with probability $p_i$ and the decision maker obtains $x_i$; otherwise, she continues searching. In this setting, two natural benchmarks arise: the \textit{value-aware decision-maker}, who knows all value realizations in advance but not the acceptance outcomes, and the \textit{full-knowledge prophet}, who knows all realizations beforehand and can choose the best option among those that will be accepted. We characterize the worst-case competitive ratios between our defined agents and show that all these values equal $1/2$. In addition, we provide sufficient conditions under which the value-aware decision-maker surpasses the $1/2$-barrier against the more informed prophet. This demonstrates the (crucial) interest for the decision maker to improve her knowledge over the values rather than over the acceptances, and is obtained via a more general result that reduces the value-aware decision-maker's problem to a classical prophet inequality with scaled Bernoulli distributions, followed by a sequence of transformations that further reduce the problem to a unique optimization problem.

Clément Contet, Umberto Grandi, Jérôme Mengin

Tournaments are widely used models to represent pairwise dominance between candidates, alternatives, or teams. We study the problem of providing certified explanations for why a candidate appears among the winners under various tournament rules. To this end, we identify minimal supports, minimal sub-tournaments in which the candidate is guaranteed to win regardless of how the rest of the tournament is completed (that is, the candidate is a necessary winner of the sub-tournament). This notion corresponds to an abductive explanation for the question,"Why does the winner win the tournament", a central concept in formal explainable AI. We focus on common tournament solutions: the top cycle, the uncovered set, the Copeland rule, the Borda rule, the maximin rule, and the weighted uncovered set. For each rule we determine the size of the smallest minimal supports, and we present polynomial-time algorithms to compute them for all but the weighted uncovered set, for which the problem is NP-complete. Finally, we show how minimal supports can serve to produce compact, certified, and intuitive explanations.

Juan Zambrano, Clément Contet, Jairo Gudiño et al.

Participatory Budgeting (PB) empowers citizens to propose and vote on public investment projects. Yet, despite its democratic potential, PB initiatives often suffer from low participation rates, limiting their visibility and perceived legitimacy. In this work, we aim to strengthen PB elections in two key ways: by supporting project proposers in crafting better proposals, and by helping PB organizers manage large volumes of submissions in a transparent manner. We propose a privacy-preserving approach to predict which PB proposals are likely to be funded, using only their textual descriptions and anonymous historical voting records -- without relying on voter demographics or personally identifiable information. We evaluate the performance of GPT 4 Turbo in forecasting proposal outcomes across varying contextual scenarios, observing that the LLM's prior knowledge needs to be complemented by past voting data to obtain predictions reflecting real-world PB voting behavior. Our findings highlight the potential of AI-driven tools to support PB processes by improving transparency, planning efficiency, and civic engagement.

Timothy Parker, Umberto Grandi, Emiliano Lorini

Responsibility is a key notion in multi-agent systems and in creating safe, reliable and ethical AI. However, most previous work on responsibility has only considered responsibility for single outcomes. In this paper we present a model for responsibility attribution in a multi-agent, multi-value setting. We also expand our model to cover responsibility anticipation, demonstrating how considerations of responsibility can help an agent to select strategies that are in line with its values. In particular we show that non-dominated regret-minimising strategies reliably minimise an agent's expected degree of responsibility.

Jairo Gudiño-Rosero, Umberto Grandi, César A. Hidalgo

We explore an augmented democracy system built on off-the-shelf LLMs fine-tuned to augment data on citizen's preferences elicited over policies extracted from the government programs of the two main candidates of Brazil's 2022 presidential election. We use a train-test cross-validation setup to estimate the accuracy with which the LLMs predict both: a subject's individual political choices and the aggregate preferences of the full sample of participants. At the individual level, we find that LLMs predict out of sample preferences more accurately than a "bundle rule", which would assume that citizens always vote for the proposals of the candidate aligned with their self-reported political orientation. At the population level, we show that a probabilistic sample augmented by an LLM provides a more accurate estimate of the aggregate preferences of a population than the non-augmented probabilistic sample alone. Together, these results indicates that policy preference data augmented using LLMs can capture nuances that transcend party lines and represents a promising avenue of research for data augmentation.

Linus Boes, Rachael Colley, Umberto Grandi et al.

Many important collective decision-making problems can be seen as multi-agent versions of discrete optimisation problems. Participatory budgeting, for instance, is the collective version of the knapsack problem; other examples include collective scheduling, and collective spanning trees. Rather than developing a specific model, as well as specific algorithmic techniques, for each of these problems, we propose to represent and solve them in the unifying framework of judgment aggregation with weighted issues. We provide a modular definition of collective discrete optimisation (CDO) rules based on coupling a set scoring function with an operator, and we show how they generalise several existing procedures developed for specific CDO problems. We also give an implementation based on integer linear programming (ILP) and test it on the problem of collective spanning trees.

Rachael Colley, Umberto Grandi, Arianna Novaro

We introduce a voting model with multi-agent ranked delegations. This model generalises liquid democracy in two aspects: first, an agent's delegation can use the votes of multiple other agents to determine their own -- for instance, an agent's vote may correspond to the majority outcome of the votes of a trusted group of agents; second, agents can submit a ranking over multiple delegations, so that a backup delegation can be used when their preferred delegations are involved in cycles. The main focus of this paper is the study of unravelling procedures that transform the delegation ballots received from the agents into a profile of direct votes, from which a winning alternative can then be determined by using a standard voting rule. We propose and study six such unravelling procedures, two based on optimisation and four using a greedy approach. We study both algorithmic and axiomatic properties, as well as related computational complexity problems of our unravelling procedures for different restrictions on the types of ballots that the agents can submit.

Grzegorz Lisowski, Sylvie Doutre, Umberto Grandi

Value-based argumentation enhances a classical abstract argumentation graph - in which arguments are modelled as nodes connected by directed arrows called attacks - with labels on arguments, called values, and an ordering on values, called audience, to provide a more fine-grained justification of the attack relation. With more than one agent facing such an argumentation problem, agents may differ in their ranking of values. When needing to reach a collective view, such agents face a dilemma between two equally justifiable approaches: aggregating their views at the level of values, or aggregating their attack relations, remaining therefore at the level of the graphs. We explore the strenghts and limitations of both approaches, employing techniques from preference aggregation and graph aggregation, and propose a third possibility aggregating rankings extracted from given attack relations.

Francesco Belardinelli, Umberto Grandi

Knowledge can be represented compactly in multiple ways, from a set of propositional formulas, to a Kripke model, to a database. In this paper we study the aggregation of information coming from multiple sources, each source submitting a database modelled as a first-order relational structure. In the presence of integrity constraints, we identify classes of aggregators that respect them in the aggregated database, provided these are satisfied in all individual databases. We also characterise languages for first-order queries on which the answer to a query on the aggregated database coincides with the aggregation of the answers to the query obtained on each individual database. This contribution is meant to be a first step on the application of techniques from social choice theory to knowledge representation in databases.

Umberto Grandi

Direct democracy is often proposed as a possible solution to the 21st-century problems of democracy. However, this suggestion clashes with the size and complexity of 21st-century societies, entailing an excessive cognitive burden on voters, who would have to submit informed opinions on an excessive number of issues. In this paper I argue for the development of voting avatars, autonomous agents debating and voting on behalf of each citizen. Theoretical research from artificial intelligence, and in particular multiagent systems and computational social choice, proposes 21st-century techniques for this purpose, from the compact representation of a voter's preferences and values, to the development of voting procedures for autonomous agents use only.

Francesco Belardinelli, Umberto Grandi, Andreas Herzig et al.

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 ac- count 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.

Ulle Endriss, Umberto Grandi

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). In this paper, we introduce a formal framework for graph aggregation 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. We consider both common properties of graphs, such as transitivity and reflexivity, and arbitrary properties expressible in certain fragments of modal logic. Our results establish several connections between the types of properties preserved under aggregation and the choice-theoretic axioms satisfied by the rules used. The most important of these results is a powerful impossibility theorem that generalises Arrow's seminal result for the aggregation of preference orders to a large collection of different types of graphs.

Umberto Grandi, Emiliano Lorini, Laurent Perrussel

We study the strategic aspects of social influence in a society of agents linked by a trust network, introducing a new class of games called games of influence. A game of influence is an infinite repeated game with incomplete information in which, at each stage of interaction, an agent can make her opinions visible (public) or invisible (private) in order to influence other agents' opinions. The influence process is mediated by a trust network, as we assume that the opinion of a given agent is only affected by the opinions of those agents that she considers trustworthy (i.e., the agents in the trust network that are directly linked to her). Each agent is endowed with a goal, expressed in a suitable temporal language inspired from linear temporal logic (LTL). We show that games of influence provide a simple abstraction to explore the effects of the trust network structure on the agents' behaviour, by considering solution concepts from game-theory such as Nash equilibrium, weak dominance and winning strategies.

Umberto Grandi, Andrea Loreggia, Francesca Rossi et al.

In collective decision making, where a voting rule is used to take a collective decision among a group of agents, manipulation by one or more agents is usually considered negative behavior to be avoided, or at least to be made computationally difficult for the agents to perform. However, there are scenarios in which a restricted form of manipulation can instead be beneficial. In this paper we consider the iterative version of several voting rules, where at each step one agent is allowed to manipulate by modifying his ballot according to a set of restricted manipulation moves which are computationally easy and require little information to be performed. We prove convergence of iterative voting rules when restricted manipulation is allowed, and we present experiments showing that most iterative voting rules have a higher Condorcet efficiency than their non-iterative version.