arXiv subjects

Umberto Grandi

Publications and source records attributed to Umberto Grandi.

At least 19 recordsLinked to original sources

arXiv2026

Characterizing Necessary Losers to Explain Tournaments Solutions

We study the problem of formally explaining why a candidate was not selected by a given tournament rule, by identifying sub-tournaments in which the candidate loses independently of how the rest of the tournament is completed. We define destructive minimal supports as any minimal sub-tournament satisfying this property, which in formal explainable artificial intelligence corresponds to abductive explanations for the question "Why does the loser lose the tournament?". For six common tournament solutions (maximin, uncovered set and its weighted variant, top cycle, Copeland, and Borda) we provide characterizations of when a candidate is either a necessary loser or a possible winner, we determine the size of the smallest destructive minimal supports, complemented by polynomial-time algorithms for their computation except for the case of Borda and Copeland rules which we conjecture to also be polynomial.

cs.AI↗

arXiv2026

Efficient Elicitation of Collective Disagreements

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.

cs.AI↗

arXiv2026

Prophet Inequalities with Delayed and Uncertain Acceptance

We introduce the prophet inequality with delayed and uncertain acceptance, a variant of the classical prophet inequality in which a decision-maker sequentially evaluates options whose acceptance is uncertain and whose outcome is revealed only after a fixed delay. That is, at each time step, the decision-maker observes the realized value of the arriving option and must irrevocably decide whether to attempt to select it or to continue searching. If an option is attempted to be selected, the process is suspended for a fixed delay $d$, during which no other options can be considered. Once the delay expires, the selection succeeds with a known probability. If successful, the decision-maker receives the realized value and the process terminates; otherwise, the search resumes. In addition to the online decision-maker, we consider two stronger benchmarks: the value-aware decision-maker, who knows all value realizations in advance but not the acceptance outcomes, and the prophet, who knows both the values and the acceptance realizations. We characterize the competitive ratios between the two decision-makers and the prophet, showing that each is lower bounded by $1/(d+2)$, and we construct instances demonstrating that these bounds are tight for two of the comparisons. In the extreme case of no delay ($d=0$), where our result recovers the classical $1/2$-competitive guarantee, we establish the tightness of the remaining competitive ratio and identify sufficient conditions under which the value-aware decision-maker can beat the $1/2$ barrier against the prophet. In particular, we show that this occurs whenever all acceptance probabilities are strictly positive, by reducing the problem to a classical prophet inequality instance over appropriately scaled Bernoulli random variables.

cs.GT↗

arXiv2025

Stability in Online Assignment Games

The assignment game models a housing market where buyers and sellers are matched, and transaction prices are set so that the resulting allocation is stable. Shapley and Shubik showed that every stable allocation is necessarily built on a maximum social welfare matching. In practice, however, stable allocations are rarely attainable, as matchings are often sub-optimal, particularly in online settings where eagents arrive sequentially to the market. In this paper, we introduce and compare two complementary measures of instability for allocations with sub-optimal matchings, establish their connections to the optimality ratio of the underlying matching, and use this framework to study the stability performances of randomized algorithms in online assignment games.

cs.GT↗

arXiv2025

Explaining Tournament Solutions with Minimal Supports

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 solutions except for 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 for tournament solutions.

cs.AI↗

arXiv2025

Algorithmic Shortlisting in Participatory Budgeting

Participatory budgeting is a democratic innovation that allows citizens to propose and vote on public investment projects. To help organizers manage large volumes of submissions, we design and test privacy-preserving methods for algorithmic shortlisting. These algorithms predict which projects are likely to be funded using only project features and anonymous historical voting data. We demonstrate the limitations of a naive approach that uses a large language model to rank projects based on past success and propose a vote-based pipeline that enables state-of-the-art LLMs to perform on par with classical machine learning. Our findings indicate that user preferences in participatory budgeting are stable enough to allow algorithmic shortlisting to approximate an initial selection of projects effectively.

cs.CY↗

arXiv2025

Prompt Injection Vulnerability of Consensus Generating Applications in Digital Democracy

Large Language Models (LLMs) are gaining traction as a method to generate consensus statements and aggregate preferences in digital democracy experiments. Yet, LLMs could introduce critical vulnerabilities in these systems. Here, we examine the vulnerability and robustness of off-the-shelf consensus-generating LLMs to prompt-injection attacks, in which texts are injected to amplify particular viewpoints, erase certain opinions, or divert consensus toward unrelated or irrelevant topics. We construct attack-free and adversarial variants of prompts containing public policy questions and opinion texts, classify opinion and consensus valences with a fine-tuned BERT model, and estimate LLM-human majority agreement rates. Across topics, default LLaMA 3.1 8B Instruct, GPT-4.1 Nano, and Apertus 8B exhibit widespread vulnerability, specially when disagreement and disagreement are finely balanced, for attacks that shift consensus toward positions aligned with GB-unionist conservative manifestos relative to pro-independence left manifestos, and for rational, instruction-like rhetorical strategies. A robustness pipeline combining GPT-OSS-SafeGuard injection detection, structured opinion representations, and GSPO-based reinforcement learning substantially reduces directional failures whenever the underlying consensus has a clear positive or negative valence. These findings advance our understanding of both the vulnerabilities and the potential defenses of consensus-generating LLMs in digital democracy applications.

cs.CY↗

arXiv2024

Responsibility in a Multi-Value Strategic Setting

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.

cs.AI↗

arXiv2024

Proportionality for Constrained Public Decisions

We study situations where a group of voters need to take a collective decision over a number of public issues, with the goal of getting a result that reflects the voters' opinions in a proportional manner. Our focus is on interconnected public decisions, where the outcome on one or more issues has repercussions on the acceptance or rejection of other issues in the agenda. We show that the adaptation of classical justified-representation axioms to this enriched setting are always satisfiable only for restricted classes of public agendas. We adapt well-known proportional decision rules to take the structure of the public agenda into account, and we show that they match justified-representation properties in approximation on a class of expressive constraints. We also identify another path to achieving proportionality on interconnected issues via an adaptation of the notion of priceability.

cs.GT↗

arXiv2024

Abductive and Contrastive Explanations for Scoring Rules in Voting

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.

cs.AI↗

arXiv2024

Large Language Models (LLMs) as Agents for Augmented Democracy

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.

cs.CY↗

arXiv2024

Enabling the Digital Democratic Revival: A Research Program for Digital Democracy

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).

cs.CY↗

arXiv2023

Understanding Political Divisiveness using Online Participation data from the 2022 French and Brazilian Presidential Elections

Digital technologies can augment civic participation by facilitating the expression of detailed political preferences. Yet, digital participation efforts often rely on methods optimized for elections involving a few candidates. Here we present data collected in an online experiment where participants built personalized government programs by combining policies proposed by the candidates of the 2022 French and Brazilian presidential elections. We use this data to explore aggregates complementing those used in social choice theory, finding that a metric of divisiveness, which is uncorrelated with traditional aggregation functions, can identify polarizing proposals. These metrics provide a score for the divisiveness of each proposal that can be estimated in the absence of data on the demographic characteristics of participants and that explains the issues that divide a population. These findings suggest divisiveness metrics can be useful complements to traditional aggregation functions in direct forms of digital participation.

cs.CY↗

arXiv2023

Anticipating Responsibility in Multiagent Planning

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.

cs.AI↗

arXiv2023

Measuring and Controlling Divisiveness in Rank Aggregation

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.

cs.MA↗

arXiv2022

Logic-Based Ethical Planning

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.

cs.AI↗

arXiv2022

On the Complexity of Majority Illusion in Social Networks

Majority illusion occurs in a social network when the majority of the network nodes belong to a certain type but each node's neighbours mostly belong to a different type, therefore creating the wrong perception, i.e., the illusion, that the majority type is different from the actual one. From a system engineering point of view, we want to devise algorithms to detect and, crucially, correct this undesirable phenomenon. In this paper we initiate the computational study of majority illusion in social networks, providing complexity results for its occurrence and avoidance. Namely, we show that identifying whether a network can be labelled such that majority illusion is present, as well as the problem of removing an illusion by adding or deleting edges of the network, are NP-complete problems.

cs.MA↗

arXiv2021

Collective discrete optimisation as judgment aggregation

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.

cs.AI↗