Consider a standard decision making setting that includes a set of possible actions (decisions or policies), and a set of individuals who assign utilities to the actions.

Is it possible to understand or imitate a policy maker's rationale by looking at past decisions they made? We formalize this question as the problem of learning social welfare functions belonging to the well-studied family of power mean functions. We focus on two learning tasks; in the first, the input is vectors of utilities of an action (decision or policy) for individuals in a group and their associated social welfare as judged by a policy maker, whereas in the second, the input is pairwise comparisons between the welfares associated with a given pair of utility vectors. We show that power mean functions are learnable with polynomial sample complexity in both cases, even if the comparisons are social welfare information is noisy. Finally, we design practical algorithms for these tasks and evaluate their performance.

We consider a voting model, where a number of candidates need to be selected subject to certain feasibility constraints. The model generalises committee elections (where there is a single constraint on the number of candidates that need to be selected), various elections with diversity constraints, the model of public decisions (where decisions needs to be taken on a number of independent issues), and the model of collective scheduling. A critical property of voting is that it should be fair -- not only to individuals but also to groups of voters with similar opinions on the subject of the vote; in other words, the outcome of an election should proportionally reflect the voters' preferences. We formulate axioms of proportionality in this general model. Our axioms do not require predefining groups of voters; to the contrary, we ensure that the opinion of every subset of voters whose preferences are cohesive-enough are taken into account to the extent that is proportional to the size of the subset. Our axioms generalise the strongest known satisfiable axioms for the more specific models. We explain how to adapt two prominent committee election rules, Proportional Approval Voting (PAV) and Phragm\'{e}n Sequential Rule, as well as the concept of stable-priceability to our general model. The two rules satisfy our proportionality axioms if and only if the feasibility constraints are matroids.

We study the problem of fairly allocating a set of indivisible goods among agents with {\em bivalued submodular valuations} -- each good provides a marginal gain of either $a$ or $b$ ($a < b$) and goods have decreasing marginal gains. This is a natural generalization of two well-studied valuation classes -- bivalued additive valuations and binary submodular valuations. We present a simple sequential algorithmic framework, based on the recently introduced Yankee Swap mechanism, that can be adapted to compute a variety of solution concepts, including max Nash welfare (MNW), leximin and $p$-mean welfare maximizing allocations when $a$ divides $b$. This result is complemented by an existing result on the computational intractability of MNW and leximin allocations when $a$ does not divide $b$. We show that MNW and leximin allocations guarantee each agent at least $\frac25$ and $\frac{a}{b+2a}$ of their maximin share, respectively, when $a$ divides $b$. We also show that neither the leximin nor the MNW allocation is guaranteed to be envy free up to one good (EF1). This is surprising since for the simpler classes of bivalued additive valuations and binary submodular valuations, MNW allocations are known to be envy free up to any good (EFX).

Detecting sets of relevant patterns from a given dataset is an important challenge in data mining. The relevance of a pattern, also called utility in the literature, is a subjective measure and can be actually assessed from very different points of view. Rule-based languages like Answer Set Programming (ASP) seem well suited for specifying user-provided criteria to assess pattern utility in a form of constraints; moreover, declarativity of ASP allows for a very easy switch between several criteria in order to analyze the dataset from different points of view. In this paper, we make steps toward extending the notion of High Utility Pattern Mining (HUPM); in particular we introduce a new framework that allows for new classes of utility criteria not considered in the previous literature. We also show how recent extensions of ASP with external functions can support a fast and effective encoding and testing of the new framework. To demonstrate the potential of the proposed framework, we exploit it as a building block for the definition of an innovative method for predicting ICU admission for COVID-19 patients. Finally, an extensive experimental activity demonstrates both from a quantitative and a qualitative point of view the effectiveness of the proposed approach.

We study the problem of allocating indivisible chores among agents with binary supermodular cost functions. In other words, each chore has a marginal cost of $0$ or $1$ and chores exhibit increasing marginal costs (or decreasing marginal utilities). In this note, we combine the techniques of Viswanathan and Zick (2022) and Barman et al. (2023) to present a general framework for fair allocation with this class of valuation functions. Our framework allows us to generalize the results of Barman et al. (2023) and efficiently compute allocations which satisfy weighted notions of fairness like weighted leximin or min weighted $p$-mean malfare for any $p \ge 1$.

Several social interventions (e.g., suicide and HIV prevention) leverage social network information to maximize outreach. Algorithmic influence maximization techniques have been proposed to aid with the choice of influencers (or peer leaders) in such interventions. Traditional algorithms for influence maximization have not been designed with social interventions in mind. As a result, they may disproportionately exclude minority communities from the benefits of the intervention. This has motivated research on fair influence maximization. Existing techniques require committing to a single domain-specific fairness measure. This makes it hard for a decision maker to meaningfully compare these notions and their resulting trade-offs across different applications. We address these shortcomings by extending the principles of cardinal welfare to the influence maximization setting, which is underlain by complex connections between members of different communities. We generalize the theory regarding these principles and show under what circumstances these principles can be satisfied by a welfare function. We then propose a family of welfare functions that are governed by a single inequity aversion parameter which allows a decision maker to study task-dependent trade-offs between fairness and total influence and effectively trade off quantities like influence gap by varying this parameter. We use these welfare functions as a fairness notion to rule out undesirable allocations. We show that the resulting optimization problem is monotone and submodular and can be solved with optimality guarantees. Finally, we carry out a detailed experimental analysis on synthetic and real social networks and should that high welfare can be achieved without sacrificing the total influence significantly. Interestingly we can show there exists welfare functions that empirically satisfy all of the principles.

Fair division is the problem of dividing one or several goods amongst two or more agents in a way that satisfies a suitable fairness criterion. That is, fair division may be considered part of the larger research area of multiagent resource allocation (Chevaleyre et al., 2006). What is special about fair division is the explicit focus on fairness concerns. These notes give a succinct introduction to the field, focusing on formal and computational aspects that are particularly relevant to research in Computational Social Choice (Chevaleyre et al., 2007b) and Multiagent Systems (Wooldridge, 2009). We begin by briefly outlining how fair division fits into (and relates to) these two disciplines. Like voting, the archetypical instance of a social choice problem, fair division amounts to selecting an outcome from a set of possible collective agreements, given the individual preferences of a group of agents. There are however two main differences when compared to voting. The first difference is that, typically, voting theory assumes that agents (voters) have ordinal preferences (that is, they rank the available candidates and can say for any two candidates which one they like more), while in the context of fair division we usually assume that agents have cardinal preferences (that is, each agent has got a utility function mapping possible outcomes to appropriate numerical values). The second difference is that a fair division problem comes with a certain internal "structure" that is typically absent from problems in voting:

The formalism of multi-objective influence diagrams has recently been developed for modeling and solving sequential decision problems under uncertainty and multiple objectives. Since utility values representing the decision maker's preferences are only partially ordered (e.g., by the Pareto order) we no longer have a unique maximal value of expected utility, but a set of them. Computing the set of maximal values of expected utility and the corresponding policies can be computationally very challenging. In this paper, we consider alternative notions of optimality, one of the most important one being the notion of possibly optimal, namely optimal in at least one scenario compatible with the inter-objective tradeoffs. We develop a variable elimination algorithm for computing the set of possibly optimal expected utility values, prove formally its correctness, and compare variants of the algorithm experimentally.