In this preference elicitation setting, our focus is on determining the parameters of a decision model that accurately captures the pairwise preferences of a Decision Maker (DM) over subsets, by comparing subsets of elements. The preferences are depicted using a highly adaptable model whose versatility stems from its ability to incorporate positive or negative synergies between elements [24]. Moreover, we provide an ordinally robust approach, in the sense that the preferences we infer do not rely on arbitrarily specified parameter values, but on the set of all parameter values that are compatible with the observed preferences. Importantly, another distinctive feature of our approach is its ability to learn the parameter set itself (not only the values of parameters). The preference model we consider can be used in different contexts, depending on the nature of the subsets we are comparing. The subsets are represented by binary vectors, showing the presence or absence of an element in the subset. The elements of a subset can be for example: individuals (in the comparison of coalitions, teams, etc.), binary attributes (in the comparison of multiattribute alternatives), objects (in the comparison of subsets in a subset choice problem), etc. For illustration, a toy example of such an elicitation context could be a coffee shop trying to determine its customers' favorite frozen yogurt flavor combination by offering them to test a small number of flavor combinations rather than having them taste each combination.

We introduce new power indices to measure the a priori voting power of voters in liquid democracy elections where an underlying network restricts delegations. We argue that our power indices are natural extensions of the standard Penrose-Banzhaf index in simple voting games. We show that computing the criticality of a voter is #P-hard even when voting weights are polynomially-bounded in the size of the instance. However, for specific settings, such as when the underlying network is a bipartite or complete graph, recursive formulas can compute these indices for weighted voting games in pseudo-polynomial time. We highlight their theoretical properties and provide numerical results to illustrate how restricting the possible delegations can alter voters' voting power.

When allocating indivisible items to agents, it is known that the only strategyproof mechanisms that satisfy a set of rather mild conditions are constrained serial dictatorships: given a fixed order over agents, at each step the designated agent chooses a given number of items (depending on her position in the sequence). With these rules, also known as non-interleaving picking sequences, agents who come earlier in the sequence have a larger choice of items. However, this advantage can be compensated by a higher number of items received by those who come later. How to balance priority in the sequence and number of items received is a nontrivial question. We use a previous model, parameterized by a mapping from ranks to scores, a social welfare functional, and a distribution over preference profiles. For several meaningful choices of parameters, we show that the optimal sequence can be computed in polynomial time. Last, we give a simple procedure for eliciting scoring vectors and we study the impact of the assignment from agents to positions on the ex-post social welfare.

The influence maximization paradigm has been used by researchers in various fields in order to study how information spreads in social networks. While previously the attention was mostly on efficiency, more recently fairness issues have been taken into account in this scope. In the present paper, we propose to use randomization as a mean for achieving fairness. While this general idea is not new, it has not been applied in this area. Similar to previous works like Fish et al. (WWW ’19) and Tsang et al. (IJCAI ’19), we study the maximin criterion for (group) fairness. In contrast to their work however, we model the problem in such a way that, when choosing the seed sets, probabilistic strategies are possible rather than only deterministic ones. We introduce two different variants of this probabilistic problem, one that entails probabilistic strategies over nodes (node-based problem) and a second one that entails probabilistic strategies over sets of nodes (set-based problem). After analyzing the relation between the two probabilistic problems, we show that, while the original deterministic maximin problem was inapproximable, both probabilistic variants permit approximation algorithms that achieve a constant multiplicative factor of 1 − 1/e minus an additive arbitrarily small error that is due to the simulation of the information spread. For the node-based problem, the approximation is achieved by observing that a polynomial-sized linear program approximates the problem well. For the set-based problem, we show that a multiplicative-weight routine can yield the approximation result. For an experimental study, we provide implementations of multiplicative-weight routines for both the set-based and the node-based problems and compare the achieved fairness values to existing methods. Maybe non-surprisingly, we show that the ex-ante values, i.e., minimum expected value of an individual (or group) to obtain the information, of the computed probabilistic strategies are significantly larger than the (ex-post) fairness values of previous methods. This indicates that studying fairness via randomization is a worthwhile path to follow. Interestingly and maybe more surprisingly, we observe that even the ex-post fairness values, i.e., fairness values of sets sampled according to the probabilistic strategies computed by our routines, dominate over the fairness achieved by previous methods on many of the instances tested.

Weighted voting games is one of the most important classes of cooperative games. Recently, Zhang and Grossi [53] proposed a variant of this class, called delegative simple games, which is well suited to analyse the relative importance of each voter in liquid democracy elections. Moreover, they defined a power index, called the delagative Banzhaf index to compute the importance of each agent (i.e., both voters and delegators) in a delegation graph based on two key parameters: the total voting weight she has accumulated and the structure of supports she receives from her delegators. We obtain several results related to delegative simple games. We first propose a pseudo-polynomial time algorithm to compute the delegative Banzhaf and Shapley-Shubik values in delegative simple games. We then investigate a bribery problem where the goal is to maximize/minimize the voting power/weight of a given voter in a delegation graph by changing at most a fixed number of delegations. We show that the problems of minimizing/maximizing a voter's power index value are strongly NP-hard. Furthermore, we prove that having a better approximation guarantee than $1-1/e$ to maximize the voting weight of a voter is not possible, unless $P = NP$, then we provide some parameterized complexity results for this problem. Finally, we show that finding a delegation graph with a given number of gurus that maximizes the minimum power index value an agent can have is a computationally hard problem.

In this paper, we investigate the so-called ODP-problem that has been formulated by Caragiannis and Micha [10]. Here, we are in a setting with two election alternatives out of which one is assumed to be correct. In ODP, the goal is to organise the delegations in the social network in order to maximize the probability that the correct alternative, referred to as ground truth, is elected. While the problem is known to be computationally hard, we strengthen existing hardness results by providing a novel strong approximation hardness result: For any positive constant $C$, we prove that, unless $P=NP$, there is no polynomial-time algorithm for ODP that achieves an approximation guarantee of $\alpha \ge (\ln n)^{-C}$, where $n$ is the number of voters. The reduction designed for this result uses poorly connected social networks in which some voters suffer from misinformation. Interestingly, under some hypothesis on either the accuracies of voters or the connectivity of the network, we obtain a polynomial-time $1/2$-approximation algorithm. This observation proves formally that the connectivity of the social network is a key feature for the efficiency of the liquid democracy paradigm. Lastly, we run extensive simulations and observe that simple algorithms (working either in a centralized or decentralized way) outperform direct democracy on a large class of instances. Overall, our contributions yield new insights on the question in which situations liquid democracy can be beneficial.

Liquid democracy is a collective decision making paradigm which lies between direct and representative democracy. One of its main features is that voters can delegate their votes in a transitive manner such that: A delegates to B and B delegates to C leads to A indirectly delegates to C. These delegations can be effectively empowered by implementing liquid democracy in a social network, so that voters can delegate their votes to any of their neighbors in the network. However, it is uncertain that such a delegation process will lead to a stable state where all voters are satisfied with the people representing them. We study the stability (w.r.t. voters preferences) of the delegation process in liquid democracy and model it as a game in which the players are the voters and the strategies are their possible delegations. We answer several questions on the equilibria of this process in any social network or in social networks that correspond to restricted types of graphs. We show that a Nash-equilibrium may not exist, and that it is even NP-complete to decide whether one exists or not. This holds even if the social network is a complete graph or a bounded degree graph. We further show that this existence problem is W[1]-hard w.r.t. the treewidth of the social network. Besides these hardness results, we demonstrate that an equilibrium always exists whatever the preferences of the voters iff the social network is a tree. We design a dynamic programming procedure to determine some desirable equilibria (e.g., minimizing the dissatisfaction of the voters) in polynomial time for tree social networks. Lastly, we study the convergence of delegation dynamics. Unfortunately, when an equilibrium exists, we show that a best response dynamics may not converge, even if the social network is a path or a complete graph.

Liquid democracy is a collective decision making paradigm which lies between direct and representative democracy. One main feature of liquid democracy is the concept of transitive delegations. Indeed, in this setting each voter may decide to vote directly or to delegate her vote to a representative, also called proxy. In liquid democracy this proxy can in turn delegate her vote and the votes that have been delegated to her to another proxy. As a result, a voter who decides to vote has a weight corresponding to the number of people she represents, i.e., herself and the voters who directly or indirectly delegated to her.

In the Markov decision process model, policies are usually evaluated by expected cumulative rewards. As this decision criterion is not always suitable, we propose in this paper an algorithm for computing a policy optimal for the quantile criterion. Both finite and infinite horizons are considered. Finally we experimentally evaluate our approach on random MDPs and on a data center control problem.

In this paper we adopt Skew Symmetric Bilinear (SSB) utility functions to compare policies in Markov Decision Processes (MDPs). By considering pairs of alternatives, SSB utility theory generalizes von Neumann and Morgenstern's expected utility (EU) theory to encompass rational decision behaviors that EU cannot accommodate. We provide a game-theoretic analysis of the problem of identifying an SSB-optimal policy in finite horizon MDPs and propose an algorithm based on a double oracle approach for computing an optimal (possibly randomized) policy. Finally, we present and discuss experimental results where SSB-optimal policies are computed for a popular TV contest according to several instantiations of SSB utility functions.