The Leximin Approach for a Sequence of Collective Decisions

In many situations, several agents need to make a sequence of decisions. For example, a group of workers that needs to decide where their weekly meeting should take place. In such situations, a decision-making mechanism must consider fairness notions. In this paper, we analyze the fairness of three known mechanisms: round-robin, maximum Nash welfare, and leximin. We consider both offline and online settings, and concentrate on the fairness notion of proportionality and its relaxations. Specifically, in the offline setting, we show that the three mechanisms fail to find a proportional or approximate-proportional outcome, even if such an outcome exists. We thus introduce a new fairness property that captures this requirement, and show that a variant of the leximin mechanism satisfies the new fairness property. In the online setting, we show that it is impossible to guarantee proportionality or its relaxations. We thus consider a natural restriction on the agents' preferences, and show that the leximin mechanism guarantees the best possible additive approximation to proportionality and satisfies all the relaxations of proportionality

Socially Aware Coalition Formation with Bounded Coalition Size

In many situations when people are assigned to coalitions the assignment must be social aware, i.e, the utility of each person depends on the friends in her coalition. Additionally, in many situations the size of each coalition should be bounded. This paper initiates the study of such coalition formation scenarios in both weighted and unweighted settings. We show that finding a partition that maximizes the utilitarian social welfare is computationally hard, and provide a polynomial-time approximation algorithm. We also investigate the existence and the complexity of finding stable partitions. Namely, we show that the Contractual Strict Core (CSC) is never empty, but the Strict Core (SC) of some games is empty. Finding partitions that are in the CSC is computationally easy, but finding partitions that are in the SC is hard. The analysis of the core is more involved. For the weighted setting, the core may be empty. We thus concentrate on the unweighted setting. We show that when the coalition size is bounded by 3 the core is never empty, and we present a polynomial time algorithm for finding a member of the core. When the coalition size is greater, we provide additive and multiplicative approximations of the core. In addition, we show in simulation over 100 million games that a simple heuristic always finds a partition that is in the core

AI for Explaining Decisions in Multi-Agent Environments

Explanation is necessary for humans to understand and accept decisions made by an AI system when the system's goal is known. It is even more important when the AI system makes decisions in multi-agent environments where the human does not know the systems' goals since they may depend on other agents' preferences. In such situations, explanations should aim to increase user satisfaction, taking into account the system's decision, the user's and the other agents' preferences, the environment settings and properties such as fairness, envy and privacy. Generating explanations that will increase user satisfaction is very challenging; to this end, we propose a new research direction: xMASE. We then review the state of the art and discuss research directions towards efficient methodologies and algorithms for generating explanations that will increase users' satisfaction from AI system's decisions in multi-agent environments.Comment: This paper has been submitted to the Blue Sky Track of the AAAI 2020 conference. At the time of submission, it is under review. The tentative notification date will be November 10, 2019. Current version: Name of first author had been added in metadat

Approximating Bribery in Scoring Rules

The classic bribery problem is to find a minimal subset of voters who need to change their vote to make some preferred candidate win.We find an approximate solution for this problem for a broad family of scoring rules (which includes Borda and t-approval), in the following sense: if there is a strategy which requires bribing k voters, we efficiently find a strategy which requires bribing at most k + Õ(√k) voters. Our algorithm is based on a randomized reduction from bribery to coalitional manipulation (UCM). To solve the UCM problem, we apply the Birkhoff-von Neumann (BvN) decomposition to a fractional manipulation matrix. This allows us to limit the size of the possible ballot search space reducing it from exponential to polynomial, while still obtaining good approximation guarantees. Finding the optimal solution in the truncated search space yields a new algorithm for UCM, which is of independent interest