A Generalised Theory of Proportionality in Collective Decision Making

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

Three fundamental pillars of decision-centered teamwork

This thesis introduces a novel paradigm in artificial intelligence: decision-centered teamwork. Decision-centered teamwork is the analysis of agent teams that iteratively take joint decisions into solving complex problems. Although teams of agents have been used to take decisions in many important domains, such as: machine learning, crowdsourcing, forecasting systems, and even board games; a study of a general framework for decisioncentered teamwork has never been presented in the literature before. I divide decision-centered teamwork in three fundamental challenges: (i) Agent Selection, which consists of selecting a set of agents from an exponential universe of possible teams; (ii) Aggregation of Opinions, which consists of designing methods to aggregate the opinions of different agents into taking joint team decisions; (iii) Team Assessment, which consists of designing methods to identify whether a team is failing, allowing a “coordinator” to take remedial procedures. In this thesis, I handle all these challenges. For Agent Selection, I introduce novel models of diversity for teams of voting agents. My models rigorously show that teams made of the best agents are not necessarily optimal, and also clarify in which situations diverse teams should be preferred. In particular, I show that diverse teams get stronger as the number of actions increases, by analyzing how the agents’ probability distribution function over actions changes. This has never been presented before in the ensemble systems literature. I also show that diverse teams have a great applicability for design problems, where the objective is to maximize the number of optimal solutions for human selection, combining for the first time social choice with number theory. All of these theoretical models and predictions are verified in real systems, such as Computer Go and architectural design. In particular, for architectural design I optimize the design of buildings with agent teams not only for cost and project requirements, but also for energy-efficiency, being thus an essential domain for sustainability. Concerning Aggregation of Opinions, I evaluate classical ranked voting rules from social choice in Computer Go, only to discover that plurality leads to the best results. This happens because real agents tend to have very noisy rankings. Hence, I create a ranking by sampling extraction technique, leading to significantly better results with the Borda voting rule. A similar study is also performed in the social networks domain, in the context of influence maximization. Additionally, I study a novel problem in social networks: I assume only a subgraph of the network is initially known, and we must spread influence and learn the graph simultaneously. I analyze a linear combination of two greedy algorithms, outperforming both of them. This domain has a great potential for health, as I run experiments in four real-life social networks from the homeless population of Los Angeles, aiming at spreading HIV prevention information. Finally, with regards to Team Assessment, I develop a domain independent team assessment methodology for teams of voting agents. My method is within a machine learning framework, and learns a prediction model over the voting patterns of a team, instead of learning over the possible states of the problem. The methodology is tested and verified in Computer Go and Ensemble Learning

Tracking the Temporal-Evolution of Supernova Bubbles in Numerical Simulations

The study of low-dimensional, noisy manifolds embedded in a higher dimensional space has been extremely useful in many applications, from the chemical analysis of multi-phase flows to simulations of galactic mergers. Building a probabilistic model of the manifolds has helped in describing their essential properties and how they vary in space. However, when the manifold is evolving through time, a joint spatio-temporal modelling is needed, in order to fully comprehend its nature. We propose a first-order Markovian process that propagates the spatial probabilistic model of a manifold at fixed time, to its adjacent temporal stages. The proposed methodology is demonstrated using a particle simulation of an interacting dwarf galaxy to describe the evolution of a cavity generated by a Supernov