Combining Voting Rules Together

We propose a simple method for combining together voting rules that performs a run-off between the different winners of each voting rule. We prove that this combinator has several good properties. For instance, even if just one of the base voting rules has a desirable property like Condorcet consistency, the combination inherits this property. In addition, we prove that combining voting rules together in this way can make finding a manipulation more computationally difficult. Finally, we study the impact of this combinator on approximation methods that find close to optimal manipulations

Verified Construction of Fair Voting Rules

Voting rules aggregate multiple individual preferences in order to make collective decisions. Commonly, these mechanisms are expected to respect a multitude of different fairness and reliability properties, e.g., to ensure that each voter\u27s ballot accounts for the same proportion of the elected alternatives, or that a voter cannot change the election outcome in her favor by insincerely filling out her ballot. However, no voting rule is fair in all respects, and trade-off attempts between such properties often bring out inconsistencies, which makes the construction of arguably practical and fair voting rules non-trivial and error-prone. In this paper, we present a formal and systematic approach for the flexible and verified construction of voting rules from composable core modules to respect such properties by construction. Formal composition rules guarantee resulting properties from properties of the individual components, which are of generic nature to be reused for various voting rules. We provide a prototypical logic-based implementation with proofs for a selected set of structures and composition rules within the theorem prover Isabelle/HOL. The approach can be readily extended in order to support many voting rules from the literature by extending the set of basic modules and composition rules. We exemplarily construct the well-known voting rule sequential majority comparison (SMC) from simple generic modules, and automatically produce a formal proof that SMC satisfies the fairness property monotonicity. Monotonicity is a well-known social-choice property that is easily violated by voting rules in practice

Social Choice for Partial Preferences Using Imputation

Within the field of multiagent systems, the area of computational social choice considers the problems arising when decisions must be made collectively by a group of agents. Usually such systems collect a ranking of the alternatives from each member of the group in turn, and aggregate these individual rankings to arrive at a collective decision. However, when there are many alternatives to consider, individual agents may be unwilling, or unable, to rank all of them, leading to decisions that must be made on the basis of incomplete information. While earlier approaches attempt to work with the provided rankings by making assumptions about the nature of the missing information, this can lead to undesirable outcomes when the assumptions do not hold, and is ill-suited to certain problem domains. In this thesis, we propose a new approach that uses machine learning algorithms (both conventional and purpose-built) to generate plausible completions of each agent’s rankings on the basis of the partial rankings the agent provided (imputations), in a way that reflects the agents’ true preferences. We show that the combination of existing social choice functions with certain classes of imputation algorithms, which forms the core of our proposed solution, is equivalent to a form of social choice. Our system then undergoes an extensive empirical validation under 40 different test conditions, involving more than 50,000 group decision problems generated from real-world electoral data, and is found to outperform existing competitors significantly, leading to better group decisions overall. Detailed empirical findings are also used to characterize the behaviour of the system, and illustrate the circumstances in which it is most advantageous. A general testbed for comparing solutions using real-world and artificial data (Prefmine) is then described, in conjunction with results that justify its design decisions. We move on to propose a new machine learning algorithm intended specifically to learn and impute the preferences of agents, and validate its effectiveness. This Markov-Tree approach is demonstrated to be superior to imputation using conventional machine learning, and has a simple interpretation that characterizes the problems on which it will perform well. Later chapters contain an axiomatic validation of both of our new approaches, as well as techniques for mitigating their manipulability. The thesis concludes with a discussion of the applicability of its contributions, both for multiagent systems and for settings involving human elections. In all, we reveal an interesting connection between machine learning and computational social choice, and introduce a testbed which facilitates future research efforts on computational social choice for partial preferences, by allowing empirical comparisons between competing approaches to be conducted easily, accurately, and quickly. Perhaps most importantly, we offer an important and effective new direction for enabling group decision making when preferences are not completely specified, using imputation methods