Explainability in Social Choice

I this tutorial I want to discuss the question of what it means to provide a level of "explainability" in collective decision making. We will approach this question with the help of the axiomatic method as studied in economic theory, and specifically in social choice theory.

The first session will be devoted to an introduction to the axiomatic method. Specifically, we are going to see how we can identify "good" voting rules by characterising them in terms of the axioms they satisfy. This provides a first level of explainability of collective decisions, in the sense that the axioms characterising a given voting rule can, at least in principle, be used to explain any decision we might arrive at when applying that voting rule.

In the second session we are going to take this idea further and discuss a recent approach where we aim at explaining decisions by means of axioms directly, without going through specific voting rules. This has the advantage of focusing on more modest a task: explaining the decision taken in one specific situation should be much less demanding than explaining an entire voting rule (given that such a rule would determine a decision in every possible situation). Therefore, such explanations are easier to understand and more widely applicable. As we are going to see, operationalising this approach involves the use of various tools from logic and computer science.

Throughout this tutorial, we are going to encounter ideas from social choice theory, logic, and computer science. But no specific technical background in any of these areas will be assumed.

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