Abstract
In normative economics, axiomatic properties of mechanisms are often formulated by taking the viewpoint of the designer on what is desirable, rather than that of the participants. By contrast, I argue that, in real-world applications, the central role of axioms should be to help explain the mechanism’s outcomes to participants. I specifically draw on my practical experience in two areas: fair division, which I view as a success story for the axiomatic approach; and voting, where this approach currently falls short.
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Notes
- 1.
Cailloux and Endriss (2016) develop an algorithm that automatically derives a justification for any outcome of the Borda rule, by applying both ‘single-profile’ and ‘multi-profile’ axioms to a sequence of hypothetical profiles. Their approach nicely formalizes the idea of explaining an outcome, but, in its current form, may not produce explanations that people would be able to follow.
- 2.
Two caveats are in order. First, the website Whale does visualize outcomes. For example, for Condorcet-based methods, the website displays the pairwise majority graph. These visualizations are useful insofar as they explain how the voting rule works, but, in my view, they do not explain its outcomes. Second, for the case of multi-winner elections, there are some examples of axioms that directly give rise to explainable outcomes. Notably, Aziz et al. (2017) recently developed the notion of justified representation for approval-based multi-winner elections, which, roughly speaking, requires that if a sufficiently large group of voters approve the same alternative, then the winning subset must contain at least one alternative approved by some member of the group. This at least allows addressing complaints by large groups that are not represented in the outcome, by arguing that the group members themselves cannot even agree on a single alternative.
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Acknowledgements
I thank Felix Brandt, Umberto Grandi, Domink Peters, Marcus Pivato, Nisarg Shah, and Bill Zwicker for insightful feedback. This work was partially supported by NSF grants IIS-1350598, IIS-1714140, CCF-1525932, and CCF-1733556; by ONR grants N00014-16-1-3075 and N00014-17-1-2428; as well as a Sloan Research Fellowship and a Guggenheim Fellowship.
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Procaccia, A.D. (2019). Axioms Should Explain Solutions. In: Laslier, JF., Moulin, H., Sanver, M., Zwicker, W. (eds) The Future of Economic Design. Studies in Economic Design. Springer, Cham. https://doi.org/10.1007/978-3-030-18050-8_27
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