# The robustness of quadratic voting

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## Abstract

Lalley and Weyl (Quadratic voting, 2016) propose a mechanism for binary collective decisions, Quadratic Voting (QV), and prove its approximate efficiency in large populations in a stylized environment. They motivate their proposal substantially based on its greater robustness when compared with pre-existing efficient collective decision mechanisms. However, these suggestions are based purely on discussion of structural properties of the mechanism. In this paper, I study these robustness properties quantitatively in an equilibrium model. Given the mathematical challenges with establishing results on QV fully formally, my analysis relies on a number of structural conjectures that have been proven in analogous settings in the literature, but in the models I consider here. While most of the factors I study reduce the efficiency of QV to some extent, it is reasonably robust to all of them and quite robustly outperforms one-person-one-vote. Collusion and fraud, except on a very large scale, are deterred either by unilateral deviation incentives or by the reactions of non-participants to the possibility of their occurring. I am able to study aggregate uncertainty only for particular parametric distributions, but using the most canonical structures in the literature I find that such uncertainty reduces limiting efficiency, but never by a large magnitude. Voter mistakes or non-instrumental motivations for voting, so long as they are uncorrelated with values, may either enhance or harm efficiency depending on the setting. These findings contrast with existing (approximately) efficient mechanisms, all of which are highly sensitive to at least one of these factors.

### Keywords

Robust mechanism design Quadratic voting Collusion Paradox of voting### JEL Classification

D47 D61 D71 C72 D82 H41 P16## Notes

### Acknowledgements

This paper was spun off from an earlier draft of the paper “quadratic voting” and all acknowledgements in that paper implicitly extend here. However I additionally thank participants at the “Quadratic Voting and the Public Good” conference at the Becker Friedman Institute and I am particularly grateful to Steve Lalley and Itai Sher for detailed comments. All errors are my own.

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