In remembrance of Robert D. Tollison

We discuss the mechanisms related to quadratic voting, from Vickrey’s counter-speculation mechanism and his second-price auction, through the family of Groves mechanisms and its most notable member, the Clarke mechanism, to the expected externality mechanism, Goeree and Zhang’s mechanism, the Groves–Ledyard mechanism, and the Hylland–Zeckhauser mechanism. We show that each mechanism that involves collective decisions has a quadratic aspect and that all of the mechanisms that we discuss are applications of the fundamental insight that for a process to be efficient, all parties involved must bear the marginal social costs of their actions.