Originally developed by Vickrey, Clarke, and Groves, then more recently popularized by Glen Weyl, this market-based voting mechanism tries to address artifacts in voting systems by allowing voters to express the strength of their preferences by “spending” more for marginal votes.
If one unit of influence “costs” one vote, two units “cost” two votes, three “cost” three votes, and so on. “Buying” a given amount of influence, then, costs half the square of the total—hence “quadratic voting.”
On a theoretical basis, this creates equilibrium incentives such that each voter would end up “spending” a number of votes they wouldn’t care to increase or decrease. On a practical basis, vote-buying and trading present significant challenges. Vitalik Buterin has been investigating this latter issues in recent years.