Date of Award

2022

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Mathematics

First Advisor

Brett Falk

Abstract

In the first part of this thesis we analyze the three most common blockchain committeesselection strategies: lottery, single-vote and approval voting, where voters can “approve” of any number of candidates. We first show that all these mechanisms converge to optimality exponentially quickly as the size of the committee grows. Approval-voting requires that even honest voters act strategically, we characterize different approval voting strategies and we show that although finding the optimal approval voting strategy is extremely complex, almost any approval voting strategy outperforms the single-vote mechanism enforced on the majority of blockchains. In the second part, we investigate a blockchain governance model where a group of n voters must choose between two collective alternatives. As opposed to the usual voting system (one person – one vote), we propose a voting system where each agent buys votes in favor of their preferred alternative, paying the m-th root of the number of votes purchased. Its novelty relies on allowing voters to express the intensity of their preferences in a simple manner. We provide a rigorous comparison of the utilitarian welfare between Regular Voting (m = 1) and Quadratic Voting (m = 2). We present closed form equilibrium solutions to the 2 voters and 3 voters games. In addition to characterizing the nature of equilibria, one of our main result demonstrates that the normalized utilitarian welfare of the mechanisms tends to one as the population size becomes large.

Included in

Mathematics Commons

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