We study the performance of the Quadratic Voting (QV) mechanism proposed by Lalley and Weyl (2016) in finite populations of various sizes using three decreasingly analytic but increasingly precise methods with emphasis on examples calibrated to the 2008 gay marriage referendum in California. First, we use heuristic calculations to derive conservative analytic bounds on the constants associated with Lalley and Weyl's formal results on large population convergence. Second, we pair numerical game theory methods with statistical limit results to computationally approximate equilibria for moderate population sizes. Finally, we use purely numerical methods to analyze small populations. The more precise the methods we use, the better the performance of QV appears to be in a wide range of cases, with the analytic bounds on potential welfare typically 1.5 to 3 times more conservative than the results from numerical calculation. In our most precise results, we have not found an example where QV sacrifices more than 10% of potential welfare for any population size. However, we find scenarios in which one-person-one-vote rules outperform QV and also show that convergence to full efficiency in large populations may be much slower with fat tails than with bounded support. The results suggest that in highly unequal societies, 1p1v or QV with artificial currency may give superior efficiency to QV with real currency.

Lalley and Weyl (2016) propose a mechanism for binary collective decisions, Quadratic Voting, 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 only able to study aggregate uncertainty 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 improve or harm efficiency depending on the setting. These findings contrasts with existing (approximately) efficient mechanisms, all of which are highly sensitive to at least one of these factors.

Since their introduction in 1932, Likert and other continuous, independent rating scales have become the de facto toolset for survey research. Scholars have raised significant reliability and validity problems with these types of scales, and alternative methods for capturing perceptions and preferences have gained traction within specific domains. In this paper, we evaluate a new broadly applicable approach to opinion measurement based on quadratic voting (QV), a method in which respondents express preferences by 'buying' votes for options using a fixed budget from which they pay a quadratic price for votes. Comparable QV-based and Likert-based survey instruments designed by Collective Decision Engines LLC were experimentally evaluated by randomly assigning potential respondents to one or the other method. Using a host of metrics, including respondent engagement and process-based metrics, we provide some initial evidence that the QV-based instrument provides a clearer measure of the preferences of the most intense respondents than the Likert-based instrument does. We consider the implications for survey satisfying, a key threat to the continued value of survey research, and reveal the mechanisms by which QV differentiates itself from Likert-based scales, thus establishing QV as a promising alternative survey tool for further political and commercial research. We also explore key design issues within QV-based surveys to extend these promising results.

This book is comprised of the latest research into CSS methods, uses, and results, as presented at the 2020 annual conference of the Computational Social Science Society of the Americas (CSSSA). Computational social science (CSS) is the science that investigates social and behavioral dynamics through social simulation, social network analysis, and social media analysis. The CSSSA is a professional society that aims to advance the field of computational social science in all areas, including basic and applied orientations, by holding conferences and workshops, promoting standards of scientific excellence in research and teaching, and publishing research findings and results. The above-mentioned conference was held virtually, October 8 – 11, 2020. What follows is a diverse representation of new results and approaches to using the tools of CSS and agent-based modeling (ABM) in exploring complex phenomena across many different domains. Readers will therefore not only have the results of these specific projects upon which to build, along with a wealth of case-study examples that can serve as meaningful exemplars for new research projects and activities, they will also gain a greater appreciation for the broad scope of CSS.

Revolutionary ideas on how to use markets to achieve fairness and prosperity for all Many blame today's economic inequality, stagnation, and political instability on the free market. The solution is to rein in the market, right? Radical Markets turns this thinking on its head. With a new foreword by Ethereum creator Vitalik Buterin and virtual reality pioneer Jaron Lanier as well as a new afterword by Eric Posner and Glen Weyl, this provocative book reveals bold new ways to organize markets for the good of everyone. It shows how the emancipatory force of genuinely open, free, and competitive markets can reawaken the dormant nineteenth-century spirit of liberal reform and lead to greater equality, prosperity, and cooperation. Only by radically expanding the scope of markets can we reduce inequality, restore robust economic growth, and resolve political conflicts. But to do that, we must replace our most sacred institutions with truly free and open competition—Radical Markets shows how.

A group of N individuals must choose between two collective alternatives. Under Quadratic Voting (QV), agents buy votes in favor of their preferred alternative from a clearing house, paying the square of the number of votes purchased; the sum of all votes purchased determines the outcome. We provide the first rigorous results for this mechanism, in a canonical independent private values environment with bounded value distributions. In addition to characterizing the nature of equilibria, we demonstrate that for all bounded value distributions, the utilitarian welfare losses of the mechanism as a proportion of the maximum possible welfare tends to zero as the population sizebecomes large.

Democratic institutions aggregate preferences poorly. The norm of one-person-one-vote with majority rule treats people fairly by giving everyone an equal chance to influence outcomes, but fails to give proportional weight to people whose interests in a social outcome are stronger than those of other people - a problem that leads to the familiar phenomenon of tyranny of the majority. Various institutions that have been tried or proposed over the years to correct this problem - including supermajority rule, weighted voting, cumulative voting, 'mixed constitutions,' executive discretion, and judicially protected rights - all badly misfire in various ways, for example, by creating gridlock or corruption. This paper proposes a new form of political decision-making based on the theory of quadratic voting. It explains how quadratic voting solves the preference aggregation problem, giving proper weight to preferences of varying intensity, and how it could be implemented as well as addressing concerns about its consequences for equity.