Making Democracy Count: How Mathematics Improves Voting, Electoral Maps, and Representation

by Ismar Volic

Overview

How we can repair our democracy by rebuilding the mechanisms that power it

What’s the best way to determine what most voters want when multiple candidates are running? What’s the fairest way to allocate legislative seats to different constituencies? What’s the least distorted way to draw voting districts? Not the way we do things now. Democracy is mathematical to its very foundations. Yet most of the methods in use are a historical grab bag of the shortsighted, the cynical, the innumerate, and the outright discriminatory. Making Democracy Count sheds new light on our electoral systems, revealing how a deeper understanding of their mathematics is the key to creating civic infrastructure that works for everyone.

In this timely guide, Ismar Volić empowers us to use mathematical thinking as an objective, nonpartisan framework that rises above the noise and rancor of today’s divided public square. Examining our representative democracy using powerful clarifying concepts, Volić shows why our current voting system stifles political diversity, why the size of the House of Representatives contributes to its paralysis, why gerrymandering is a sinister instrument that entrenches partisanship and disenfranchisement, why the Electoral College must be rethought, and what can work better and why. Volić also discusses the legal and constitutional practicalities involved and proposes a road map for repairing the mathematical structures that undergird representative government.

Making Democracy Count gives us the concrete knowledge and the confidence to advocate for a more just, equitable, and inclusive democracy.

Product Details

ISBN-13:	9780691248806
Publisher:	Princeton University Press
Publication date:	04/02/2024
Pages:	408
Product dimensions:	6.12(w) x 9.25(h) x (d)

About the Author

Ismar Volić is professor of mathematics and director of the Institute for Mathematics and Democracy at Wellesley College. His work has appeared in publications such as The Hill, Cognoscenti, and Education Week.

What People are Saying About This

From the Publisher

“The rules for electing candidates to public office have a profound effect on democracy, a fact not generally appreciated. Ismar Volić’s beautifully written book shows just how crucial these rules are—and how they can be improved.”—Eric Maskin, Nobel Laureate in Economics, Harvard University

“A clear, accessible, and enjoyable introduction to the mathematical machinery behind American democracy. Challenging us to imagine how elections could be different, Volić explains how mathematicians think about the basic elements of our democratic system, from voting and apportionment to gerrymandering. In a moment when many worry about American polarization, Volic’s perspective is refreshing and necessary.”—Alma Steingart, author of Axiomatics: Mathematical Thought and High Modernism

“Do you remember how shocked you were at the outcome of the 2016 presidential election? One candidate received millions more votes, and yet she lost! The Electoral College was a major culprit, but there are lots of other ways for seemingly reasonable processes to go astray. In Making Democracy Count, you will learn how the immutable mathematical laws behind commonly accepted voting schemes make such astonishing outcomes possible. Read this book and you will learn what can be done to make the word ‘democracy’ achieve what it claims. Highly recommended.”—Paul J. Nahin, author of The Mathematical Radio

Editorial Reviews

"Volić surveys voting and apportionment methods, including impossibility results, in a readable way with real-life examples."

Mathematics Magazine

Finalist for the PROSE Award in Popular Science and Mathematics, Association of American Publishers

"Winner of the Euler Prize, Mathematical Association of America"

"Volić often effectively follows up clear illustrations using small sets of data with real-world examples. . . . Overall, this fascinating book is thought provoking and strongly recommended."—-N. W. Schillow, Choice

"The book reads nothing like a math textbook. It stays approachable, even while diving deep into its subject matter. . . . There’s no one better to teach this material than Ismar Volić."—-Deb Otis, National Civic League

"As the United States grapples with persistent challenges in its electoral system, Volić’s work is a timely contribution, offering a rigorous analysis of how mathematical principles can enhance the fairness and integrity of democratic processes."—-Hank Lacey, Law of the West

From the Publisher

2024-09-03
A writer and academic explores how math can be used to understand and critique the world of politics.

“Math is a clarifying way of looking at the world,” Volić writes in his introduction; by introducing readers to this specific perspective, he hopes to lead them to a new view on the contentious topic of politics. The author explains that, for him, democracy is “a piece of civic infrastructure that runs on mathematics.” That idea forms the backbone of a university class he teaches on the topic that regularly outrages students as they realize the counterintuitive nature of many long-standing political systems. With this book, Volić aims to bring that classroom experience to a wider audience. He structures his detailed examination of math and politics by first analyzing voting, then issues of representation, finally providing an explanation of how all of his ideas came together using concrete examples of civic infrastructure, both historical and contemporary. Volić walks readers through the ins and outs of simple majorities and pluralities and lays out the basics of mathematic theorems—the pinnacles of mathematical knowledge—noting the difficulty of translating notions like the “best” voting system into mathematic language. Early on, Volić brings out one of his most salient and important arguments, detailing how many “convenient numbers” used in the world’s democracies are largely unjustified. His primary example is membership in the House of Representatives being fixed at 435 seats, but there are several other examples that similarly become infuriating when looked at objectively. The author provides numerous examples, from Eurovision protocols to the 2010 Oakland, California mayoral race, to illustrate the instant runoff system, which here receives ample attention and detailed explanations, forming a cornerstone of Volić’s recommendations. From there, the author moves on to perhaps the most enraging political processes of them all, discussing gerrymandering and the electoral college, walking readers through the fine points of everything wrong with a system that works against fair representation. (He also offers several examples of proportional representation in other countries outside the U.S.)

Volić’s book is rich with ideas and explanations, and he writes with an enthusiasm for his subject that is infectious. It’s easy to imagine the author in front of a classroom, leading the students to lightbulb-moment realizations while being humorous and approachable. His writing is calibrated to speak to the greatest number of people, not just college-level students or academics. Volić’s humor, in particular, renders even the most complicated sections accessible. “The rest of this chapter will be exasperating. Irritating,” he writes at one point; he even puts a winking spin on his footnotes, proclaiming, “If you don’t know what MAGA is, you’ve either spent the last seven or so years in a well or you’re reading this 150 years from the time it was written.” Despite the passionate prose, the numerous tables, laws, and theorems can start to blur together—the subject remains complicated and academic at its core. Happily, there is just enough of Volić’s voice—and his own story as an immigrant from Bosnia Herzegovina—to keep even the most math-averse reader pushing through the difficult sections, eager to hear more of his ideas.

A fascinating perspective on challenging subject matter.

Kirkus Reviews