If you haven’t yet read Making Democracy Count: How Mathematics Improves Voting, Electoral Maps, and Representation by Ismar Volić (Princeton University Press, 2024) I strongly recommend that you do, especially if you live in the United States. It truly is an epiphany, one of the most important books I have ever read. And don’t let “mathematics” in the title scare you. The mathematics in this book is easy and straightforward, and greatly strengthens the validity of the recommendations presented. The book is organized so that a busy person can read just a few pages a day, with ample natural stopping points throughout its 340+ pages. The current edition is hardcover, and can be found for as little as $15. A paperback edition is due out in February.
The author, Ismar Volić, is Professor of Mathematics at Wellesley College and Director of the Institute for Mathematics and Democracy.
What follows here is a high-level introduction to some of the most important topics covered in the book. This is in no way a substitute for reading the book, however. Volić presents many alternatives, the pros and cons of each, and provides many examples, often from recent history. You need to read this book!
Majority vs. Plurality
A “majority” means that at least 50% of the voters select the winning candidate. A “plurality” means that whoever gets the most votes wins, no matter how small the percentage. Whenever there is an election with more than two candidates running, the winner often garners less than 50% of the vote in the plurality-based voting used in most U.S. elections. A candidate can win despite the majority having voting against them. This is inherently undemocratic. In this type of voting, we have no idea what a voter’s second choice would have been if their favored candidate does not win. Time and again plurality gives us minority rule.
Plurality: More disadvantages
- Extremely susceptible to external manipulation (e.g. the spoiler effect)
- Extremely susceptible to strategic voting (e.g. tactical voting, insincere voting, dishonest voting)
- Two-party systems benefit, effectively shutting out other political parties and independents
Ranked Choice Voting (Instant Runoff)
A voter is allowed (but not required) to rank two or more candidates so if their first choice is eliminated because that candidate had the fewest votes, their vote then goes to their second-choice candidate, and so on. This process of elimination of the candidate with the fewest votes continues until the winning candidate has received a majority of the votes.1
Supermajority vs. Simple Majority
In a two-candidate election, a simple majority (>50%) is the best voting method. A supermajority (some amount greater than a simple majority) is often arbitrary and unmathematical, and it’s inherently undemocratic.
What if you’re electing more than one candidate?
Ranked Choice Voting can be generalized if more than one candidate is to be elected. Here’s how it works. Depending only on the number of seats needing to be filled, a threshold percentage is determined. For all those who voted for the candidate with the most votes, only the fraction of your vote needed to meet the threshold is applied to that candidate, and the remainder of your vote goes to your second choice, and so on. For each voter, the fractions always add up to 100%. This method is called Single Transferable Vote.
Important Advantages to Ranked Choice Voting and Single Transferable Vote
- Eliminates the “spoiler effect”. You can vote for who you like the best, regardless of their chances of winning, and your vote won’t inadvertently help to elect a candidate you don’t like.
- Makes it possible to move away from our current two-party duopoly. Other political parties and independent candidates become viable, thus strengthening our democracy.
- Greatly reduces negative campaigning
- Greatly reduces political polarization
- Increases voter turnout
- Eliminates the needs for runoff elections and even primaries, reducing election administration costs and saving taxpayer dollars
Amartya Sen: 1998 Nobel Prize in Economics
Individual liberties are incompatible with social needs. A delicate balancing act is needed.
The U.S. House of Representatives
- 435 seats is completely arbitrary
- Until 1913, the size of the U.S. House of Representative has increased with population; since then, it has been frozen at 435 (except temporarily at 437 when Alaska and Hawaii became states)
- A bigger House would go a long way toward correcting the multifaceted mess of the 1929 Reapportionment Act
- Most of the world’s democracies have a lower chamber size that is close to the cube root of the population; if the U.S. followed that rule, we would have ~700 representatives instead of 435
- Increasing the size of the U.S. House would stimulate greater political diversity and would help alleviate the effects of gerrymandering
- Apportionment (determining how many House seats each state gets) uses a decent mathematical method known as Huntington-Hill; a slight improvement could be made if we used the Webster method of apportionment
Gerrymandering
- Politicians choose the voters rather than the voters choosing the politicians
- Independent, non-partisan commissions should determine federal and state congressional districts. After the 2020 census, only four states had independent commissions: Arizona, California, Colorado, and Michigan.
- Increasing the size of the House of Representatives and consequently adding more districts and decreasing their size will decrease the ability to gerrymander them
- Implementing multi-member districts with proportional representation and single transferable vote will eliminate gerrymandering once and for all; this will necessarily increase the size of the House and usually the size of the districts.
Multi-Member District Considerations
- Works best if 3 to 5 representatives are elected for each district
- If only 2 representatives for each district are elected, the entry bar is set too high (e.g. no effective challenge to the current two-party entrenched duopoly)
The Electoral College
Needs to be abolished. No other democracy in the world has anything like it. An amazing amount and variety of mathematical dysfunctions converge to make the Electoral College wholly unsuitable in a functioning democracy. The President needs to be chosen based solely on the national popular vote.
The Elephant in the Room: Campaign Finance Reform
Admittedly, campaign finance reform is beyond the scope of this book, mostly because mathematics has little to offer in support. It is entirely a political problem. Volić’s only comment about this occurs in a footnote on p. 40: “Citizen’s United reversed campaign finance restrictions, giving an upper hand to wealthy candidates.” In my opinion, Citizen’s United was one of the worst U.S. Supreme Court decisions in recent decades, and even calls into question the legitimacy of the Court. A top priority must be campaign finance reform if we are to have a properly functioning democracy. As it is, almost all candidates are bought and paid for by donors and special interests before they even take office. Ideally, all political campaigns should be publicly funded so no candidate has a financial advantage. Level the playing field so that the ideological merits of each candidate, their integrity, and record of public service is used to determine their worthiness, rather than how much propaganda their money can generate.
Concluding Thoughts
The democracy reforms needed in the United States are structural in nature. As the world’s oldest still-functioning democracy, the United States is beginning to show its age and is in need of a refresh. Many newer democracies have corrected some of our deficiencies and we could learn a thing or two from them. Thinking that we can effect substantive change only by continuing to feed the “two-headed monster” that is the Democratic and Republican parties is folly.
The ideas presented in this book need to become a regular part of our national conversation. Insist that political candidates publicly support at least once of these reforms, or refuse to vote for them. These reforms are inherently non-partisan. They will improve the quality of life of all citizens, regardless of their political party or persuasion. You can be sure that the most intense opposition to these ideas will come from those who currently hold an inordinate amount of power and wealth, and that don’t want to lose any of their current privileged status. But we vastly outnumber them. If we turn our collective ignorance to knowledge and apathy to action in sufficient numbers, we will succeed.
- In very rare cases, RCV instant runoff can result in a plurality rather than a majority election (the candidate wins with less than 50% of the vote). This can only happen when there are a large number of exhausted ballots (i.e. a significant number of voters do not rank candidates, or stop ranking them, say, after two candidates). Worst case scenario: everyone votes for just one person and does not specify a second choice when there are more than two candidates. ↩︎
Democracy Resources (not an exhaustive list!)
Institute for Mathematics and Democracy
Ranked Choice Voting Resource Center
Transparent Election Initiative
Democracy Resources (Arizona)