A voting system in profile

One of the most common voting systems in use is the plurality vote. Plurality votes play a key role in most modern democracies. When there are more than two options, however, a plurality vote is deeply flawed. Most notably, a plurality vote with multiple candidates is highly vulnerable to spoiler effects, “center squeeze” effects, and can elect candidates who would lose against any other candidate in a head-to-head contest.

Plurality ballots (ostraka) from the ostracism of Themistocles (482 B.C.E.). Source.

Plurality voting is nevertheless widespread, and has been around for a very long time. For example, the classical Athenian practice of ostracism was carried out using a plurality vote. Each voter…

Why winning a lot of counties doesn’t mean much.

Biden won about 500 counties. Trump won about 2400. It’s a striking statistic that boils down to two distinct facts. First, “county” doesn’t mean the same thing in different states. Second, even within the same state, counties are very far from equal.

Red states have more counties

In general, the largest numbers of counties are found in the southeastern states and the Midwest. Northeastern and western states have the fewest counties. This geographic pattern happens — coincidentally — to align with current regional divides in politics.

Number of counties by state

Counties in western states were usually formed when the states were very sparsely populated. It’s hard to justify a…

A step forward.

In 2008 and 2010, California voters went to the ballot box and voted on three electoral reform measures. The reformers won all three ballots.

  • Proposition 11 established the California Citizens Redistricting Commission (CCRC) and gave it the power to draw legislative districts.
  • Proposition 14 established the top-two primary system.
  • Proposition 20 expanded the CCRC’s mandate to include Congressional maps.
Future movie star, California governor, and election reform advocate Arnold Schwarzenegger poses for a photograph in 1974. Fun fact: In 1974, the governor of California was a Republican movie star who was succeeded by Jerry Brown. Jerry Brown also was governor after Arnold Schwarzenegger. (Image source.)

The most prominent supporter of all elements of this reform package was Governor Arnold Schwarzenegger, a non-traditional Republican who had been initially elected in a way that bypassed the normal primary process. As noted above, these reforms were passed into law…

Part 1: Heir to the Empire

This May 4th, I decided to put the Thrawn trilogy in my reading queue. I’ve read them before, but the last time was sometime before Disney put out The Last Jedi. Once upon a time, as a young Star Wars fan, I thought that the prequels had completely overturned a lot in Star Wars novels written before The Phantom Menace.

A quick picture of a segment of my desk right now.

Now that I’ve finished re-reading Heir to the Empire, I’m left thinking that I really didn’t have the proper perspective at the time. In broad strokes, I think the Thrawn trilogy fits better with the prequels than the Disney sequels…

Theorems of two Kenneths

In some ways, the field of voting theory can be seen as having been shaped by two French mathematicians (Jean Charles de Borda and Marie Jean Antoine Nicolas de Caritat). The course of modern voting theory can largely be explained in terms of two theorems published in the 1950s by two Kenneths: The positive result of Kenneth May, and the negative result of Kenneth Arrow.

May’s theorem

Kenneth May.

May’s theorem, published in 1952, is simple and straightforward, which is why it is often overlooked. It can be described as follows:

If a voting system for deciding between two options always produces a winner…

Questioning an article that makes a statement.

Nathanial Rakich and Lauren Bronner recently published a feature titled Advantage, GOP on FiveThirtyEight. The thesis of the piece is that the deck is stacked in favor of the Republican Party. This is a dangerously wrong simplification, and it exaggerates the degree to which the system is undemocratically stacked in favor of the GOP.

And it’s not just the Senate — the Electoral College, the House of Representatives and state legislatures are all tilted in favor of the GOP.

It is dangerous for two reasons. Democrats are given a reason to discount elections as illegitimate and disengage from the democratic…

When majority votes can’t solve the problem.

Three people come together to try to make a decision — perhaps something as simple as what to have for dinner. The first suggestion made is spaghetti, but it turns out that two of them would rather have pizza. Then one person suggests lasagna would be better than pizza, and is quickly seconded.

But, adds the second, they would rather simply have spaghetti than lasagna. The third agrees. The first person groans in frustration and picks up a Chinese takeout menu. …

A brief introduction

In a nutshell, voting theory, also known as social choice theory, is the theory of how to go from a set of individual desires to a common social outcome. Each one of these methods is known as a voting system or voting rule. For example, most jurisdictions within the United States use either plurality voting or a plurality with majority runoff. Maine has adopted a system known as ranked choice voting (previously known as instant runoff voting).

Three books I unequivocally recommend on the topic of voting theory. Read from left to right. Poundstone’s book is a good lay introduction to what the field is about without going into technical detail; Hodge & Klima’s book is an excellent technical introduction; Saari’s book is useful for deeper understanding.

This area is closely related to decision theory and game theory. Voting theory is mathematical, relying on breaking down different voting systems logically…

Why the physical short is bad.

The recent Gamestop short squeeze highlighted short selling. As I’ve explained here at slightly greater length, a short sale is basically selling an IOU note denominated in stock. After completing the short sale, the short seller holds some amount of cash and has the obligation to deliver a share of stock to another person at a particular point in time.

Standard explanation of a short. Emphasis added showing how the short seller has the same obligation whether or not the short is “naked.” Image remixed from 1 and 2. Original images by user Grochim on Wikimedia.

This is true both for “naked” short selling (theoretically illegal) and “covered” short selling (entirely legal). The difference with a “covered” short is that there is a small fee involved. This is sometimes known more precisely as a “physical short,”…

The simplest explanation of shorts you’ll read today.

At its most basic essence, selling short is selling an IOU note. There are several variations on how a “short sale” works, but at the end of the transaction, here’s the situation:

  • The short seller has cash.
  • The short seller owes someone else one or more shares of a specific stock.

That’s it. From the perspective of the short seller, they have effectively sold an IOU (“I owe you”) note denominated in shares of a specific stock. This is true for both “naked” shorts and “covered” shorts. …

Tomas McIntee

Dr. Tomas McIntee is a mathematician and occasional social scientist with stray degrees in physics and philosophy.

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store