In 2018, there have been several court cases where a group of voters have claimed they have been disenfranchised–that their vote didn’t count.

Click to read…

These cases are mostly brought by Democrats, who received a larger portion of the vote in a state, but placed fewer members in Congress or the state legislatures. This article (Nature, June 8, 2017) explains how math can be used to evaluate “fairness”, using objective measures that are easy to understand (e.g. such as comparing perimeters and areas of districts).

Activity: Use the internet to find details on these cases (choose one or more) and answer these questions:
1. How many “seats” were voted on?
2. Compare the party vote to the total vote, and calculate percentage of votes.
3. Compare the number of seats won to the total seats, and calculate the percentage of seats.
4. Discuss your sources (very important) and the results. As an example, here is a good article on the national level: Brookings Institute article on misrepresentation in Congress.

Here are pages 2 & 3 of the article from Nature, June 8th, 2017

Click for part 2.

Click for part 3.

by Adam Kucharski
(Basic Books 2016)

As a math major, I get a kick about the way gambling has been branded as the “Gaming Industry,” as if it were a productive activity for a successful society.  I don’t gamble because I know the odds. Most people sense that you really can’t win over the long term. But there are exceptions. Some have found ways to beat blackjack, roulette, lotteries, horse racing, online betting, and more. Mr. Kucharski does an excellent job of explaining how people have found these winning strategies, using probability data to identify deviations from randomness (e.g. a poorly crafted roulette wheel) and inaccurate odds that can be played for financial gain.

The author details many schemes dating back over 100 years. For example, in the 1890s, a Monaco newspaper published the results of a casino’s roulette spins—every spin—providing useful data to study the odds, right? Mathematician and statistical genius Karl Pearson was studying roulette wheel randomness and determined that the spin data was suspicious, because there were not enough “runs” of a color (e.g. 3 spins hit red numbers in a row). He was right. The reporters were just making it up the result. They only put effort in keeping the red/black ratio near 50%!

There are many more stories of systems and the people who discovered them. Modern systems tend toward computer based analysis—none seem particularly easy, but require significant work and time to exploit. Then, if you do find a system for winning, the casinos (or other venues) will lawfully ban you from gambling, as Edward Thorp, the “father of card counting” in the early 1960s, was banned from Las Vegas blackjack tables, and resorted to wearing disguises to sneak in.

There is a thorough reference section and index. My only suggestion for improvement would be to use more graphics. I highly recommend this book for curious gamblers, students, and those teaching statistics.

Teachers:
A good activity for statistics students might be to present, with graphics, a summary of how a particular gambling system worked, and how some of these methods resulted in game rules changing, such as adding cards to the blackjack “deck.”