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April 15th, 2019 (Permalink)

Charts & Graphs: The IRS Baked Two Pies for Tax Day

The two pie charts below appear near the end of the booklet of instructions1 for filling out and filing the 1040 tax form put out by the Internal Revenue Service that is due today. The charts serve no purpose in helping figure taxes, and most taxpayers probably ignore the page where the charts occur in the rush and hassle of preparing a return. Instead, the charts give information on what percentage of the government's income comes from income taxes, and what those taxes pay for. Income & Outlays

These charts are three-dimensional pie charts which, as I've pointed out previously2, can be misleading. These are particularly bad examples of this type of chart since the angle from which the "pies" are portrayed is quite acute. This means that the areas of the pies are distorted, so that some look larger in comparison to others than they should. Furthermore, these are "deep dish" pies with thick edges that make the wedges facing the viewer appear to be larger than similarly sized wedges at the back of the pies, whose edges cannot be seen.

For instance, in the "Income" chart, the wedge for "Corporate income taxes" looks almost the same size as that next to it for "Borrowing to cover deficit", despite the fact that the former is only 7% of the pie while the latter is 17%. Similarly, the wedge for "Social security, Medicare,…" behind them represents almost a third of income, but appears to the eye to be about a quarter.

In the "Outlays" chart, the wedge facing the viewer representing "National defense,…" appears to be considerably more than 20% of the pie. In contrast, the largest segment, labelled "Social security, Medicare,…", is over twice the percentage of that for "National defense,…", but doesn't appear to be twice the size.

I don't suppose that these charts were intentionally constructed to mislead, especially since the percentage for each segment is included next to its label. However, there's not much point in baking a pie chart if you have to read a bunch of numbers in order not to be fooled. Instead, a couple of tables listing the parts and their percentages would have conveyed the same information with no risk of misleading the reader. If we must be served with pies, then the angle from which we view them should be close to 90°.


  1. P. 112. See also: "Major Categories of Federal Income and Outlays for Fiscal Year 2017", Internal Revenue Service, accessed: 4/14/2019.
  2. Charts & Graphs: Three-Dimensional Pie, 5/5/2013.

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March 31st, 2019 (Permalink)

Recommended Reading

With tax day rapidly approaching, here are some ways to spend your time instead of filling out forms:


  1. Check 'Em Out, 7/2/2007.
  2. Thanks to Lawrence Mayes for calling this article to my attention.

March 30th, 2019 (Permalink)

New Book: Thinking in Bets

…[T]his is not a book about poker strategy or gambling. It is, however, about things poker taught me about learning and decision-making.1

Annie Duke is not the usual suspect for a new book citation on this weblog; here's how she describes herself in her book's Introduction:

When I was twenty-six, I thought I had my future mapped out. … I had graduated from Columbia University with degrees in English and psychology. I had attended graduate school at the University of Pennsylvania, where I won a fellowship from the National Science Foundation, earning a master’s and completing my doctoral course work in cognitive psychology. But I got sick right before finishing my dissertation. I took a leave of absence, left Penn, got married, and moved to a small town in Montana. Not surprisingly, my NSF fellowship didn’t cover my cross-country experiment in adulting, so I needed money. My brother Howard, a professional poker player…, suggested I check out the legal poker games in Billings. … My plan was to earn some money during this break from school, stay on the academic path, and continue playing poker as a hobby. My temporary break turned into a twenty-year career as a professional poker player. … To say that I had strayed from the academic path might seem like an understatement.1

I don't play poker, so I'd never heard of Duke before I somehow stumbled across this book, whose subtitle is: "Making Smarter Decisions When You Don't Have All the Facts". I would only add that you never have all the facts so the book should cover all decision-making.

The title "Thinking in Bets" seems to be a way to emphasize the importance of thinking in terms of probabilities. This also seems to be the point of the title of the first chapter: "Life is Poker, Not Chess". Poker differs from chess in two ways: luck plays a role in poker, but not in chess; you can't see the cards your opponents are holding in poker, but you can see all of your opponent's pieces and their positions in chess.2 Thus, poker is more like life than chess is, since both chance and ignorance play a large role in what happens in life.

Reading a book is a bet: you bet your time, attention, and effort in hopes that the rewards that you receive will be worth it. There's uncertainty in that you won't find out whether the book was worth it until you've made the effort. I haven't read this book yet, so I don't know whether it's worth reading, but based on what I've looked at so far I would bet on it.3


  1. Annie Duke, Thinking in Bets: Making Smarter Decisions When You Don't Have All the Facts (2018), "Introduction".
  2. Duke makes this distinction in the following interview: "Poker Champion Annie Duke on Making Smart Bets in Life, Politics, and Football", Reason TV, 2/20/2018. This is not to say that uncertainty plays no role in chess: you can't read your opponent's mind, so you can't be certain of his or her future moves. Also, the game is so explosive combinatorially that it's practically impossible, even for supercomputers, to look more than several moves ahead in a game.
  3. I also based my decision on the following interesting interview with Duke about this book: "Annie Duke: 'Thinking in Bets'", Talks at Google, 6/21/2018.

March 12th, 2019 (Permalink)

Three-Dice Monty

Last month, "Three-Card" Monty*, the carnival con artist, shamelessly attempted to swindle a young couple on Valentine's Day using a pair of tricky dice! Now, he's back in his booth on the midway, but this time he has three strange dice.

Imagine that you approach Monty's booth and see on the counter before him three cubical dice: one colored red, the second white, and the third blue.

"As you can plainly see," Monty says to you, "these are three unusual dice. As you probably know, a standard die has one through six dots on its six faces. The number of dots on these dice range from one through nine, instead. Moreover, each of these nine numbers appears twice, both times on the same die. The numbers are distributed in such a way that each die has different numbers on its faces than the other two, so no number is shared among them. This means that when two of the dice are rolled against one another, they never tie. In every other way these dice are the same as standard dice: they're not loaded or gimmicked in any way.

"The first die has the numbers two, four, and nine, twice each on its six red faces. The second, white die has, instead, the numbers one, six, and eight. Finally, the last, blue die has the numbers three, five, and seven. The numbers on each die total thirty.

"Wouldn't you agree that they are evenly matched? I offer you an even money bet that the die I select will beat yours. That is, each of us will put up a dollar, each will roll his die, and the die that comes up with the highest number wins. Moreover, to be perfectly fair to you I offer you the first choice: you may select any one of the three dice and I will take one of the remaining two. What could be fairer than that?

"So, my friend," Monty finished, "which die do you choose?"

Is the bet that Monty is offering you fair? Should you accept or reject his wager? Assuming that you accept it, which die should you choose?

* In case you don't know Monty: he is a trickster, but he always speaks the exact truth. However, this does not mean that he necessarily tells the whole truth. Also, while he is a sharpster, he prides himself in not doing any sleight-of-hand. For previous puzzles involving Monty, see:

March 8th, 2019 (Permalink)

Rule of Argumentation 41: Be as definite as possible!

Before proceeding to this month's rule, I want to mention something that I should have explained earlier in this series, probably in the introduction: Each of these rules is a heuristic or "rule of thumb". In other words, there are exceptions to all of them, that is, situations in which you should not follow them, but such situations are exceptional.

Previous rules in this series were rules that governed the overall process of arguing: appealing to reason, acknowledging one's own fallibility, and focusing on arguments themselves rather than arguers. This is the first rule that deals with the content of argumentation. It says that the claims and arguments you make should be as definite as possible.

In order to be as definite as possible myself, I will explain what I mean by both "definite" and "possible":

Next Month: Rule 5


  1. Previous entries in this series:
  2. Unfortunately, there doesn't appear to be a synonym for "unambiguous" lacking a negative prefix, so I choose the ambiguous "definite" so as to remain as affirmative as possible in this rule.
  3. For more on the types of ambiguity, including subtypes and examples, see the entry for the fallacy of Ambiguity.

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