I’m a mathematics teacher, and I have some arithmetic problems for you to solve.

1. Mitt drives to the beach and back.

Q. Mitt Romney drives 50 miles from his home one of his homes to the beach and back one summer, with or without a dog on the roof. He averages 50 miles an hour on the way out, and he averages 10 miles an hour on the way back. What was Mitt’s average speed on the road?

A. It was 16-2/3 mph¹, but Mitt’s campaign insists he’s no slowpoke and that he averaged 30 mph. (They also say the trip explains his tan.)


2. “Going Dutch” with Mitt.

Q. You and Mitt Romney have lunch together at Chick-fil-A. The bill is $15, and he only has a $10 bill, so he pays 2/3 of the bill. Later, you have dinner together at the country club, and the bill is $300. He puts in $100, and this time you pay 2/3 of the bill. Are you even-Steven?

A. Of course not, but Mitt says you are, because he paid 1/3 once and 2/3 once.


3. Mitt Sees Red.

Q. In the four squares below, about what percentage of the area overall is red?


A. About 10%. Certainly way less than half. Mitt disagrees. He says the percentage of red is over 75%, and he surprises you by providing actual details instead of saying he has a secret calculation that solves the problem and comes out the way he wants it to. He says there are three 100% red squares and one 5% red square, for an average of 305%/4 or about 76%. Ann tells you to stop giving him a hard time.


Earlier today, the Romney campaign website posted a letter from PriceWaterhouseCoopers “PWC” LLP summarizing the Romneys’ tax returns for the years 1990-2009. The carefully-worded letter² states that

The average of the annual “effective federal personal income tax rates” as computed based on the returns as prepared during the period is 20.20%.

PWC computed each year’s “effective federal personal income tax rate” as instructed by the Romneys.

As you requested, we compute each annual “effective federal personal income tax rate” as total taxes owed divided by adjusted gross income as shown on the federal income tax returns as prepared.

First of all, the Romneys’ “adjusted gross income” (AGI) may be less than what most of us think of as simply “what the Romneys made.” For example, the expenses of carrying on a trade or business (such as dressage) can be deducted from total income. The Romneys’ tax rate on their total income is lower than that on their adjusted gross income. Maybe a little, maybe a lot.

More importantly, however, is how Mitt and Ann instructed PWC to compute a number they could call an “average.”

Despite appearances, no one has said that the Romneys paid 20.20% of their adjusted gross income in federal income taxes during the period 1990 – 2009. They probably paid less.

The 20.20% figure is not the Romney’s federal income tax rate for income they earned during the period 1990 – 2009. It’s the average of 20 separate annual rates. Mathematically, it’s a weighted average of their annual rates.

If you think the average of 20 annual rates is the same as the 20-year average annual rate, you’re wrong. By that flawed logic, Mitt averaged 30 mph, you and he are even-Steven for splitting meals, and the colored squares in the picture above are 75% red. Go away.

Further blurring the issue, the campaign today also posted a letter from Brad Malt, the “trustee of the Romney’s [sic] blind trust,” about Mitt’s taxes. Malt tries to say that PWC calculated something that it didn’t calculate.

Regarding the PWC letter covering the Romneys’  tax filings over 20 years, from 1990 – 2009:

Over the entire 20-year period, the average annual effective federal tax rate was 20.20%.

Malt omitted two short and crucial words: of the. PWC did not say that Romneys’ average annual effective federal tax rate was 20.20%. They said that if you average the 20 separate effective rates on their 20 federal tax returns, you get 20.20%. It’s a silly thing to calculate, but it’s what the Romneys told them (and presumably paid them) to do.

The Romneys’ overall tax rate might have been lower than 20.20%. It might have been higher, too, but given the outrage over the relatively low rates they pay compared to working Americans, if it were higher, he’d have said so. And Mitt won’t release his tax returns. We can only assume the worst.

If you value the truth, vote for Barack Obama on November 6, 2012.

¹ Let’s figure it out. Mitt drove a total of 100 miles. It took him 1 hour (50 miles at 50 mph) to drive the first half of the trip and 5 hours (50 miles at 10 mph) to drive the second half. He drove a total of 100 miles in 6 hours, so his average speed was 16-2/3 miles per hour.

² The letter is signed personally, in blue, by PriceWaterhouseCoopers LLP, because why wouldn’t they sign it? Corporations are people.

2 Responses to “Mitt’s Arithmetic Problem”

  1. David Levine Says:


    I think you missed one. Reading the letter, from PWC about charitable donations, I propose a new math problem.

    Mitt Romney has $3 in his pocket. He generously gives $1 to a down-and-out dressage competitor. What percentage of his money did he give? According to Mitt, he gave 50% because he is computing his percentage by dividing his donation by his ADJUSTED assets.

    Even better if he gave $2, he would have given 200%. That’s so much more than the 110% that most coaches ask of their players.

  2. CTo Says:


    I love your 200% suggestion. Since when the money paid to churches can also be compared or considered as tax? Isn’t it true buying your way to the heaven a business or for profit activity, assuming all money contributed to church does not generate more profit for the church…Does the church now have elected officers who are not gender, age, faith, racial, and class bias?

    Who is in-charge or managing the organization, may I ask?

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† I (†) am a dagger (pl. daggers, Fr., obèle). I am a good friend of the asterisk; in fact, my alternate English name, obelisk, rhymes with asterisk. Respect my friend. My homograph is a weapon used for hitting, stabbing or thrusting.

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* I (*) am an asterisk (pl. asterisks, Fr., astérisque). I rhyme with obelisk, not Vercingetorix or candlestick. I am not an asterick. Please, folks. This is who I am. Respect me.

One Response to “A Very Important Footnote*”

  1. Steve Kass » A Followup Footnote† Says:

    […] I (†) am a dagger (pl. daggers, Fr., obèle). I am a good friend of the asterisk; in fact, my alternate English name, obelisk, rhymes with asterisk. Respect my friend. My homograph […]

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For your entertainment, some choice quotes from Carl Paladino’s campaign web site, most with pithy commentary. Would that it were all a joke.

  • “Carl will work for charter schools for the poorest of our urban students as an alterative to dysfunctional schools of today.” Unfortunately, this is our universe, not an alterative one.
  • “Carl will consolidate schools to countywide districts to eliminate redundancy of administration and allow for more funds to be devoted to lowering class sizes and excellence.” If anyone knows how to lower excellence, CP does.
  • “This is – and more – long, long overdue.” [No pithy commentary.]
  • “I am particularly incensed Assembly Speaker Sheldon Silver’s no-show job at a high-priced personal injury law firm.” We should all be incensed CP’s illiteracy. I am.
  • “(See more HERE.)” (where HERE is not a link). Thank you no. I don’t care to see more.
  • “Carl strongly support the State University at Buffalo 2020 plan and similar programs for other higher education institutions in the State to be able to grow in both size and student population with out State intrusion.” I can has cheezburger, with out State intrusion, please.
  • “[Candidate for lieutenant governor Greg Edwards] graduated Panama High School in 1978 and then went to Allegany College in Pennsylvania.” Where correctly spelling the name of the college is apparently not a requirement for graduation.

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In a segment of Pro Se, today’s installment of This American Life, radio host Ira Glass spoke with Francisco Calderon, a New York district attorney, about a case he lost¹ to a defendant who represented himself in court. I’m not a regular listener, and based on today’s episode, I won’t become one. The show’s web site describes the segment, Disorder in the Court, this way:

Earlier this year, admitted drug user Jorge Cruz decided to act as his own lawyer in an Albany, New York criminal court. Impossibly, he won. Ira talks to Francisco Calderon, the assistant district attorney who prosecuted the case, about what it feels like to lose to an amateur.

Perhaps I have too much faith in the American legal system. I believe that judges and juries base their decisions on the evidence and on the law. Absent information to the contrary, I assume the jury didn’t find the prosecution’s evidence sufficient to convict Cruz. Glass didn’t mention this possibility, but the facts and rhetoric in Glass’s interview with Calderon suggest it.

The rhetoric (which offended me) matched the website’s subjective description of the segment. “… admitted drug user … Impossibly, he won.” Because Cruz was an admitted drug user, Glass seems to imply, he must have been guilty.

Glass never touched on the question of whether Cruz was guilty, nor on the legal standard of reasonable doubt. Calderon said he never “connected” with the jury, who he thought sympathized with the picture of Cruz as a poor drug addict who couldn’t have afforded the $5,000 worth of drugs he was accused of possessing. The felony-weight cocaine was seized from under a mattress in a hotel room registered to Cruz’s brother. Cruz admitted to using drugs in the room, but he claimed not to know there was a stash in the bed. Cruz’s brother and a third person in the room pleaded guilty to felony drug charges and were sentenced without a trial.

Calderon worried that the more he objected to Cruz in the courtroom (and no doubt he had valid objections to Cruz, who had no legal training to know what sort of questioning was allowed), the more he’d come across as a bully. Glass analogized that juries expected something like a boxing match between well-matched fighters.

A trial isn’t a fistfight between lawyers where the jury decides who landed the best uppercut. Sure, a lawyer who can’t “land a punch” might prevent the jury from understanding the facts, but (television notwithstanding) the defendant is the one on trial, not the lawyers.

If life were as simple as “he’s a drug user, he must be guilty,” we wouldn’t need much of a legal system, nor would we have the Sixth Amendment to the U.S. Constitution.

In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the State and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him; to have compulsory process for obtaining witnesses in his favor, and to have the Assistance of Counsel for his defence.

Jorge Cruz availed himself of his constitutional right, and he chose to represent himself. He was acquitted by the jury on the most serious charge, but I’m not convinced his choice to serve as his own attorney was an important factor in the outcome.

Disorder in the Court fits the American narrative that champions the underdog and devalues experience, education, process, and authority. (The irony² isn’t lost on me that this same narrative helps boost the blogger ego.) Yet at the same time, it whispers a contrasting message that authority is always right, and that when it fails, something else is to blame. Taken only a bit further, these are the narratives that give rise to and sustain Joe the Plumber, Glenn Beck, and Sarah Palin – narratives that are as resolutely American “as apple pie,” but that verge on the truly distasteful and dangerous.

Other segments of Pro Se were also disappointing. In Swak Down, a former student teacher tells how he addressed a violent incident by deciding to “forgo all the rules, and administer frontier justice on the fly,” believing (still) that no other approach would have worked. In Underling Gets an Underling, a former production assistant tells the story of how she handled her frustration about how she was being treated: she placed a phony Craigslist ad for her own production assistant, hired an unwitting fellow, and then treated him as unfairly and dishonestly as she felt her boss was treating her.

This American Life may or may not be representative of American life, but it left a bad taste in my mouth today. It needs a big dash of opprobrium at least.

¹ A contemporary account of the case in the Albany Times Union notes that while Cruz was acquitted of felony cocaine possession, the jury did find him guilty of misdemeanor heroin possession, and he was sentenced to time already served in the Albany County jail.

² I know, I know.

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