Unexpectedly Intriguing!
August 5, 2008

Political Calculations Totally Vindicated

Shameless, Gratuitous Gloating to Follow!...

It's a banner day here at Political Calculations, as we declare an unexpected victory in our minor quibble with Jake at Econompic Data, in a matter that had even sucked Barry Ritholtz into the swirling vortex of the proper application of basic mathematics principles.

Thanks to a sharp-eyed reader, we're pleased to announce that we have a definitive, legal-precedent setting ruling in our favor in this dispute that actually comes as a setback for the Republican Party in the state of Arizona. Here's Capitol Media Services' Howard Fischer description of the situation (via the Arizona Daily Star):

Judge orders rewrite of sales tax analysis

PHOENIX — A state judge ordered late Friday that the description of a proposed tax increase for transportation be rewritten to exclude a calculation of how much the levy will increase.

The description is to be put into pamphlets mailed to the home of every registered voter.

Maricopa County Superior Court Judge Edward Burke said it may be "mathematically correct" to say that Proposition 203, which would boost state sales taxes from 5.6 cents on every dollar spent to 6.6 cents, equals a 17.8 percent increase in what people will pay in sales taxes.

But the judge said such calculations "are likely to mislead many voters."

He accepted the arguments by Paul Eckstein, the attorney for tax backers, that the figure was deliberately inserted by Republican lawmakers to convince voters to reject the levy.

Fischer goes on to explain why the Arizona state legislature provides plain-language explanations to accompany the actual language of proposed ballot measures, but we'll jump ahead to focus instead on the core elements of each party's arguments:

Mike Braun, who represents the Legislative Council, told Burke the law requires the panel to not only explain each ballot measure but also how approval would affect existing law.

He said it would be "helpful" to tell voters that whatever they are paying in state sales taxes would increase by 17.8 percent if Proposition 203 is adopted.

Eckstein, however, told the judge the accuracy of the calculation is beside the point.

"An analysis can be 100 percent accurate, and it can be unfair and misleading," he said.

Burke agreed.

For example, he said, raising the tax rate from one cent per dollar to two cents has an "absolute percentage increase" of 1 percentage point. But it has a "relative percentage increase" of 100 percent.

"Many voters are likely to confuse relative and absolute percent increases," the judge wrote.

To see the parallels between this story and our concerns regarding how Jake had presented unemployment data, let's review some basic mathematics. Namely, the basic mathematics associated with percentage problems.

Percentage problems involve the relationship between three separate components: the percent (or rate), the base (the value to which the rate is applied) and the resulting amount, which is the product of the rate and the base. The basic relationship between these three components may be expressed mathematically as follows:

Amount = Rate * Base

The following formulas illustrate how this math applies to both the state sales tax change and the unemployment data at the root of our own dispute:

Sales Tax = Sales Tax Rate * Retail Purchase Price

Number of Unemployed = Unemployment Rate * Number of People in Labor Force

As you can see, the components for the state sales tax example has a direct parallel component in the unemployment data example. The problem, as described by the judge in this case in non-mathematical terms, comes when the absolute percentages represented by the math above are confused with relative percentages. This is what we would call the percentage of a percentage problem.

In both cases, the relative percentage change of the calculated amounts were determined (the percentage change in sales tax in the example from the article and the percentage change in number of unemployed in Jake's case), which then were mixed in with the absolute percentages, using text in the sales tax example, and graphically in the case of Jake's unemployment data.

Because no distinction was being made in how the figures are determined in both cases, the end result is that the presentation of the information is misleading, even though it is "mathematically correct." And unless a higher court reverses the ruling, that distinction is now an established legal precedent.

Did we mention there would be shameless, gratuitous gloating? Purely optional on your part, but here you go...:

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