The magnitude of problems (apropos of #librossiniva)

“A million dollars, a billion, a trillion, whatever. It doesn’t matter as long as we do something about the problem”¹, but how do you solve the problem if you don’t know its magnitude?

I don’t know if you’re familiar with Godwin’s law about debates on the Internet, the one that says:

“As an online discussion grows longer, the probability of a comparison involving Nazis or Hitler approaches one”²

The corollary was supplied by Richard Sexton:

“It follows that a USENET discussion has run its course when one of the participants mentions Hitler and the Nazis.”

In other words, once somebody brings up Hitler and Nazism the discussion no longer makes sense. It has gone off the rails.

I want to propose a similar law, but for the discussion about VAT on books (the #librossiniva, “books without VAT”, campaign):

“As the discussion about VAT on books in Chile grows longer, the probability that someone will botch the arithmetic approaches one.”

This argument over VAT on books in Chile is ancient. I remember that in the late 80s it was the writer Enrique Lafourcade’s battle cry. I suspect, and I’m sure there must be evidence, that somebody back then made the same classic mistake: to calculate the net price of the book, they subtracted the VAT percentage from 100. Online alone I’ve seen it three times, and although I have the links I’m not going to post them, to protect my readers from the horror :) ³.

The point is very simple: if the book is worth 100, and VAT in Chile is 19, the amount the buyer pays, the one that shows up on the invoice or receipt, is $119.

The trouble comes when the calculation is done backwards. Since VAT is 19%, the reasoning leads them to subtract 19% from the invoice amount. Let me show you the complicated inverse calculation that almost always gets done:

Price of the book with VAT: 119
19% of the price above: 22.61
Price of the book without VAT: 119 - 22.61 = 96.39

And with that they have magically knocked 3.61 pesos off a book that cost $ 100.

Believe it or not, I know plenty of educated people, with university degrees, who do this same wrong calculation (including engineers, sadly).

When Luzifer (Mario Waissbluth) answers Jodorowsky’s questionnaire and is asked what miracle he would like to witness, he replies that he would like to see the day when every graduate of Latin America’s schools understands what they read and knows how to calculate a percentage.

Now, someone will argue that this is irrelevant, that 3 pesos more or 3 pesos less don’t matter as long as the problem of VAT on books gets solved. The truth is that it does matter.

I insist: how can you solve a problem if the people debating it have no idea of its magnitude?

And that happens with many public debates in our country (and in every country). It happens with the debate over the minimum wage, the profitability of the isapres (the private health insurers), the nationalization of lithium, or energy savings. Again and again arguments are brandished that rest on sloppy arithmetic.

Numbers don’t lie, right? As I showed a few years ago (in the post numerical deceptions), a badly framed calculation can be the foundation for the ruin of a public policy. What’s more, numbers can be presented in such a way that they make us take decisions that can be very costly (one example is anchoring, which I covered earlier).

In general I’m in favor of there being no taxes at all. A VAT of 19% on anything is obscenely high. It is real oppression against us, because we are the ones who pay it. If we are going to fight to lower taxes, let’s do it for real: get rid of VAT, or lower it to more reasonable rates.
Why fool ourselves and lie to ourselves yet again? Behind these campaigns is the desire not to have to file VAT. There is no altruistic spirit and no wish for people to read more. That is the plain truth.

Cutting VAT on books has always been presented as a solution to the problem of how little people read in Chile. The argument goes that people don’t read because such a high VAT discourages buying books. A simple look at the price of books in other countries reveals that this argument isn’t true. We can come up with many other reasons that better explain why people don’t buy books, from habits to the inability to understand them. I think the explanation is very simple: the book market is small and the money is in textbooks and educational books, which people are forced to buy.

This small market leads publishers and booksellers to set high margins (yes, sometimes over 100%). Look at the big bookstores with their roomy, luxurious spaces in the rich neighborhoods of our city. You are not paying just for the books. If VAT on books were eliminated in Chile they would still be expensive, and few people would keep buying them, I can assure you of that. Let’s admit it: in Chile books are not much appreciated.

But this kind of campaign is a first step, the argument goes. Well, it seems to me it would be better to take other steps first. Like improving reading comprehension and promoting critical reasoning (logical and arithmetical).

The day people know how to properly size up the magnitude of their problems they will be able to face them properly, and that starts with knowing how to handle numbers.

And don’t give me stories about reader altruism.