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## The Do-Nothing Alternative March 16, 2015

Posted by tomflesher in Examples, Micro, Teaching.
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Consider the following situation: You are at a casino. You have a crisp new \$100 bill in your pocket and an hour before your friend arrives. There are several options available: blackjack, poker, and slot machines. Each has its advantages and disadvantages. Blackjack offers a 45% probability that you will double your money over the next hour, but a 55% probability you will lose it all. Based on your understanding of statistics, you know this means you should expect to have about \$90 at the end of the hour. Poker is a better proposition – since it is a game of skill, you have a 60% chance of earning an extra \$50 (for a total of \$150), but a 40% chance of losing all of your money. That means you can expect to have about \$90 in your pocket at the end of the hour. Slot machines, to go to the other extreme, are a highly negative expected-value proposition. You stand a 1% chance of winning \$1000, but a 99% chance of losing all of your money. As a result, you could expect to have about \$1 in your pocket at the end of the hour.

Thinking like an economist, you quickly winnow your options down to blackjack or poker, since you cannot abide such a risky proposition. Then, however, you’re stuck – the expected values are the same. Which game is it rational to play?

Similarly, consider this problem raised in a freshman course on ethics: You are on your way out of a coffee shop carrying a double shot of espresso and a \$1 bill you received as change. Two homeless people, one man and one woman, each step toward you and simultaneously ask you for the dollar. Since you don’t have any coins, you cannot split the value between the two people. Who should you give your dollar to?1

What do these two situations have in common? In each of them, you are attempting to choose between two options that result in negative consequences for you. In the gambling scenario, you have two options, each with the expectation of losing \$10. In the coffee shop scenario, you have two people each asking for \$1. In neither case is there a compelling reason to choose one option over the other. The underlying assumption, though, is that we must choose an option at all.

The do-nothing alternative is often (but not always) a hidden option when making choices. For example, in the gambling scenario, you have the option to literally do nothing for an hour until your friend arrives. This leaves you \$100 with certainty. In the coffee shop scenario, you have the option to politely refuse each person’s request, leaving you free to keep your dollar. Not every situation allows a do-nothing option; for example, a baseball manager faced with the option of starting his worst starting pitcher or a pitcher who is usually used only in long relief cannot opt to simply start no pitcher. However, a voter who is disgusted with all available candidates may bemoan his “forced” vote for the lesser of two evils without acknowledging that he has the option simply not to vote at all. The do-nothing option is often low-cost but has low returns as well, making it a great way to avoid choosing the best of a bad lot, but a lousy choice for a firm seeking growth.

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1 This was met with considerable debate about the probability that the homeless woman had children.

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