## Beginning of article

```INTRODUCTION
I.   THREE MODELS OF TAX COMPLIANCE
A. Simple Costs and Benefits
1. The model
2. Evaluating the model
B. Expected Value
1. The model
2. Evaluating the model
C. Expected Utility
1. The model
2. Evaluating the model
II.  THE UNCERTAINTY MODEL OF TAX COMPLIANCE
A. Motivating the Uncertainty Model
B. The Uncertainty Model
1. The certainty component
2. The uncertainty component
3. Combining the components
4. Weighing outcomes
5. A tax compliance example
III. THE UNCERTAINTY MODEL'S USEFULNESS FOR TAX LAW
A. Attitudes Toward Uncertainty
B. Manipulating Uncertainty
D. Future Research: Identifying Attitudes Toward Uncertainty
E. The Simplicity Objection
CONCLUSION
```

The most rational man I ever met, whom I shall call Ysidro, determined his own ... preference[s].... When told that he did not satisfy all of the ... axioms [of game theory], he replied that he thought it more rational to satisfy his preferences and let the axioms satisfy themselves.

--Paul Samuelson (1)

INTRODUCTION

Imagine you are offered a choice between, on the one hand, \$100, or, on the other hand, the opportunity to bet on a coin flip, where you will get \$50 if the coin comes up heads and \$150 if it comes up tails. If you are like most people, you prefer the certain \$100, even though the risky choice has the same expected value. (2) Now imagine another choice: the coin flip game, which gives you an even chance at \$50 or \$150, or a different game, which will give you an unknown chance at \$50 and an unknown chance at \$150. Most people pick the coin flip, the game that features a known probability (that is, an even chance of winning), over the second game, which presents an unknown probability. (3) The first choice, between \$100 and a coin flip, tests how you feel about risk, that is, a known probability. The second choice, between the coin flip and the other game, tests how you feel about uncertainty, an unknown probability.

A taxpayer trying to decide whether to comply with the tax law faces uncertainty, not risk. He does not know whether he will be audited by the Internal Revenue Service (IRS), and perhaps he does not even know whether his tax position is correct as a matter of law. And he also does not know the chance that he will be audited, or the chance that his tax position is correct. If the IRS were rolling dice to determine whether to audit the taxpayer, the taxpayer would know the chance that he would be audited (assuming he knew that the IRS's dice were not weighted). If, for example, rolling a pair of sixes would trigger an audit, the taxpayer would know that he had a 1 in 36 chance of being audited. He would not know how the roll of the dice would turn out, but he would know the chance that the roll would go against him. If a roll of the dice determined whether a taxpayer would be audited, and the taxpayer knew that, the taxpayer would be making a decision under risk--an unknown outcome with known probabilities.

Rather, when the taxpayer decides whether to comply, he grapples with a decision more like the decision of how much to bet on the outcome of a football game. Not only does the taxpayer not know who is going to win the football game, but he also does not know with certainty the chance that a given team will win. And when the taxpayer decides whether to comply with the tax law, not only does he not know whether he will be audited and his position will be disallowed; he also does not know the chance that he will be audited and his position will be disallowed. The taxpayer's decision whether to comply is thus a decision under uncertainty, an unknown outcome with unknown probabilities.

Many people are averse to uncertainty, both in general (4) and in the tax compliance context. For example, …