# The Legal Analyst: A Toolkit for Thinking about the Law

By Ward Farnsworth | Go to book overview

30 The Base Rate

We just talked about a principle of probability—the product rule—that is easy to grasp, though sometimes also easy to forget. There is one other such principle that we need to talk about. It’s usually called the base rate.

After much study, the police determine—never mind how—that for every 100 people who ride on an airplane, one of them, on average, is carrying drugs. They bring a police dog named Merlin to the airport to help find the culprits. Merlin sniffs every passenger who exits a plane, and he barks when he smells drugs. Merlin is highly skilled. He never misses drugs when they’re present. He occasionally is prone to giving false alarms, but not often; if no drugs are present, he is 90 percent likely to keep quiet. Smithers steps off the plane, and Merlin barks at him. How likely is it that Smithers is carrying drugs?

I pose this question because many people get it wrong; you should very much want to get it right, because it comes up in different ways all the time. It seems at first that Smithers probably has drugs. Merlin makes mistakes only 10 percent of the time; if he barks, Smithers is 90 percent likely to be carrying drugs, isn’t he? No. The chance that Smithers has drugs is about 1 in 11 (or 9 percent, if you prefer). The trick is that you have to remember not just Merlin’s chance of being right but also the background chance that Smithers has drugs in the first place, which is low. Think of it this way: for every 100 passengers that come off the plane, only one of them will be carrying drugs. Merlin will always bark in those cases. But then when the other 99 passengers come off the plane without drugs, Merlin also will bark some of the time—10 percent of the time, to be exact. So out of this batch of 100 passengers, maybe Smithers is the one with the drugs, but chances are better that he’s one of the 10 Merlin will accuse wrongly. Here is another way to express the point: when you hear of a 10 percent rate of error, you need to carefully ask, 10 percent of what? It might seem to mean that 1 out of every 10 people Merlin barks at will be innocent, but in fact it means that 1 out of 10 people who are innocent get barked at anyway—which is not the same thing. So to make sense out of Merlin’s barks, you need to know how likely each person in the pool is to be guilty in the first place. You

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The Legal Analyst: A Toolkit for Thinking about the Law

• Title Page iii
• Contents v
• Preface vii
• Acknowledgments xi
• Part I - Incentives 1
• 1 - Ex Ante and Ex Post 3
• 2 - The Idea of Efficiency 13
• 3 - Thinking at the Margin 24
• 4 - The Single Owner 37
• 5 - The Least Cost Avoider 47
• 6 - Administrative Cost 57
• 7 - Rents 66
• 8 - The Coase Theorem 75
• Part II - Trust, Cooperation, and Other Problems for Multiple Players 85
• 9 - Agency with Eric Posner 87
• 10 - The Prisoner's Dilemma 100
• 11 - Public Goods 109
• 12 - The Stag Hunt 117
• 13 - Chicken 126
• 15 - Voting Paradoxes 144
• 16 - Suppressed Markets with Saul Levmore 152
• Part III - Jurisprudence 161
• 17 - Rules and Standards 163
• 18 - Slippery Slopes with Eugene Volokh 172
• 19 - Acoustic Separation 182
• 20 - Property Rules and Liability Rules 188
• 21 - Baselines 198
• Part IV - Psychology 207
• 22 - Willingness to Pay and Willingness to Accept- The Endowment Effect and Kindred Ideas 209
• 23 - Hindsight Bias 218
• 24 - Framing Effects 224
• 25 - Anchoring 230
• 26 - Self-Serving Bias, with a Note on Attribution Error 237
• Part V - Problems of Proof 247
• 27 - Acoustic Separation 249
• 28 - Standards of Proof 257
• 29 - The Product Rule 273
• 30 - The Base Rate 281
• 31 - Value and Markets 294
• Notes 305
• Author Index 329
• Subject Index 335
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