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

By Ward Farnsworth | Go to book overview

29 The Product Rule

How likely is it that two flips of a coin will both come up heads—and how do you know how likely it is? It is 25 percent likely. You know it because the chance that each flip will be heads is 50 percent, or .5; to get the chance that both flips will go that way, you multiply the chance of its happening each time: .5 times .5, which is .25, or 25 percent—the chance of two heads in a row. This is called the product rule: to figure out the chance of several probabilities all going a particular way, you multiply them by one another and find your answer in the product. That’s all the math you need to understand for this chapter. It isn’t much, but it’s important; the legal system sometimes has a surprisingly hard time remembering it.

In the previous chapters we talked about various standards of proof: principally proof beyond a reasonable doubt and proof by a preponderance of the evidence, the latter rule amounting to a likelihood of better than 50 percent that the plaintiff’s claims are right. But that sketch was too simple, for it assumed that there is just one issue in a case; in many of the examples we pondered, the one issue was causation—in plain terms, whether the defendant’s wrong (not bringing a rope onto the ship, or not going back to search for the missing sailor) made a difference. But in most cases there isn’t just one thing the plaintiff must prove. There is a list, known as the elements of the claim, and two or more of them may be in dispute. Think again of the forgetful sea captain we talked about last chapter. A member of his crew drowns. In an actual suit on these facts there might be two disputed things the plaintiff has to prove: that bringing a rope onto the ship would have made a difference, as we saw, and that it was negligent not to have a rope, which is a different point.

Well, now we have a problem. Let’s imagine that the jury thinks the plaintiff is 60 percent likely to be right about each of those issues. It sounds like the plaintiff should win—but perhaps that’s wrong. For how likely is it that the plaintiff is right on both points? If we apply the product rule we see that it is only 36 percent likely: .6 × .6=.36. So there appears to be a 64 percent chance that the plaintiff’s case is bad. Yet the plaintiff nevertheless will win, for juries typically are told to find for the

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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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