The Source of Blackstone's Intuition:
Larry Solum links to a provocative paper, The Source of Blackstone's Intuition: Why We Think it Better to Free the Guilty than to Convict the Innocent, by Samson Vermont. The gist of the argument is that our intuition that it is better to let 10 guilty persons (or even n guilty men) go free than convict one innocent person is partly irrational because it is based on a "psychological quirk" — the greater mental accessibility of a false conviction than a false acquittal. I've just skimmed the paper, and it's pretty interesting. The problem, I think, is that there are lots of quite rational reasons to agree with the intuition. Samson acknowledges some of them in footnote 9, but there are others, such as the uncertainty of whether the theories of punishment work in a particular case. Without knowing the relative significance of the rational and irrational as an empirical matter, it's hard to assess Samson's argument. Nonetheless, it's an interesting paper.
Unintended consequences: If police and prosecutors had to satisfy a lower standard of proof, they would surely convict some guilty people who'd have gotten off otherwise. But on the other hand, they would investigate all cases less thoroughly. So they would actually fail to convict the really-guilty scumbag we nail under the current n > 1 system, since an innocent party would prematurely take the rap.
China, for example, is a justice system with virtually no false acquittals (probably n much less than 1). The closing anecdote from the A. Volokh paper linked by Orin:
Maybe for society overall. (Although n=99 is admittedly a tough sell...)
Saving the Innocent?
Saving the Innocent? (Part II)
These numbers are expectation values, e.g. a particular system will allow on average some (unknown) 99 guilty to go free in order to avoid convicting some (equally unknown) innocent. As such, they are as meaningless to the canonical person in the same way as other expectation values derived from enormous ensembles, such as the expectation value of the number of your children (2.1 or so), the expectation value of a lottery ticket (zip), and your life expectancy (varies). People do not make decision based on these numbers.
What they do make decisions on is beliefs in probabilities. In this case, they probably compare the probability of conviction of the guilty and of the innocent. As long as the probability of the former is enough higher than the latter, they're happy.
Assuming some competence in your police force, there will be more guilty than innocent that are charged, and this necessarily means a larger number of guilty will get off than innocent will be convicted. For example, if P_convict(guilty) = 99%, P_convict(innocent) = 1%, N_charged(guilty) = 1000 and N_charged(innocent) = 100, then (a) most people will feel this is a very effective legal system, but indeed (b) 10 guilty guys will get off and 1 innocent guy will be wrongly convicted. Big deal. This is all amusing statistics, but hardly impacts actual decision making, since that will focus on P_convict.
Another, similar reflection is that people are exquisitely sensitive to low probability high payoff (positive or negative) events. That's why they buy more lottery tickets when the prize is higher, even though this is mathematically idiotic, since expected winnings decrease with the size of the prize, since the odds go up faster, in most lotteries, than the size of the prize. It also explains the unusually high profitability of selling insurance, but I digress.
Anyway, if a given legal system were tweaked to increase the (very small) number of wrongly-convicted innocents by even a small number, while decreasing the (much larger) number of unpunished guilty, people will be very sensitive to the large relative increase in wrongful convictions, and less sensitive to the small relative decrease in unpunished guilty. But what else is new? I'm amazed anyone in academia feels this is worth actual time and effort pontificating over.
To Splunge: The expectation of a lottery ticket is not zero. For the big multistate lotteries, it typically varies from $0.10 to $0.50. Since expectation is a sum of all possible outcomes weighted by their probability, a really large jackpot will give you significant expected value even though the probability is small. The problem (or benefit) with lottery tickets is that the variance is really high.
If you want to call lottery tickets 'worthless', you should use the 95% percentile outcome or the Value-At-Risk or something else other than expected value.
The reason is that the big American state lotteries are required by law to distribute a certain percentage of their ticket sales as prizes (typically 40%). Thus, if there is no winner, the prize rolls over to the following week. Each time the prize rolls over, the expected value rises, even though more people are buying tickets. It used to be that once every year or two some lottery would develop an expected value exceeding $1, making it a worthwhile but risky investment. Now, however, the odds are so low in MegaMillions that I haven't seen the expected value after taxes cross $0.50/ticket.
Note that since the odds are based on the # of balls in the drawing, additional ticket sales do not affect your odds of winning, but they do affect the odds that the winner will split the prize with another winner.
When looking at lotteries from sociological/economic perspectives, it is important to keep two ideas separate:
1. Lotteries, in their modern state-sponsored form, are a terrible proposition for the ticket buyer. Almost any other form of legal gambling is better. Certainly many forms of illegal numbers games are also much, much better bets.
2. Setting aside #1 for a moment, it is not necessarily irrational for many people to play the lottery. Assume you are 50 years old, have minimal job skills, and live below the poverty level. Assume you buy 2 bucks worth of lottery tickets every week. That's 104 bucks a year. In what way are you "better off" saving 104 bucks a year than playing it on an extreme long shot that could instantly vault you out of poverty? Is 104 bucks a year going to do that? I think not. So not all poor folks are fools or dupes of the powers that be. Sometimes waiting in that line to buy a lottery ticket at the 7-11 is economically rational behavior given the other possible uses that two bucks could be put toward.
As for the paper: I saw it on ssrn in, I think, a previous draft. The idea behind it is important: what kind of error rates in convictions is optimal, looking at the problem from various perspectives? I've often thought that this is where our death penalty jurisprudence went horribly wrong. The problem is not really with the need for more individualized consideration of sentencing factors (raised in a violent household, "retarded," "child" murderer, "racial disparities in application," etc.); these attacks on the death gained little traction with the American public, which continued to support the death penalty by large majorities. When opponents shifted gears and started focusing on factual innocence (Innocence Project/DNA evidence) we started to see a shift in opinion polls. People really are (it's good to see) squeemish about executing an innocent man. So the solution is a higher standard of proof in death penalty cases: some kind of "beyond any doubt" standard rather than "beyond a reasonable doubt." I'll look at the paper again; it struck me that the early version failed to place enough emphasis on the nature of the punishment vs. the "acceptable" error rate. Most of us don't worry much about a $70 speeding ticket handed out on the simple word of a cop who was following the alleged speeder. We do worry about a man being put to death on the same (single eyewitness) testimony ...
I especially howled when he tried to fit his data to trend functions (can't call them trend lines, as he is much to sophisticated to limit himself that way). And then he extrapolated using his two different trend functions. Add in a lot of snarky comments, like when Lot lost his wife and got condiments in return.
What bugs me the most is something this article shares with lower-quality empirical studies of "irrationality" -- it makes wild assumptions about what people "should" consider rational, and it treats people who may have different values or assumptions as if they are irrational.
For example, personally I would *much* rather be murdered by a previously-acquited murderer than be wrongfully convicted and executed -- being wrongfully executed would also destroy my good name, brand my children with shame, stop my life insurance from paying out, and use up most of my estate in paying for the defense. The real, rational, economic costs of wrongful execution are much higher than the costs of murder, and these should be factored in to any analysis of whether Blackstone is irrational or not.
As another example I would take the studies he cites about it being "irrational" to prefer no vaccine for a disease that kills 10 children rather than a vaccine that will kill a smaller number of children. IMHO, these poll results reflect less an evolutionary bias in our thinking and more a rational, modern skepticism towards things that experts tell us we should do. Perhaps all they mean is that when researchers tell subjects about a hypothetical vaccine with an assumed death rate, the subjects instead think about real-world medicines like Vioxx and Seldane, which caused many more deaths than were expected at the time of their approval.
Three problems with that analysis:
1. It may reflect DK's preferences, but probably not the preferences of most of his fellow citizens, who seem to favor captial punishment by a wide margin. That is, most of us don't want DK's preferences imposed on us.
2. The broad preference for capital punishment indicates a rational calculation, along these lines: I'm very unlikely to be falsely accused of a capital crime, but a wrongly acquitted murderer (or a murderer who has been paroled) is quite likely to commit another murder.
3. DK's assertion that the "real, rational, economic costs of wrongful execution are much higher than the costs of murder" is the faulty product of his incomplete analysis. Not only does he ignore the rational calculation made by proponents of capital punishment, but he also overlooks its deterrent effect, which I have addressed here.