Mapping Problems

Abortion, Law, Morality

A lot of problems, in both law and moral philosophy, come from the attempt to map a continuous variable to a binary response. Examples:

Abortion

A one week old embryo is not a human being. A nine month old fetus is as human as a newborn baby. The transition is continuous. We have a hard time dealing with continuous categories, more or less rather than yes or no, as the heated arguments over abortion demonstrate. Few supporters of legal abortion, even those who set no limit on how late in the pregnancy it should be permitted, are willing to support infanticide, although it is hard to see any convincing argument for a moral difference between a nine month fetus and a newborn. Most of the laws supported and enacted by opponents of abortion only come into effect weeks or months after fertilization.

Violating Rights

Punching someone is an initiation of force, an assault. Turning on the light in your house a block away is not. Turning on the light results in photons striking someone a block away. One can imagine a continuous progression via a more and more intense beam of light from the light in your window to a megawatt laser beam. At what point does it become an assault, a rights violation?

A neighbor pumping water out of his well, some of which is flowing from under your land, a satellite going over your house, do not feel like trespasses. One can imagine a continuous transition from either of those to something that does. Absent continuous legal remedies or continuous moral judgement one ends up picking some arbitrary line, treating everything below it as zero, everything above it as one, and feeling uncomfortable with the result any time something is close to either side of the line. De minimis non curat lex.

Accounting

I sue you for a million dollars. If the court concludes that there is a .4 chance that I am in the right, I get nothing. If it thinks there is a .6 chance, I get a million dollars. All probabilities less than .5 are treated as zero, greater than .5 as one.

Accountants follow the same rule. If your accountant thinks the probability of your losing the suit is .4 he mentions the existence of the lawsuit in a footnote but does not treat it as a liability. If he thinks the probability is .6 he puts it in the accounts as a million dollar liability.

Why? An accountant is selected by, working for, the people running the company who may want him to fudge the accounts to mislead stockholders, investors, or tax authorities. One way of preventing that is to have accountants use simple rules wherever possible.¹ That explains many of the ways in which accounting substitutes a simple answer for a correct one, with the treatment of probability only one example. Others are the preference for cost price over market price and the reluctance to take account of intangibles, even important ones such as brand name reputation.

The Law

The severity of an offense is a continuous variable that can be continuously mapped to the severity of the punishment but certainty of guilt, also a continuous variable, is mapped in our legal system to a binary verdict: Guilty or Not Guilty. You are guilty of a tort and owe full damages if the probability of guilt is greater than of innocence, “a preponderance of the evidence.” You are guilty of a crime and get the full punishment if you are guilty “beyond a reasonable doubt.” In each case an arbitrary line divides fully guilty from fully innocent

One can imagine a legal system where tort damages and criminal punishment scaled with certainty as well as with seriousness; if the probability you are guilty of a tort is .25 you owe quarter damages; if the punishment for a guilty offender is four years in prison an offender with a fifty percent chance of guilt gets two years.

To some extent that probably happens, in practice if not in theory, through judges or juries adjusting their verdict in response to their confidence of guilt. If the jury thinks the defendant is probably but not certainly guilty of a killing they can find him innocent of first degree murder, guilty of second degree murder or manslaughter. A judge with discretion over sentencing can impose the minimum of the range on a defendant who he is not entirely sure is guilty.

It also happens, in an odd and unofficial way, through plea bargaining. The stronger the evidence is for the more serious charge the greater the probability of being convicted of it, hence the more serious the lesser charge it is in the defendant’s interest to accept. That too is an informal way of modifying punishment to reflect probability of guilt.

Self-imposed Limits

Part of my strategy for keeping down my weight is to weigh myself every morning; if my weight is above 160 lbs I am not allowed to eat ice cream that day. The difference between 160 and 160.1 is no more significant than the difference between 159.9 and 160² but the rule is still useful. A more complicated rule would be easier for the part of me that enjoys eating to game in order to evade constraints imposed by the part of me that wants to keep my weight down.

The same pattern of arbitrary limits arbitrarily imposed appears in the public sphere. Rhetoric about climate change is often put in terms of holding warming down to some specific limit, 1.5°C in the 2015 Paris agreement. There is no reason to believe that things would be much worse at 1.6° than at 1.5°.  But an arbitrary limit makes it possible to have an unambiguous conclusion; nations did or did not succeed in what some of them promised to do and people get to be mad at them if they didn’t. Arguments and rhetoric can become more extreme as the limit is approached.³

Solutions?

In some cases one could go from a continuous fact to a continuous solution, as tort law does in adjusting the size of the damage payment to the amount of damage. One reason not to do it that way for certainty of guilt is that we do not trust juries to produce precise judgements.  Instead of asking the hard question — what is the probability that the defendant was negligent — we ask a simpler question: Was he probably negligent? If you are not competent to answer a complicated question there is much to be said for limiting yourself to simple ones.

A second reason is that we are uncomfortable with admitting that we sometimes punish innocent people. A 50% chance of guilt means a 50% chance of innocence; scaling criminal punishment as described above would mean that half the time we are putting an innocent man in jail. Our reluctance to do that is reflected in the Blackstone quote:

for the law holds that it is better that ten guilty persons escape than that one innocent suffer. (Blackstone)

In Jewish law:

"that even if A pursues B with intent to kill and B takes refuge in a house, and the pursuer follows him, and we enter the house after them and find B in his last gasp and his enemy, A, standing over him with a knife in his hand, and both of them are covered with blood, the Sanhedrin may not find the pursuer A liable for capital punishment, since there are no direct witnesses who actually saw the murder…

it is better and more desirable that a thousand guilty persons go free than that a single innocent person be put to death" (Maimonides, Sefer ha-Mitzvot, Negative Commandments, 290)

Taken to its limit, the implication is that punishment requires certainty of guilt. That was the theory in medieval law, with unfortunate consequences described in my previous post.

1. Similarly, as I pointed out at the end of an earlier post, there is something to be said for simple arguments in the context of disputes such as that over the effects of climate change. A complicated analysis done right can give you a more nearly correct conclusion but it is harder to check if you do not trust the person offering it.

2. And although my scale is that precise it is not, on the evidence of repeat experimentation, nearly that accurate.

3. One would think that once the limit is passed and the world lost we could get back to worrying about other things: Eat, drink and be merry for tomorrow we die. In my experience it doesn’t happen that way.