This branch of mathematics [probability] is the only one, I believe, in which good writers frequently get results entirely erroneous. — Charles Sanders Pierce
Get your facts first and then you can distort ‘em as much as you please. — Mark Twain
These are two quotes I used as chapter headings in a book on probability and decision making. In reading the various positions politicians are taking in preparation for the fall elections, I have spotted several logical errors that always favor the speaker — big surprise.
Rather than discussing specific candidates or issues, here is a non-political example paraphrased from an excellent book, Calculated Risks by Gerd Gigerenzer. This error happens so often that it has a name: “The Prosecutor’s Paradox.” I’ve discussed this example before, so bear with me if you recognize it.
OJ Simpson was tried for the murder of his wife. A question arose early in the proceedings about the admissibility of evidence of prior marital violence. OJ had a history of battering his wife. During the trial, Alan Dershowitz argued that this history was not relevant to the case, and therefore the jury should not be exposed to it because the facts of battering could prejudice them. He based his contention on the known statistics that only one out of 2,500 batterers will become a murderer. (Note: the frequency of murders of battered women is about 45/100,000 in America. This statistic varies by country and time.) His statistics are correct.
But is that argument justified? If you were a judge making the decision as to whether the jury should see the history of battering, what would be your response: allow the jury to see the history, or suppress it as being both irrelevant and prejudicial?
You have the data necessary to make that call on a logical basis, but it is, in the words of Mark Twain, distorted to fool you into the wrong decision based on valid input. Dershowitz has not lied, but like a good magician, he distracted us from the real action.
To see how this works without using any complicated math, assume a pool of 100,000 battered women. By the conditions given above (remember that 100,000/2,500 is the number of batterers who become murders according to Dershowitz’s presentation):
- 99,955 of them will not be murdered.
- 45 will be murdered.
- 40 will be murdered by their battering partners, and, therefore…
- five will be murdered by others.
We conclude from that simple calculation that 40/45 victims were killed by men who had previously battered them. Yes, that means that eight out of nine murder victims were killed by someone who had previously battered them.
When stated that way, introducing this evidence to the trial seems like a no-brainer. In trying to suppress the evidence of prior battering, the defense was doing its job of casting the truthful data in as favorable light for the defendant as possible. No lies were told, but the truth was obscured by focusing on the wrong topic.
This type of distortion (or favorable reporting of facts) is common in political speech in which honest data is used to support either party’s position. With a little bit of practice, you can pick out the obvious distortions.
The next time you hear a politician talking about the effects of taxation on the economy, listen for this kind of truthful, but misleading, analysis. Extremely sophisticated programs exist to predict stock trends in stocks. Surely similarly sophisticated programs can predict the response of an economy to various tweaks. So why do people argue about it? “Can’t we all just get along?” The answer is “No, we cannot.” This is because, if everyone agreed upon a particular massive program to reasonably predict the economic response to a partisan input, then the ability of either side to use honest statistics in clever ways would decrease. We have the tools, but our system is not motivated to use them.
The ability to make a rational analysis takes more hits when the subject being discussed is not well-defined by one or more parties. Abortion debates would be less acrimonious if everyone agreed on some basic definitions like when meaningful human life begins. If you believe the meaningful human life begins with a fertilized egg (or, more properly, a fertilized egg is a meaningful human life — the exact moment of fertilization is problematical), then logical presentations by people with other views are not likely to carry much weight. Some people think humanity is a digital concept: You are either human or not. Others think humanity is analog with a measurable transition through several states from inert matter to a self-sufficient being and back to inert matter. This lack of consistent definition prevents framing a logical argument satisfactory to all. We could reach a consensus, but we refuse.
What about legalization of narcotics? Once the question is posed that way, a natural line of argument is opened, which is prejudicial. The proper question, as in OJ’s trial, is different. We should really ask, “Why make narcotics illegal?” Presented like that, we do not have the implicit assumption that narcotics have always been illegal and thus tainted with evil overtones. Presented the first way, the “Just say no” way, the conversation starts with a prejudiced beginning and that determines much of what follows. Perhaps some narcotics and dangerous substances should be illegal or at least tightly controlled (I vastly prefer eating at restaurants with no smoking allowed and driving on roads with sober neighbors!), but let us at least phrase the question properly.
Part of what prompted this piece was hearing arguments on NPR radio about a store in the city that wants to add alcohol to its sales. Opponents say there are already many bars and liquor stores in the neighborhood; we do not need another because they just breed illegal activity. The proponents argue that since there are already many sources of alcohol in the neighborhood, adding one more will not make any difference in the crime rate. Same data: different conclusions. Go figure.