Q&A: Statistical Conviction in the Absence of Information
Statistical Conviction in the Absence of Information
Question
Hello Rabbi,
Following your latest lecture in Ra’anana about majority in Jewish law and in general, I thought to suggest a sharpening of the explanation you offered for the intuition that one should not convict on the basis of a statistical consideration in the absence of information:
For example, when there is a mixture of 9 blue balls and 1 red one, and all the balls are similar to one another in weight, shape, density, material, etc., and a person draws one ball from the mixture while blindfolded, then the chance that he will draw the red ball is 10%, because one may assume symmetry among all the balls (and that assumption would be justified). But if we did not know what material the balls were made of, or what their shape, density, weight, etc. were, then the assumption of symmetry among the balls would already be an unfounded assumption, and the reason one would nevertheless assume it is only in order to minimize the size of the error statistically. In the same way, when there is a group of prisoners rioting, or a group of buses that get into accidents, in order to convict any particular person one has to assume that he is symmetrical with respect to the whole group—that is, that he is similar to them in “material,” “shape,” etc. In the case of prisoners or bus drivers, it is obvious that each person differs from the next in many ways, and therefore the assumption of symmetry among them is unjustified. When one assumes symmetry among people, this is really begging the question, because one assumes that each person is similar to the general group, and as a group this is a criminal group (almost entirely so). And the reason symmetry is nevertheless assumed among people is only in order to minimize the magnitude of the statistical error, and this is not an ordinary determination of a statistical distribution (but perhaps only of the expected value of the distribution). An analogy would be a die with N faces, where the size of each face is not necessarily equal and is unknown. The probability that the die will land on a certain face is the size of that face divided by the total surface area of the die. In an ordinary die, the probability for each face is one divided by N. But in the above die (whose faces are unequal), the probability for each face is unknown, and only the expected probability is one divided by N. All the confusion stems from the fact that people identify the expected probability with the probability itself.
In the same way, when one does a moral study examining how people behave in moral dilemmas—even if the results of the study are that 80% of people choose the bad option—when a new person comes before me, I may not assume that he will choose the bad option, because only the expected probability that he will choose the bad is 80%, but the probability itself is not 80%; rather it is unknown (because there is no symmetry among people). Therefore this is different from the assumption that most women give birth at nine months, where the probability itself is known and not only the expected probability (because physiologically, the assumption of symmetry among women is justified).
Best regards,
Answer
This explanation is very close to what I suggested in the columns that dealt with this (226 and 228). Two formulations: 1. A majority that is before us is not probabilistic. 2. Human choices do not create a probability distribution. The second formulation is roughly what you are writing here. I even gave an example of a mixture of balls that are drawn by a person’s choice, where the chance is unrelated to the number of balls.
Discussion on Answer
This whole issue is also connected to following the majority in a religious court, where following the majority is in principle unjustified because it assumes symmetry among the different judges, out of lack of choice in the absence of information, in order to minimize the chance of error. And maybe one could actually say that the majority of judges represent the collective hat found within every judge.
I don’t know whether the term “collective” is a successful formulation here. Maybe it would be more correct to speak about the topographic outline that I defined in The Science of Freedom (where I also explained why statistics works with regard to human decisions).
By the way, the Sefer HaChinukh really writes that when the judges are not equal, we do not follow the majority.
Maybe in fact our choice is made up of three layers: the topographic outline (which is embedded in our DNA), our collective belonging (which is influenced by society’s values), and the individual layer. The proof for the existence of the collective layer beyond the topographic outline is the very fact that there are differences between different collectives at the level of choice. For example, the percentage of vegetarians in India is greater than in other places in the world, and the percentage of racists in Nazi Germany was probably among the highest in the world in their time.
On a related note, I’ve always wondered how studies about people’s moral choices can work when they generalize them beyond the sample group on which the study was conducted. Seemingly, there is a mechanism here of a majority not before us applied to an individual’s choice. But now I thought that since each person’s choice is made up of two layers, a collective hat and an individual hat, the sample group reveals the choice of the collective, and when examining another group of people outside the sample group, it must yield the same moral-choice results (as a group), because the outside group is in fact a representation of the same collective to which the sample group belongs. But theoretically, if we took a sample group of people who each grew up on a different planet, and afterward tried to generalize the sample’s results to another group of people who also each grew up on a different planet, there would be no connection at all between the sample’s results and the second group—because there is no collective here to which the people belong.