Q&A: Double Doubt
Double Doubt
Question
In the topic of double doubt, we see that later authorities discuss doubt in terms of possibilities, without addressing doubt in terms of chances (probabilities).
How, from a modern perspective, when it is clear that the possibilities are not the significant factor at play (since I can always find another far-fetched possibility for which there is no opposing presumption), should all this be understood?
Answer
When the doubt is about probabilities, that falls under the law of majority. If the doubt is evenly balanced, then it is a doubt in terms of possibilities. Clearly, in most cases we have no way to determine the weight of each side (the probability, the chance), and then we go by the possibilities. That is also how statistics works.
Discussion on Answer
That is a separate question. Applying the laws of doubt involves halakhic rules. But probabilistically, I did not understand your question. In double doubt we really do rule leniently. Are you asking about a doubt on top of a majority?
A. What exactly is meant by “halakhic tools”?
B. Seemingly, in double doubt we rule leniently even if statistically the majority comes out stringent (for example, in the first doubt the sides were 70/30, and in the second 60/40 in favor of the more stringent side), but because we do not take into account the probabilities of actual occurrence and only the number of sides, the result is lenient.
A. My claim is that even if the laws of doubt are statistical, applying these tools is done according to halakhic principles. The same is true in the legal world as well (see, for example, columns 227–8). Clearly, law and Jewish law are not mathematics. Still, it is possible that the laws of doubt are indeed tied to probability calculations.
B. In my opinion, usually not (except in places where the rules of Jewish law instruct us not to follow the statistics; see what I wrote in section A). If the doubt is not evenly balanced, then it is not doubt but majority. Double doubt is where there are two evenly balanced doubts. There is a long discussion about doubt on top of a majority, but in my opinion that really is not double doubt in the ordinary case. You should remember that sometimes we do not have a probabilistic calculation, and therefore even if there is some reason to suspect that one side has a majority, we will treat it as an evenly balanced doubt and count sides. But when there is a concrete calculation showing that the sides are not evenly balanced, it seems to me that usually we would not view that as double doubt. Certainly not according to all opinions and not in all situations.
If doubt in terms of probabilities is always governed by majority, then why is there no discussion in double doubt of the “minority” accumulated from the first doubt to the second? (Or once we decide the first doubt, does “the winner take all”?)