Q&A: Doubt, Majority, and Expected Value
Doubt, Majority, and Expected Value
Question
Regarding what we discussed about Pascal’s Wager, you said that if you are faced with a decision where there is a small chance that something serious will happen, in your view one should go with the more likely outcome without taking expected value into account (since the experiment is a one-time event).
But after all, in the world of Jewish law, there is a major rule: a Torah-level doubt is treated stringently. That is, even if most halakhic decisors (or the greater probability) permit something, we still follow the small chance (or the minority of decisors) that it is forbidden. There are exceptions, and cases of double doubt. I assume the reason we follow the minority is because the expected gain (or loss) is still significant, and that is what ultimately affects the decision (even though here too the experiment is one-time).
Answer
That’s a mistake. A doubt exists only when the probabilities are evenly balanced. When they are not evenly balanced, we follow the majority. And the same is true in a case of a majority and minority among halakhic decisors.
But in any case this discussion is not relevant to our issue, because when there is a doubt whether a piece of meat is pork or lamb, that is not a choice between two sides that has an expected value. Eating lamb has no halakhic significance, whereas eating pork does. So here this is not a matter of expected-value calculations at all, but of the level of concern at which one must be wary of a prohibition.