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If anyone has any mathmo/statso friends that I don't know, can you pass them over?
In one place, we have Rabbi A, who rules "a", and Rabbi B, who rules "b". In another place, Rabbi A rules "b", and Rabbi B rules "a". We assume that Rabbi A cannot believe both "a" and "b" simultanously, which begs the question - which place reflects Rabbi A's position, and which one got itself confused? To resolve this, we bring an example from a third place, where Rabbi A rules "a" and Rabbi B rules "b," and take best-of-three. Assume that these three examples are the only ones available.
Now, my teacher says that best-of-three is an unreasonable approach. He uses an analogy of coins, saying "If you tossed three times and got two heads and a tail, it would be incorrect to assume that your next toss would be a head, therefore, if you have two sources showing that Rabbi A thinks "a" and one source showing that Rabbi A thinks "b," it is unreasonable to assume that Rabbi A probably holds "a.""
This just doesn't seem right. Basically because of the difference between a rabbi and a coin; a rabbi has memory, whereas a coin does not. We don't assume that a coin remembers previous heads and is therefore more likely to come down heads, but we do assume that Rabbi A remembers previous "a" judgements and tends to apply similar reasoning. So that is a question that relates to how many coin-tosses you need before you can reasonably conclude that a coin is biased. I only have vague memories of how you do this - but from the start it's a lot more reasonable to assume that Rabbi A is biased, than to assume that a coin is biased. But I can't formulate this sufficiently well to convince my teacher. If one had more samples of Rabbi A's thinking, it would presumably get better - how many more? I can't remember how you do this kind of test.
In one place, we have Rabbi A, who rules "a", and Rabbi B, who rules "b". In another place, Rabbi A rules "b", and Rabbi B rules "a". We assume that Rabbi A cannot believe both "a" and "b" simultanously, which begs the question - which place reflects Rabbi A's position, and which one got itself confused? To resolve this, we bring an example from a third place, where Rabbi A rules "a" and Rabbi B rules "b," and take best-of-three. Assume that these three examples are the only ones available.
Now, my teacher says that best-of-three is an unreasonable approach. He uses an analogy of coins, saying "If you tossed three times and got two heads and a tail, it would be incorrect to assume that your next toss would be a head, therefore, if you have two sources showing that Rabbi A thinks "a" and one source showing that Rabbi A thinks "b," it is unreasonable to assume that Rabbi A probably holds "a.""
This just doesn't seem right. Basically because of the difference between a rabbi and a coin; a rabbi has memory, whereas a coin does not. We don't assume that a coin remembers previous heads and is therefore more likely to come down heads, but we do assume that Rabbi A remembers previous "a" judgements and tends to apply similar reasoning. So that is a question that relates to how many coin-tosses you need before you can reasonably conclude that a coin is biased. I only have vague memories of how you do this - but from the start it's a lot more reasonable to assume that Rabbi A is biased, than to assume that a coin is biased. But I can't formulate this sufficiently well to convince my teacher. If one had more samples of Rabbi A's thinking, it would presumably get better - how many more? I can't remember how you do this kind of test.