no third solution

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Liars & Truthtellers

December 14th, 2006

I’ve been thinking alot about a parable* I heard in sixth grade (yes, my memory sometimes extends that far backwards in time.) The teacher introduced a scenario, in which you are hypothetically stranded on a desert island, inhabited by two tribes: Truth-tellers, and Liars. As you are seeking safety/rescue, you come to a fork in the trail, and there is a bystander. You have no idea whether he is a truth-teller or a liar, but you do know that one of the divergent paths leads to safety/rescue.

You can ask only one question, and the bystander will only give an answer of “Yes” or “No.” What do you ask him, and which path do you take?

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Basically, I’ve been thinking about this parable in the context of government, benevolence, and other gobbledygook, like, the “common welfare” and the “public good.”

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The long and short of it is, you need to phrase your question in such a manner that you can guarantee a falsehood, and then do the opposite, such as: Would a member of the other tribe recommend that I take the left path?

If the respondent is a truth-teller, and the left path is the correct path, he will respond, “No,” because if asked which path to take, the liar would tell you to take the (incorrect) right path. If the respondent is a liar, he will respond “No,” because he cannot tell you the truth; i.e., that a member of the other tribe would honestly tell you to take the left path. Therefore, if the response is “No,” then you take the path to the left.

If the respondent is a truth-teller, and the left path is not the correct path, he will respond “Yes,” indicating that members of the other tribe would mislead you. If the respondent is a liar, he will respond “Yes,” indicating that the other tribe would mislead you, when in fact they would not. Following similar logic, we can be sure that if the response to our query is “yes,” then we should not take the path to the left, but instead, veer rightwards.

Somehow, this ties into the nature of man and his government. I’m working on connecting the proverbial dots…

*You may have heard a simpler version of this parable, where the respondents are not restricted to yes or no answers, like this one, for instance.

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no third solution

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