Is Honesty Really The Best Policy?

Relevant wiki: Truth-Tellers and Liars

Better to ask the compulsive liar. You can be certainly confident that his answer is a lie and can therefore safely pick the other door. (After all, there are only two doors so if you know the door he is pointing you to is wrong, then the right door has to be the other door).

But if you ask the occasional liar, you do not know whether he is telling you the truth or not, so you will be uncertain of whether to pick the door he points you to or to pick the other door.

Always ask the compulsive liar, for he/she can always state the wrong idea. Therefore, you can reverse his/her statement and turn up to your advantage. If you ask the occasional liar, There is 1/2 chance to state the lie. It would be a risk if he/she directs you to choose a door where it could be both true and false. 50/50 < 100

In the usual terminology at this site, we have a Knave (Compulsive Liar) and a Jester (Occasional Liar) but no Knight (Truth Teller). In the given situation we have the (enormous) luxury of knowing which is which, asking the Knave is just as good as asking the Knight since both give completely consistent, if opposite, answers to questions. Asking the Joker gives no information at all here, with responses that are nothing but random noise. This seems analogous to the situation in information theory when having all the bits right or all of them wrong are equivalent only amounting to a change in encoding scheme for the same information. The problems arise when some intermediate number of bits are randomly inverted and with, as I dimly recall, the worse case at half wrong.

A long time ago in a mathematics class about logic (as opposed to the philosophy department class) there was a very contrived liar/truth teller exercise that required an bi-conditional (if and only if) statement to solve. At the time I brought up the point that these fictional people only respond to the form of questions rather than to the intent. If the liars had some insight into the intent, they would effectively all become jokers and these puzzles wouldn't work at all. Is there a mathematical solution to intelligent malice?

The answer is ask the Compulsive Liar.

You should pick the compulsive liar, because you know to pick the exact opposite of what he says. The occasional liar could be telling the truth or lying, so you don't know if you should pick the opposite or what he's saying.