The three hats - In retrospect

[Ghost Post]

May be our assumption that the wise men all want to win is flawed.

Suppose there was intense rivalry between the wise men and the utility of getting one of them killed exceeded the utility of winning the contest.

Then one wise man could conspire and kill any of the others.

Suppose only one hat was blue, all this person was to do was keep quiet and let one of the others jump to the erroneous conclusion that his own hat is blue consequently hanging himself.

Any comments ?

[Unheard Voice]

Sure, it may be possible, but unlikely. These three sages may be from different parts of the kingdom and may have no knowledge of the other whatsoever, which lacks a reason for one to purposely kill another. The first paragraph of the puzzle said:

"The three wisest sages in the land were brought before the king to see
which of them were worthy to become the king's advisor. After passing
many tests of cunning and invention, they were pitted against each other
in a final battle of the wits."

If they were from different parts of the kingdom, and if the above sentence says what I think it says, (that they all passed some tests before they were pitted against each other), then this will be the first time that they will meet. Why would they want to kill each other?

And besides, if they did have previously met and one of them did want to kill another, the situation one which the "killer" is the one with the only blue hat raises a question of "How would the sage be sure that the one he wants to kill will incorrectly say that he has a blue hat?" (Unless he wants to kill both of them, and killing one of them is a step towards that goal).

Also, the one that would be chosen to become the advisor of the king could tell the king that the existence of two intelligent people elsewhere in the kingdom may pose a threat to his power. The king might respond by killing these two people. This means that one of the sages can become the advisor AND can kill either or both of the other sages if he desires and the king agrees. Why wouldn't a sage choose this choice instead? (Unless he just doesn't want to be an advisor...)

[ZenBeam]

I posted this as a puzzle in VSP: Three hats and the evil sages. There are some comments there.

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It is too clear, and so it is hard to see.

[rex]

The solution to this puzzle can be correct only if all three sages were wise enough to eliminate the "1 blue hat" possibility and the "2 blue hats" possibility. The one that spoke up, declaring his hat blue, would have to put a lot of trust in the intelligence of his two counterparts.