Do you really mean "should" in the sense that it's morally better to choose oneself? If so, could you provide some justification for that? My view would be that saving the 10 isn't morally required but would be virtuous in a supererogatory sense.

In quick bullet points:

• The eleventh man is not morally responsible for anyone dying, regardless of what he chooses
• It is better to live than die
• I see the king's question as simple as "do you want to live?"
• The answer is as simple as, "yes."

The cost of the eleventh man living is not paid by himself, it is paid by the king in the form of a moral choice.

Also, to be clear, the man cannot sacrifice himself. He does not kill himself; he is not sacrificing anything; his life is not actually his to sacrifice. The king can kill him no matter what the answer is. The way I look at it, this scenario is exactly the same as the king making the eleventh guess a random number correctly or everyone dies. The man has no power over the situation. Any power is an illusion because all of the power is the king's.

Likewise, the man cannot save anyone. The ten are not his to save. The king decides who lives and dies.