The trouble is, if people don't experience the feeling of defeat, they don't tend to undergo proper relinquishment, and will revert back to the indefensible stronger position in time.

I don't consider it my responsibility to update their beliefs, even if that person is wrecking havoc with their actions. If they are acting irrationally, their power should be stripped from them and the environment updated to account for their stupidity. But I don't think making them feel defeat is going to make an irrational person suddenly rational.

As Stuart said,

You might 'break' some of them into a completely new way of thinking, but most likely you will simply undo all your hard work up till then.

Making them feel it is ridicule and embarrassment. Most of the people I know will act more irrationally in this situation, not less.