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You misunderstood. The people moving aren't doing it as a threat. They really want to move. But it is the boss that doesn't want to lose an employee and have to train a new guy, and maybe pay that new guy more than the current employee is getting, so they counteroffer.

Pay well, pay adequately

If the pay is good and adequate, then there will be no reason for the person to look for another job.

If the pay is good and adequate, then there will be no reason for the person to look for another job.

Which goes to my point of the threat. They want to leave because they aren't satisfied with the pay - if they really want to leave, no counteroffer will matter, yet it is is common for them to take it and stay.

This one I don't quite agree with. I know that some do it as a threat, but most don't. When one looks for a job, it is because they want to move. When they file for resignation they are resolved to move, and the counteroffer is not guaranteed to come. I've seen a lot of resignations where there were no counteroffers. Unless the person knows they are irreplaceable in the company, that is only when they can use it as a threat. In all my time working, I haven't seen anyone use resignation as a threat.