When considering this tactic, ask yourself one question: "Do I work for psycopaths, or for (relatively) rational human beings?" If rational, go ahead and let them know the market rate of your labor by showing a competing offer, knowing full well that you're ready to take it and move on. It's only business. If you work for psychopaths, just take the offer and leave because fuck that shit.
I feel like any company large enough to have a significant HR department won't count as a "rational human being". They'll probably fall into the "psychopath" category by virtue of dispassionately and emotionlessly assessing how much of a liability you are to them if you're willing to demand they make counter-offers.
Being a psychopath isn't about holding a grudge, it's about acting in pure self-interest with no regard for the effect on others. So psychopathy is a good way to describe an HR dept that does its intended job.
Exactly - given the prevalence of "psychopath" in common conversation as violent, unreasonable etc., perhaps I should have specified further or instead used "sociopath".