I am amazed about how many people are making this claim confidently in this thread. It's clearly wrong. Very, very often it's definitely worth the cost, because very often you will never see the same criminal again. Consider:
"Don't pay ransoms, because (1) you'll get extorted again once the criminal knows you're an easy mark and (2) if everyone always refuses to pay, criminals will have no incentives to try and extort."
versus
"Don't pay muggers, because (1) you'll get mugged again once the mugger knows you're an easy mark and (2) if everyone always refuses to pay muggers, muggers will have no incentive to mug."
Yes there are cases, like if you're the government, where you are very long-lived and your reputation is reliable such that having a stated, followed policy of not being extorted works. But for individuals, it's just not feasible most of the time. You probably won't see that mugger/extorter ever again, and it's very unlikely that most victims will refuse.