It's easy to see why an individual, organization or nation would both want to establish a firm policy of not negotiating with pirates, hostage takers and the like, and, in any given crisis, would want to pay the ransom. The policy removes the incentive for future acts of piracy, hostage taking, etc., while once one's own family members, fellow citizens, or even super tanker is being held, it's hard to avoid doing what it takes to get them back.
But suppose that paying the "ransom" is actually in the long-term interest of the victim. To be concrete, let's assume the following:
1) It is in the long-term interest of India to relinquish sovereignty and control over Kashmir;
2) A substantial fraction of the people who are now interested in committing terrorist acts against the civilian population of India would lose their motivation (either abandoning terrorism altogether or directing their actions at non-Indian targets) if India were to relinquish Kashmir;
3) For India to relinquish Kashmir, either unilaterally or as a result of a negotiated settlement with Pakistan, would be seen as capitulating to terrorists.
Under these circumstances, it is understandable for India to dig in its heels precisely to avoid rewarding terrorism.
Nonetheless, one suspects that if 1 and 2 hold, then the rational thing for India to do is pursue its own interest, even if that happens to coincide with what some terrorists want. But that is only because, as I've set up the assumptions, there are no further demands made on India after it lets go of Kashmir.
Suppose now that we substitute Israel for India and the West Bank and Gaza for Kashmir. Here too, there are undoubtedly Palestinians currently willing to attack Israelis who would make their peace with an Israel that recognized a Palestinian state on the West Bank and Gaza. However, some substantial number of radical Palestinians would not, and so the possibility of rational intransigence for Israelis arises: Even if it is in the interest of Israel to relinquish the West Bank and Gaza, doing so under fire could be seen to reward armed attacks and thus encourage further attacks by those who object to the entire State of Israel, not merely to the occupation of the West Bank and Gaza.
Thus, the logic of refusing to give in to pirates, hostage-takers, terrorists, and so forth can lead not only to extreme short-term sacrifices (of the refusal to pay ransom sort) but also to sacrifices of long-term interests.
Posted by Mike Dorf