There's an important point that was left out. Historically, in the times of chazal, the reason to take Jewish captives was in order to make money, so refusing to pay would discourage future kidnappings. In our current situation, they are motivated to Rachmana litzlan do terrible things regardless. If they don't feel they will get what they want in exchange for hostages, they just won't have an incentive to keep them alive...
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The entire discussion of the Halachah of not buying back captives at over market values, is at the end of the day irrelevant.
In that case, the captors want *money*, so ransoming the captives with *money* will result in further captives be taken for their ever higher *money* value. Therefore, as noted in the article, many achronim rule that we do in fact ransom at exorbitant rates if the captives are in imminent danger of losing their lives. We therefore pay a lot of *money* to save *lives* even if that will later cost further *money*.
In the case of hamas and similar, their entire goal is to murder as many Jews as possible. In furtherance of that goal, they take hostages, and then in exchange for Jewish *lives* they demand the men, arms, money, and PR needed to further take other Jewish *lives*. How many *lives* is market value for *lives*?! How can you say "Let's save these *lives* by giving them the means to take other *lives*"? You cannot compare the halachos of trading *money* for *lives* at the cost of further *money* to the case of trading *lives* for *lives*!
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