Intervention is unpopular in practice
In the US, polls indicate high concern for deadly civil wars such as in Syria, but low support for military intervention. A similar scenario has played out in past examples of genocide and suffering, such as Rwanda and Cambodia.
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In 2013, shortly after President Bashir al Assad of Syria used chemical weapons against his own people, pollsters asked US citizens whether they wanted military intervention in the deadly civil war. A meager 9 percent favored humanitarian intervention (HI) in the middle-Eastern country. While nearly every American would condemn human rights abuses and suffering in theory, they rarely support the practice of stopping it. Due to the failures of past interventions, such as Iraq, it is difficult to find support for future interventions. Considering most of the nations that consider HI are democracies, it does not appear just to pursue a policy that is so unpopular among voters. Military intervention should not be completely precluded from occurring, but the recent examples of foreign conflict have had very low popularity, especially after the conflict begins. Nations can still help foreign citizens in crisis, but it is clear that military intervention is not a popular choice to aid those abroad.
Public support may not be the best litmus test for whether to intervene in a humanitarian crisis. If we take Rwanda as an example, there is a degree of political guilt for the lack of decisive action taken in 1994. Some scholars and policymakers have indicated that more action would have stopped or lessened the eventual mass genocide that took place in the small African nation. At the time, there was not overwhelming support for military action, other than a small UN peacekeeping presence. With the benefit of hindsight, it's clear that more could have been done to prevent the degree of death and suffering that occurred. If we only acted according to public support, then little humanitarian action will be taken to protect human rights.
[P1] Recent potential interventions are very unpopular among those polled. [P2] Past conflicts lost support after they began. [C] Despite clear humanitarian abuses, such as in Syria, intervention is often only supported by a small fraction of those polled. Even conflicts that had initial support eventually became very unpopular after lengthy involvement.
Rejecting the premises
[Rejecting P1] Unpopularity may be due to a lack of information on the atrocities being committed. [Rejecting P2] Recent conflicts may have become unpopular, but inaction on past genocide is now regretted, such as Rwanda and Cambodia.