[[http://www.overcomingbias.com/2008/01/circular-altrui.html|Overcoming bias]]

Suppose that a disease, or a monster, or a war, or something, is killing people.  And suppose you only have enough resources to implement one of the following two options:

   - Save 400 lives, with certainty.
   - Save 500 lives, with 90% probability; save no lives, 10% probability.

Most people choose option 1.  Which, I think, is foolish; because if you multiply 500 lives by 90% probability, you get an expected value of 450 lives, which exceeds the 400-life value of option 1.  (Lives saved don't diminish in marginal utility, so this is an appropriate calculation.)

"What!" you cry, incensed.  "How can you gamble with human lives? How can you think about numbers when so much is at stake?  What if that 10% probability strikes, and everyone dies?  So much for your damned logic!  You're following your rationality off a cliff!"

Ah, but here's the interesting thing.  If you present the options this way:

   - 100 people die, with certainty.
   - 90% chance no one dies; 10% chance 500 people die.

Then a majority choose option 2.  Even though it's the same gamble.  You see, just as a certainty of saving 400 lives seems to feel so much more comfortable than an unsure gain, so too, a certain loss feels worse than an uncertain one.

You can grandstand on the second description too:  "How can you condemn 100 people to certain death when there's such a good chance you can save them?  We'll all share the risk!  Even if it was only a 75% chance of saving everyone, it would still be worth it - so long as there's a chance - everyone makes it, or no one does!"

You know what?  This isn't about your feelings.  A human life, with all its joys and all its pains, adding up over the course of decades, is worth far more than your brain's feelings of comfort or discomfort with a plan.  Does computing the expected utility feel too cold-blooded for your taste?  Well, that feeling isn't even a feather in the scales, when a life is at stake.  Just shut up and multiply.