[madnak]

You're assuming a lot.

For one thing, even if Iraq had huge stockpiles of nukes, they probably wouldn't have used them on us. Having and using are two different things, but your calculations don't distinguish. Also, even a nuke in NYC wouldn't kill anywhere near 8 million. That's ridiculously large. Smaller-scale biological and chemical weapons would kill significantly under 82,000.

You assume that only 82,000 Iraqis die if we invade. If we invade and Iraq has weapons, then Iraq will almost definitely use those weapons, and the death toll may be extreme. The war still isn't over and people are still dying, so the 82,000 figure may be significantly lower than it should be. You also ignore the American deaths (over 3,000) that resulted from our invasion.

Of course, even the basic approach may be flawed - there are tremendous costs to war aside from the deaths. There are also considerations like our limited resources and the ethics of invasion. A good example is that if we only have the resources to invade one region, then Iraq has to be the best place to invade - if some other country is more of a threat, then that's the country we should be invading. Finally, the question of how much diplomacy/investigation we should do before declaring war is highly relevant in the decision.

Sticking with your reasoning - statistically, you can't just go half and half on the cost of avoiding war. That itself depends on the likelihood of WMDs. Other than that, you seem okay. So the cost of going to war is always 82,000, but the cost of avoiding war is 8,200,000x. We see an equilibrium when 82,000=8,200,000x, so we're "justified" by that reasoning when we are >.1% scertain of WMDs.