[madnak]

Your second case is correct, btw. Assuming 100,000 lives will be lost when we go to war, we need to save 500,000 lives in order to justify going to war. But this just jiggles the variables. It's not really a "better way of looking at it." There is no mathematical way to determine whether war is justified - there are too many variables and too many unknowns (and too much subjectivity). The question is political in nature, it's not statistical in nature.

The danger of making gross assumptions and then using math to "justify" a position on that basis is illustrated best by John von Neumann and his claim that the US should have bombed Russia during the Cold War. Despite a probable death toll of millions on both sides, and the potential end of humanity as we know it, he "mathematically" established that we should initiate global war based on considerations similar to your own. Thankfully, nobody listened.