There was some discussion on NPR this morning about the role luck plays in people's success in the US. While we've all heard about how you need to work hard to get ahead, suppose some folks just got lucky? Both academics on the show were arguing that if luck played more of a role in personal success, then it was OK to redistribute money more since it was all just a lottery anyway.
One of the benefits of mathematics is that it keeps you from falling prey to cognitive illusions, like the one above. If you say that output is some combination of effort AND luck, then the outcome of effort is more uncertain, so you need to give people even stronger incentives to work. This means that redistributive taxes, which reduce the share of output you get to keep, become more harmful the more luck driven the output becomes. This is the exact opposite of the point the NPR folks were making.
The error in their thinking was that they equated getting money through luck with getting money through zero effort. Gold prospecting, which is about as luck driven as you can get, requires you to go out and look for gold. The NPR folks presumably thought wealth occurred while you sat at home watching TV, because they ignored the effect of incentives on work and how those incentives would have to be strengthened if the output from effort grew more uncertain.
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