bigjeff5 comments on Generalizing From One Example - Less Wrong
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That sounds like either the optimism bias or the positive outcome bias. They are related, but I think the optimism bias fits best.
People tend to over-estimate their chances of success, and under-estimate their chances of failure. If 90% percent of people eventually go broke after winning the lottery, chances are more than half of them were certain it wouldn't happen to them.
The UK government has special procedures in place to help avoid project failures due to the optimism bias.