A self-modifying AI is built to serve humanity. The builders know, of course, that this is much riskier than it seems, because its success would render their own observations extremely rare. To solve the problem, they direct the AI to create billions of simulated humanities in the hope that this will serve as a Schelling point to them, and make their own universe almost certainly simulated.
Plausible?
See LW wiki's Doomsday Argument for reference.
The problem I have with this kind of reasoning is that it causes early reasoners to come to wrong conclusions (though 'on average' the reasoning is most probably true).
Any argument from probabilities will cause unlucky reasoners to come to wrong conclusions, but that doesn't stop us from arguing from probabilities.