Sure, but in a democratic system with perfect information you should expect to lose the vote on your hypothetical "me vs 1000" trolley problem right? And in the absence of perfect information you'd I guess you'd mount a special interest lobby and hope for the best...
If it were me vs random one thousand and obviously so, yes. But fortunately, the Wobegon Effect makes it so that anyone can conceive of themselves being me (or even better, of themselves being better than me - considering I'm not particularly a safe driver).
It is precisely because it is democratic then that makes it possible for any individual to exploit human cognitive errors. An authoritarian meritocracy would not fall for those tricks.