By your logic, I guess I shouldn't worry about my carbon footprint.
Public-choice scholars have long argued that voting is
instrumentally irrational because the probability that a
single vote will change the outcome of an election is nearly
zero. Dennis Mueller made the point well when he noted
that "the probability of being run over by a car going to or
returning from the polls is similar to the probability of
casting the decisive vote. If being run over is worse than
having one’s preferred candidate lose, then this potential
cost of voting alone would exceed the potential gain"
While your individual vote might not statistically matter in choosing the winner, in aggregate, it most certainly does. Voting is not an individual thing, it's a collective thing and judging it by the individual is simply the wrong approach.
An outcome you do not prefer is not automatically irrational. You just don't prefer it. The solution is not to wish everyone would act against their own interests to produce your preferred outcome, but to change the incentives so that your preferred outcome is the natural result of rational choices.
It has nothing to do with my preference. An outcome that fails to result in anyone voting for a system intended to get people to vote, is a failed outcome, no matter how you look at it.
1. On average, better politicians get elected because the voting decisions of society's best-equipped voters are being amplified.
2. Only a small part of the population has to bother themselves with following political news. Since they're such great voters they'll probably do it in much greater depth (reading actual bills and scientific papers; carefully scouring campaign websites instead of believing rumors they hear on TV.)
Most everyone has a friend they consider much smarter than themselves, just do what he says.
This applies to much more than voting.