When you flip a coin, it's customary to ask the other person, "heads or tails?"
That choice is meaningless.
You picking "tails" doesn't change the probability of you getting what you want. It could just as easily have been assigned to you by someone else. But what it does do, is establish buy-in.
From the moment you call "tails", you've bound yourself to abide by the result of the flip. And that's really the point - nobody cares whether you're heads or tails, they just care that you agree to it.
That seems to me to be kind of an intriguing little insight, a glimpse into the way the human mind has arranged its little rituals and social games. We could probably find parallels everywhere. But the most obvious one to me is the democratic process.
The democratic process is an interesting little game, where we are given the choice between two ostensibly different candidates. But the choices are never really what we want - they are always, from our perspective, the lesser of two evils. This means that year after year, we are voting for evil politicians we do not want.
So why vote?
When we vote, we establish buy-in. We convince ourselves it was our choice, and we give others the ability to blame us for the problems that arise. "If you didn't vote, don't complain" the saying goes. Or, "Don't blame me, I voted for Mickey Mouse!"
When things go wrong, we blame the other party, the other side of the coin flip. Rather than address the problem, or the candidates, or the system that put this all in place, we blame it in on the other group. After all, they bought in; they called it.