How often does a single vote decide an election? Never? Therefore your optimal move is not to waste your time voting - you gain nothing. If everyone thought that way it would be bad perhaps? But they don't so it doesn't matter to you.
It might be argued discussing politics contributes to some emergent consensus forming that benefits society, but that consensus will form whether you participate or not and in exactly the same way unless you win the social lottery and have a disproportionate influence. So you are better off not wasting your time on political discussion, just keep track of the political trends the same way you would keep track of the trajectory of a storm heading towards you.
Tragedy of the commons applies to potential just as much as it does to existing resources. The Nash equilibrium is to consume all the resources you can right down to exhaustion because you alone cannot preserve them and others will consume them whether you do or not.
It is also a Nash equilibrium to conserve your time and not spend it on activities that would benefit the collective but not yourself - in the presence of a collective your contribution (and therefore influence and gain) approaches zero.
Isn't there a Nash equilibrium where everybody takes the action that is best for the group not just themselves, and this achieves a better outcome individually? This seems like the rational outcome most voters are pursuing.
But I don’t think that’s a useful way to model political participation. It’s a social activity. Many participants don’t see the time spent on it as a cost. Also, it is possible to multiply your political force by working with others.
As you point out, it makes no rational sense to vote, the personal effort isn't worth increasing the probability that your preferred candidate will win by epsilon. Not only is the expected benefit small, but that benefit is all socialized.
People vote either out of sheer ignorance/unthinking of this reality, or because it makes them feel emotionally good (a sense of duty to society, entitlement to virtue signal at dinner parties, or whatever). I'm not complaining, if people want to provide an uncompensated service to society, that's great.
There isn't one. It's just a restatement of public choice theory and how little influence individual voters have. Of course, as soon as you consider there are other ways to do politics besides voting it becomes meaningless.
