ehhh... You are getting really pedantic here. Your argument is basically well voting doesn't matter so we should have a dictatorship instead of democracy. Your vote does matter in the aggregate, its not supposed to be a 1:1 outcome. Its an aggregate process. You don't measure the speed of each tire on a car you just measure the car speed overall.
I guess if your position really is votes don't count unless its the one to tip the scale no one would be debating you because its irrelevant. Maybe lead with that.
> Your argument is basically well voting doesn't matter so we should have a dictatorship instead of democracy
I am actually not saying that at all, which is what makes this a paradox. I think democracy is important and that getting an accurate determination of the will of the people is important... but it still doesn't make sense, from a pure game theory perspective, to vote in an election.
It isn't REALLY a paradox, because both things are true - voting is a good way to get a representative sample, and a single vote isn't going to change that sample very much.
In many ways, this is just basic statistics, and we experience this every single election night - elections are called WELL in advance of every single vote being counted, because we already know with statistics what the result will be. Now, there are a few examples of this going wrong, but those are mostly times where the rush to call an election makes people call it when the statistics say there is still a reasonable chance for a comeback.
Honestly, it if was up to me, elections should be determined by a random sample. Randomly select N citizens from the country to be the voters that year, and use that result. If N is sized correctly, you will get the same result you would with an actual election, and we don't have to have everyone waste their time voting.
This would never happen, of course, and I honestly can kind of understand why; the results aren't the only thing that is important, feeling connected to the process and that your voice matters also is important. It is a bit of a agreed upon delusion, though.
If you only pay attention to national elections sure. Tons of local and state elections come down to a couple hundred votes all the time.