Well you both could have turned out, but the amount of raw information you would contribute would be identical to if you both didn’t show up.
This is untrue unless you only consider the identification of a winner (or absolute margin of victory) to be raw information. In practice turnout is also raw information and is closely watched. The decision to vote or not is indeed a decision that expresses information.
You suggest elsewhere that a system that produces the same outcome but requires people to take time and gas money to go to the polls is inefficient (though without using that word). However, again that is only true if you believe that the mere act of showing up conveys no useful information. I'm not convinced that is the case.
The argument is stronger if considered within a system of compulsory voting.