Rationally the effort of you, personally, going to vote only matters if it changes the outcome. However the odds of a single vote doing that are very, very low. The odds of it changing the reported statistics even by 0.1% are also low. At a national level the odds of doing either are effectively non-existent.
Therefore rationally there is no point in an individual voting.
I know this. But emotionally I feel better knowing that I tried to use my voice, even though logically I know that the act was meaningless. I long ago came to accept that my emotions do not respond to logic, and therefore I have come to let emotion drive my goals, and then use logic to achieve those goals.
Therefore I am willing to engage in a logically pointless activity in return for the emotional satisfaction I derive. Even though I am aware that the emotional satisfaction is illogical.
> Rationally the effort of you, personally, going to vote only matters if it changes the outcome.
As above, I disagree with you about what the real purpose of an individual's vote is.
> Therefore rationally there is no point in an individual voting.
If you find that rationality and logic indicate that an individual should not vote, then you haven't used enough of them.
Specifically, if everyone was rational according to the definition you're implying, then bad things would happen. That sounds to me like it's the wrong definition.
> Therefore I am willing to engage in a logically pointless activity in return for the emotional satisfaction I derive.
You're doing a lot of assuming you're right, and then concluding that anyone who disagrees with you is wrong. That's poor reasoning. In particular you say
If you find that rationality and logic indicate that an individual should not vote, then you haven't used enough of them.
Specifically, if everyone was rational according to the definition you're implying, then bad things would happen. That sounds to me like it's the wrong definition.
You have reasoned from the premise to an apparently absurd conclusion, and therefore conclude that the premise was wrong. But in fact what you should do is look farther to see whether the premise is, in fact, RIGHT! To that end I strongly recommend that you read The Logic of Collective Action by Mancur Olson. This sets out the classic theory of public goods which, among other things, concluded that very often bad things happen if everyone acts in their own self interest.
Now rather than seek a reason to reject the premise, analyze it. My claim is that if your reason for voting is X (for any particular X you want), then unless your act of voting has a chance of affecting X, you logically shouldn't spend energy voting. Why would that be? Well when you vote you have a cost (your effort) and a reward (something you care about becomes more likely). If your expended effort has essentially chance of resulting in a reward, then logically that effort was wasted.
This applies whether X is "get the election outcome you want" or "makes politicians care about the electorate" (which is the reason you gave for why people should vote) or anything else. If your vote isn't the deciding factor one way or another, then it is a waste of energy for you to vote. And that applies to both of the criteria I just listed.
In fact if you want to make politicians care it is far, far more effective to send an email, make a phone call, or send a piece of snail mail. Then you get to not just make them aware that someone is out there, but you actually get to tell them your specific concerns. Now odds are that you won't sway them. But the effort involved is on part with voting, and it is much more effective. So if you're willing to vote to make them care, you should send email about something every weekend!
When you look at things this way, my voting actually is logically defensible. After all the warm fuzzies I get from my emotional reaction to voting is a guaranteed return on effort that justifies the effort I expend. There is no question that the act of my voting makes the difference in my getting that feeling. So it makes sense for me to vote.
Therefore rationally there is no point in an individual voting.
I know this. But emotionally I feel better knowing that I tried to use my voice, even though logically I know that the act was meaningless. I long ago came to accept that my emotions do not respond to logic, and therefore I have come to let emotion drive my goals, and then use logic to achieve those goals.
Therefore I am willing to engage in a logically pointless activity in return for the emotional satisfaction I derive. Even though I am aware that the emotional satisfaction is illogical.