No child finds "because I say so" a very good reason. Why not say, "I will explain why later. Please remind me then." If its a small matter, they will forget; if not, you can explain when you are not under stress. I guess I am not in a position to criticize.
But with the voting, the Freakonomics authors point out that if you are purely selfish, it is not rational to vote. The chance you will cast the deciding vote are probably lower than the chance you will be stabbed on the way to the polling station.
My responses to this theme:
1. People should not be narrowly self-interested. Like recycling, your action may not change anything, but all together people can have an effect. One could argue that every glass recycled has an effect, even if it is tiny, but your vote will very likely not have any effect. However, a small effect and a chance of having a huge effect have a similar value.
2. Vote not just for yourself, but for everyone that will be voting the way you will be voting. It is unfair to have them go to the polls on your behalf, and then have you not bother. It is simply rude not reciprocate.
3. This argument might be fallacious, but I like it: Think about polls. Pollsters ask 700 Americans about an issue and get a result within 3% of the correct answer. What each person answers is representative of about 700,000 voters. So imagine you just called on the phone. The question: will you vote? What you say is representative of hundreds of thousands of people just like you. If you go to the polls, whatever social forces has brought you there are acting on the rest of the population. It would be dishonest for me to argue that your decision will change the decision of other people, but in a way, if you vote for it, they will vote for it. So vote! That is, if you agree with me.
4. I would change how we vote for representatives. My solution: have two people elected from each district, and when the representatives vote in the legislative body, their vote will be weighted by the number of votes they received. So, lets say candidate Miers gets 40% of the vote and candidate Alito gets 50% (10% other)*. When they vote on a proposed statute, Miers will get 4/9th of a vote, Alito gets 5/9th of a vote. There would be no more problems with gerrymandered districts, because it would not help either party to concentrate the votes of the other. There would always be an incentive to vote. Even if the outcome of who would win the most votes was clear, each vote cast would increase the power of your preferred candidate. And every citizen could feel represented in the legislature.
*This could also be combined with a transferable vote; every vote would count.