I feel like you could put in a lot more work making this post more rational. It could use a cost/benefit analysis, or, even better, the form of the volunteering problem from the article on mixed strategy nash equilibria. Be more explicit about more things.

the individual's vote is proportionately very small. This means it cannot have an effect on the outcome.

Read that again. Do you see the same problem I see?

Perhaps reading this recent thread that's almost identical would be interesting to you.