When you are attempting to get people, online voting contest
who you don’t have a close/good relationship with (i.e. a history of reciprocity) to do things for you, you need to give them an incentive.
The most obvious incentive is financial reward, but of course this may be against the contest’s rules. The next incentive (that I think of at the moment) is self-gratification.
Using the example you provided, you can craft a message that conveys something along the lines of «Vote for Education and show the world how much you care about children.» Of course, this is not a very subtle appeal, but it can be the essence of your message. Just get creative about how you say the above, that is think conceptually about that message rather than literally.
You can also appeal to their sense of competition and implore the age-old «us vs. them» strategy. Example Message: «Vote for Education, so we can show those children-hating people over in XYZ that we care enough to fight for children.» Or something like that. Again be subtle but make your message about us vs. them.
One last strategy I can think of is crafty but I think will be tough to pull off. You can create your own contest, in which you select a winner out of all the people who voted for Education (again using the example you provided). I suspect this isn’t against the rules, but the issue will be how you collect the lists of your contestants, i.e. those who voted for your issue.