Optimizing electoral votes in a political simulation... 200,000+ possibilities, how to run through them?
200000 is not a terribly large number, a brute force solution in Python would probably run in reasonable time. You'd have to implement a function that calculates your influences depending on your answers to the 14 issues and then just check all the possibilities. Python has some nice library functions that can help in the itertools package, but programming questions should better be asked on Stackoverflow.

A solution that is requires more learning to implement would writing down the problem as an Integer Linear Program and feeding it to a solver. That would probably scale much better than a naive brute force solution. It also sounds more sciency. But as I said, your problem instance is reasonably small.