"Empathy" isn't a binary in this context. You can exercise empathy and aid your community by making sure everyone you know votes red. That's the kind of cooperation that humans have evolved with. What you're talking about is undifferentiated, universal empathy, where someone would be willing to risk the lives of those close to them for a greater chance to help those who are outside their immediate reach to persuade.

I suspect if you played this game, lots of tight-knit, high-cooperation groups would undertake coordinated campaigns to ensure the survival of their members by ensuring everyone votes red.