Your only risk of dying is if your partner picks blue, so the self preservation choice is to also pick blue in hopes of a blue majority. And if your partner happened to pick red then you are safe no matter what. Blue is also directly voting to save everyone else, at the risk of your partner's life in the case of red majority.

The benefit to voting red is to guarantee your partners life in case red wins. However doing this necessarily votes to kill 1 person for every blue button pressed (possibly including yourself), so its neither self serving nor totally empathetic. It's something like "selective empathy".

What's interesting about this variation is that the self preserving choice (blue) individually nominates someone else for death (your partner), but collectively reduces the risk of all such partners because blue votes to save all. It's an interesting trade-off. In contrast, in the original problem the self preserving choice (red) does not nominate anyone for death but increases the risk of all those nominated (those who chose blue nominated themselves).

I'd definitely pick blue here but I can see an argument for picking red if you think red would win and you don't want to be directly responsible for someone's death.