I don't think that there is a single word for this.
I would be inclined to call it a "self-interested vote" rather than a "selfish vote". Example sentence: "65% of voters reported voting in their own self-interest in the recent election".
I prefer "self-interested" as it has slightly less of a value judgement than "selfish" - though if you want to convey the negative value judgement, "selfish" may be the better word.
This is a political point rather than one about language, but there is an argument that if everyone votes in their self-interest then the overall result will then reflect the general welfare. Certainly, if no-one votes in their own self-interest, it's not clear that the result will be in anyone's interest.