FB let's you upload lists of 'purchases' to match, we can just make a vote a purchase.

and then they black box tie them to impressions/ad events.

It only works with early voting, where you get a list of voters who have cast or sent in mail ballot each day.

though arguably you're already targeting a tight list in FB of likely early voters (who are likely to vote themselves even without seeing an ad) so who knows if the ad actually got any extra votes in.

You could do an AB test, randomly show ads to only half the audience and measure lift but there are only a couple weeks of early voting usually and relatively small audiences unless you're statewide. I imagine it would work better for Presidential i've never worked on one, kind of a bucket list dream but also would suckkkk for a few years

You can also upload a final voting list after the fact as offline conversions, but doesn't make much difference after the votes are counted though I guess cool stats