The elections are not run by volunteers here. I am the Judge of Elections for my district. I get paid by the county for that day, as do all of the other poll workers here. By my rough calculations, the county had to pay out about $2 for each person who voted in my district in the most recent primary election - 379 voters showed up (of 766 registered), and we have a total of 5 people who are each paid just over $100 for the day, plus one-half of a constable (shared with the adjacent district which votes in the same room).
This does not include the wages paid to the staff who configure the voting machines, deliver them to my polling place, collect and aggregate the results at the end of the night, among others. Nor does it include the costs of the printed books of registered voters, signage which we must post to inform voters of the law, and other supplies which must be generated for each election and discarded afterwards (because they are specific to the election - the set of eligible voters changes, the signage is unique to the election depending on what is on the ballot, etc).
This was even the highest turnout election I have run. An odd-year primary (which contains only local offices on the ballot) can have as few as 50 voters turn out, but the costs are essentially fixed, so the per-voter cost is significantly higher.
Since the elections in my state are closed, only registered Democrats and Republicans can vote on most issues. This one had two ballot initiatives, one of which was cancelled before the election (but after all of the machines were programmed and materials printed) and will re-appear on the November ballot, and the other which only affected another city 300 miles away (and even then, only de jure and not de facto, because the action in question was already taken, and the amendment is only to strike the law of something which no longer exists).
Running an election such as this costs literally millions of dollars across the state - one estimate I found put it over $25 million overall, which would put the cost per registered voter at about $3, and more like $6 per actual vote cast (given ~50% average turnout, which is fairly accurate for this primary election).