Another natural experiment about the accuracy of AccuVote machines occurs because almost half the polling places in New Hampshire still hand-count their ballots on election nights.

In 2020, there were three recounts of multi-town state representative districts which included both hand- and machine-counted communities. Since these recounts involved the exact same ballots, they offer a way to compare accuracy of the two methods with fewer confounding variables. So that’s what I did.

■In Grafton District 17, the recount changed 27 votes in the two hand-counted towns (Alexandria and Bridgewater) and 17 votes in the four machine-counted towns. The machine-counted towns had more than four times the total number of votes cast as the hand-counted towns, so this is a big win for AccuVote.

■In Merrimack District 20, the recount changed 28 votes in Chichester (hand count) and 25 in Pembroke (machine count). That’s an insignificant difference but Pembroke had twice as many votes cast, so from a percentage point of view this is another win for AccuVote.

■Hillsborough District 4 had two party primary recounts, in both the Democrat and Republican races. Overall, 17 votes changed in three hand-counted towns compared to 9 votes changing in the machine-counted town of Wilton. Since Wilton is by far the biggest town in the district and cast almost half the total votes, that’s a third win for the machines.

Anybody who has volunteered to help their moderator and town clerk count ballots on election night will not be surprised by this. Keeping accurate tallies of thousands of little dark circles on hundreds of paper ballots under deadline pressure, with all those annoying reporters yelling at you to release the results, is tough. Errors are inevitable.

This is a case where machines are better than people.

By the way, if you’re surprised about how many places hand-count ballots, that’s because relatively few voters are involved. Only smaller communities still do hand counting; no city does it nor do large towns like Derry, Merrimack or Bow.

Some hand-count towns adopted AccuVote recently because of COVID, to reduce crowding on election night.