The Onion

As I understand it, the Amish aren't strictly forbidden from using electricity or technology so much as they aren't allowed to include those things in the Amish way of life without approval. Different communities come to different conclusions about what should be allowed, but in general, if it's a device they aren't going to own, they tend to be a lot more permissive about it. I would imagine that most would have no problem with voting machines, since it's basically something they would only interact with outside of their normal daily lives.

How inclined they are to vote, I have no idea. A quick googling shows plenty of talk about courting the Amish vote, but that has less to do with Amish views on the topic and more to do with the fact that they are warm bodies in a swing state.

The sect around me does not vote as a rule. They use voting as a threat whenever the English try to enact some rule that affects their situation.

In the past 20 years these restrictions on their "religious freedom" have included the following:

License plates and road taxes for buggies

Helmet requirements for children riding bikes on state highways.

Requiring them to clean up their horse poop scattered on public roads and waterways

Requiring their children to receive a bare minimum of education.