Anyone here into cryptosystems? Electronic voting? I would be interested in a solution to the following problems or some variants.

Consider a distributed system like the Fediverse where each server is owned by an independent party. Some servers are more trustworthy than others.

On a less trustworthy server S, someone makes a post. This post can be upvoted by people on any server. S aggregates the votes and sends only the number of votes to other servers.

The other servers can of course ask for a complete list of voters, and then verify the vote count. But this results in a lot of data exchange.

Without asking for a complete list of voters, how can other servers check if the count reported by S is correct? It would be sufficient to know that it is correct with high probability (as opposed to knowing for certain).