I think that in order to solve such a question, we first need to consider something else. Why, if votes are so important to you, can’t you just create a bunch of accounts and vote honestly on any server?

As soon as we are really sure that 1 person is 1 vote, and not 10, 100, 10000 or any other number, then it is already possible to build trust checks between servers. Although it seems that this has not been solved even by large social networks.

The answer to your question in general is this: store the votes by servers and then double-check the result randomly.

S returns: 50 votes for a post from server A, 30 for a post from server B, 10 for a post from server C, etc. Then you can randomly check on these servers whether the amount is correct. However, there is no way to check the voices of server S, so they either have to be thrown out or still trust the server at its word.