How to send a vote using Advance Poll and Services Voting Api?
Ok, I figured out how this is supposed to work. The required JSON document to POST to the set_votes service must be this:

{
  "votes":[
    {
    "entity_id":"1328",
    "tag":"f5a8bb465",
    "value":"1"
    }
  ]
}


entity_id is the nid of the Advance Poll, tag is the choice_id of the Poll Choice you want to cast the vote for, and value must always be 1, it's the vote.

In case you need to know those IDs, it may be a good idea to expose them through the node or the view services. Or use the Devel module