How would I construct my update instruction for two arrays on two different collections?

Working with Data Drivers
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1

Context:
Okay so I am making a polling website. There are basically two ways to vote. Simple vote which just counts the number of votes for a movie. And ranked voting where each user ranks each movie and then the winner is decided using instant runoff. Here is my idea of how to handle it: I have a poll collection which just stores the rank for each movie for ranked polls and number of votes for each movie for simple. So something like this:

{
_id: ObjectId
pollType: string
movies: array
  0: Object
    id: ObjectId
    title: String
    rank: number
    votes: number
}

Then I have a vote collection which a vote is added each time a user votes.

{
_id:ObjectId
pollId: Objectid
votedMovies: Array
  0: Object
    id: ObjectId
    title: string
    rank: number
}

When the user votes I will then retrieve all the votes for a poll and for simple votes increment the vote count based on what movies where in the votedMovies Array. For ranked voting I would get each movie rank for every vote and then do a instant runoff calculation. Finally I would then update the polls votes and rankings for each movie.

Question:
So far I’m only worried about the simple vote. How would I update the number of votes for each movie on the poll collection? This is what I have so far:

async function updateVotes(id){
   const cursor =  db.collection('votes').find({poll: id});
   console.log(id);
   const pollid = new ObjectId(id);
   
   console.log(poll);

   await cursor.forEach(function(doc) {
    const poll = await polls.updateOne({_id:pollid}, {$set: {"movies.$[]"}}); //problem line
   });
}