Return top 3 grouped results from relationship

I have a table, comments, that looks like this:

+====+=========+
| id | message |
+====+=========+
|  1 |      Hi |
|  2 |   World |
+====+=========+

I have a second table, comment_stats, which keeps track of the total number of votes on each comment, that looks like this:

+====+============+=======+
| id | comment_id | votes |
+====+============+=======+
|  1 |          1 |    10 |
|  2 |          2 |     0 |
+====+============+=======+

And lastly, I have a third table, comment_votes, which keeps track of each individual user's vote for each comment, that looks like this:

+====+============+=========+=========+
| id | comment_id | user_id |    type |
+====+============+=========+=========+
|  1 |          1 |      10 |       0 |
|  2 |          1 |       9 |       0 |
|  3 |          1 |       8 |       1 |
|  4 |          1 |       7 |       2 |
|  5 |          1 |       6 |       1 |
|  6 |          1 |       5 |       5 |
|  7 |          1 |       4 |       3 |
|  8 |          1 |       3 |       3 |
|  9 |          1 |       2 |       1 |
| 10 |          1 |       1 |       0 |
+====+============+=========+=========+

As you can see, each comment can be voted on by other users (comment_votes) and the total votes are kept track of in comment_stats. Each vote has a type. There are a total of 6 possible types (0-5).

My current Comment.php class looks like:

class Comment extends Model
{
    protected $with = [
        'votes', 'stats'
    ];

    public function votes()
    {
        return $this->hasMany('App\Vote');
    }

    public function stats()
    {
        return $this->hasOne('App\Stat');
    }
}

My Stat.php class looks like:

class Stat extends Model
{
    protected $with = [
        'topTypes'
    ];

    public function comment()
    {
        return $this->belongsTo('App\Comment');
    }

    public function topTypes()
    {
        // Need to return an array of the top 3 types here
    }
}

And my Vote.php class looks like:

class Vote extends Model
{
    public function comment()
    {
        return $this->belongsTo('App\Comment');
    }
}

I'd like to retrieve the top 3 types for each comment. So for comment_id = 1, the output would be [0, 1, 3] (as an array), in that order. 0 appears 3 times, 1 appears 3 times, and 3 appears twice. If there is a tie, it should get the lower integer type.

I'm trying to get the JSON to end up looking something like this, so that the top_types is part of stats:

{
    "id": 1,
    "message": "Hi",
    "stats": {
        "id": 1,
        "comment_id": 1,
        "votes": 10,
        "top_types": [0, 1, 3]
    }
}

How could I achieve this? All of these relationships are driving me insane.

via Chebli Mohamed