I'm looking to perform a composite aggregation on the following documents:

[
{
  "title": "Document 1",
  "tags": ["elasticsearch", "aggregation", "elasticsearch"] 
}
{
  "title": "Document 2",
  "tags": ["elasticsearch", "search", "search"]
}
{
  "title": "Document 3",
  "tags": ["aggregation", "search"]
}
]

When running this aggregation:

{
  "size": 0,
  "aggs": {
    "tags_count": {
      "terms": {
        "field": "tags.keyword"
      }
    }
  }
}

I am expecting each value to be counted individually regardless of whether or not it's duplicated, like so:

{
  "aggregations": {
    "tags_count": {
      "buckets": [
        { "key": "elasticsearch", "doc_count": 3 },
        { "key": "search", "doc_count": 3 },
        { "key": "aggregation", "doc_count": 2 }
      ]
    }
  }
}

However, I actually get this:

{
  "aggregations": {
    "tags_count": {
      "buckets": [
        { "key": "elasticsearch", "doc_count": 2 },
        { "key": "search", "doc_count": 2 },
        { "key": "aggregation", "doc_count": 2 }
      ]
    }
  }
}

Is there a way to achieve my expected behaviour?

Tldr;

I don't think you will be able to bend the classic aggregations to your needs, you will need a custom script aggregation.

Solution

Set up

In order to run build this script I created the following dataset:

POST 79469094/_bulk
{"index": {}}
{"title": "Document 1","tags": ["elasticsearch","aggregation","elasticsearch"]}
{"index": {}}
{"title": "Document 2","tags": ["elasticsearch","search","search"]}
{"index": {}}
{"title": "Document 3","tags": ["aggregation","search"]}

Script

Using a script aggregation like the following should do the trick.

GET 79469094/_search
{
  "size": 0,
  "aggs": {
    "tags_count": {
      "scripted_metric": {
        "init_script": "state.counts = [:]",
        "map_script": """
          for (tag in params._source.tags) {
            state.counts[tag] = state.counts.containsKey(tag) ? state.counts[tag] + 1 : 1;
          }
        """,
        "combine_script": "return state.counts",
        "reduce_script": """
          Map finalCounts = [:];
          for (state in states) {
            for (entry in state.entrySet()) {
              finalCounts[entry.getKey()] = finalCounts.containsKey(entry.getKey()) ?
                finalCounts[entry.getKey()] + entry.getValue() : entry.getValue();
            }
          }
          return finalCounts;
        """
      }
    }
  }
}

Results

{
  "took": 30,
  "timed_out": false,
  "_shards": {
    "total": 1,
    "successful": 1,
    "skipped": 0,
    "failed": 0
  },
  "hits": {
    "total": {
      "value": 3,
      "relation": "eq"
    },
    "max_score": null,
    "hits": []
  },
  "aggregations": {
    "tags_count": {
      "value": {
        "search": 3,
        "elasticsearch": 3,
        "aggregation": 2
      }
    }
  }
}