Is PGSQL not executing my index because of the ORDER BY clause? - ruby-on-rails

Question

I have a rails query that looks like this:
Person.limit(10).unclaimed_people({})
def unclaimed_people(opts)
sub_query = where.not(name_id: nil)
if opts[:q].present?
query_with_email_or_name(sub_query, opts)
else
sub_query.group([:name_id, :effective_name])
.reorder('MIN(COALESCE(kudo_position,999999999)), lower(effective_name)')
.select(:name_id)
end
end
Translating to SQL, the query looks like this:
SELECT "people"."name_id" FROM "people"
WHERE ("people"."name_id" IS NOT NULL)
GROUP BY "people"."name_id", "people"."effective_name"
ORDER BY MIN(COALESCE(kudo_position,999999999)), lower(effective_name) LIMIT 10
Now when I run an EXPLAIN on the SQL query, what's returned shows that I am not running an index scan. Here is the EXPLAIN:
QUERY PLAN
--------------------------------------------------------------------------------------------------------------------------------------------
Limit (cost=728151.18..728151.21 rows=10 width=53) (actual time=6333.027..6333.028 rows=10 loops=1)
-> Sort (cost=728151.18..729171.83 rows=408258 width=53) (actual time=6333.024..6333.024 rows=10 loops=1)
Sort Key: (min(COALESCE(kudo_position, 999999999))), (lower(effective_name))
Sort Method: top-N heapsort Memory: 25kB
-> GroupAggregate (cost=676646.88..719328.87 rows=408258 width=53) (actual time=4077.902..6169.151 rows=946982 loops=1)
Group Key: name_id, effective_name
-> Sort (cost=676646.88..686041.57 rows=3757877 width=21) (actual time=4077.846..5106.606 rows=3765261 loops=1)
Sort Key: name_id, effective_name
Sort Method: external merge Disk: 107808kB
-> Seq Scan on people (cost=0.00..112125.78 rows=3757877 width=21) (actual time=0.035..939.682 rows=3765261 loops=1)
Filter: (name_id IS NOT NULL)
Rows Removed by Filter: 317644
Planning time: 0.130 ms
Execution time: 6346.994 ms
Pay attention to the bottom part of the query plan. There is a Seq Scan on people. This is not what I was expecting, in my development and production database, I have placed an index on the foreign name_id field. Here is the proof from the people table.
"index_people_name_id" btree (name_id) WHERE name_id IS NOT NULL
So my question is why would it not be running the index. Could it perhaps be from the ORDER BY clause. I read that it could affect the execution of an index. This is the web page where I read it from. Why isn't my index being used?
In particular here is the quote from the page.
Indexes are normally not used for ORDER BY or to perform joins. A sequential scan followed by an explicit sort is usually faster than an index scan of a large table. However, LIMIT combined with ORDER BY often will use an index because only a small portion of the table is returned.
As you can see from the query, I am using ORDER BY combined with LIMIT so I would expect the index to be used. Could this be outdated? Is the ORDER BY really affecting the query? What am I missing to get the index to work? I'm not particularly versed with the internals of PGSQL so any help would be appreciated.