If I sort by {a: -1} and use $first, I should get the largest 'a' value within each group.

For example, using $bucket I get the expected result:

> db.c.find()
{ "_id" : 0, "a" : 0 }
{ "_id" : 1, "a" : 1 }
{ "_id" : 2, "a" : 2 }
{ "_id" : 3, "a" : 3 }
{ "_id" : 4, "a" : 4 }
{ "_id" : 5, "a" : 5 }
{ "_id" : 6, "a" : 6 }
{ "_id" : 7, "a" : 7 }
{ "_id" : 8, "a" : 8 }
{ "_id" : 9, "a" : 9 }

> db.c.aggregate([ {$sort: {a: -1}}, {$bucket: {groupBy: "$a", boundaries: [0, 5, 10], output: {a: {$first: "$a"}} }} ])
{ "_id" : 0, "a" : 4 }
{ "_id" : 5, "a" : 9 }

While the same thing with $bucketAuto gives the smallest value within each group:

> db.c.aggregate([ {$sort: {a: -1}}, {$bucketAuto: {groupBy: "$a", buckets: 2, output: {a: {$first: "$a"}} }} ])
{ "_id" : { "min" : 0, "max" : 5 }, "a" : 0 }
{ "_id" : { "min" : 5, "max" : 9 }, "a" : 5 }

It looks like internally $bucketAuto is doing something like:

• stable-sort by the group key
• scan the sorted input
  • accumulate each document into the current bucket
  • start a new bucket every N documents (based on input size / num buckets)

But this doesn’t work for order-sensitive accumulators like $first, because the sort loses some information about the original order--even using a stable sort. The documents within each dynamically-chosen bucket are sorted by (group key, input position), instead of by input position.