[mopierotti]

However some map-reduce implementations implicitly expect reducers to be commutative, which the author became appropriately suspicious of because of the "typical examples" of map-reduce.

I found this interesting paper on the subject of non-commutative reducers: "Nondeterminism in MapReduce Considered Harmful?" https://www.microsoft.com/en-us/research/wp-content/uploads/...