BUG: Non deterministic level order in MultiIndex with join (pandas-dev#37199)

Author: phofl

doc/source/whatsnew/v1.2.0.rst

@@ -505,6 +505,7 @@ Reshaping
 - Bug in func :meth:`crosstab` when using multiple columns with ``margins=True`` and ``normalize=True`` (:issue:`35144`)
 - Bug in :meth:`DataFrame.agg` with ``func={'name':<FUNC>}`` incorrectly raising ``TypeError`` when ``DataFrame.columns==['Name']`` (:issue:`36212`)
 - Bug in :meth:`Series.transform` would give incorrect results or raise when the argument ``func`` was dictionary (:issue:`35811`)
+- Bug in :func:`join` returned a non deterministic level-order for the resulting :class:`MultiIndex` (:issue:`36910`)
 -
 
 Sparse

pandas/core/indexes/base.py

@@ -3597,8 +3597,12 @@ def _join_multi(self, other, how, return_indexers=True):
         from pandas.core.reshape.merge import restore_dropped_levels_multijoin
 
         # figure out join names
-        self_names = set(com.not_none(*self.names))
-        other_names = set(com.not_none(*other.names))
+        self_names_list = list(com.not_none(*self.names))
+        other_names_list = list(com.not_none(*other.names))
+        self_names_order = self_names_list.index
+        other_names_order = other_names_list.index
+        self_names = set(self_names_list)
+        other_names = set(other_names_list)
         overlap = self_names & other_names
 
         # need at least 1 in common
@@ -3608,8 +3612,8 @@ def _join_multi(self, other, how, return_indexers=True):
         if isinstance(self, MultiIndex) and isinstance(other, MultiIndex):
 
             # Drop the non-matching levels from left and right respectively
-            ldrop_names = list(self_names - overlap)
-            rdrop_names = list(other_names - overlap)
+            ldrop_names = sorted(self_names - overlap, key=self_names_order)
+            rdrop_names = sorted(other_names - overlap, key=other_names_order)
 
             # if only the order differs
             if not len(ldrop_names + rdrop_names):

pandas/tests/reshape/merge/test_join.py

@@ -787,3 +787,20 @@ def _join_by_hand(a, b, how="left"):
     for col, s in b_re.items():
         a_re[col] = s
     return a_re.reindex(columns=result_columns)
+
+
+def test_join_inner_multiindex_deterministic_order():
+    # GH: 36910
+    left = pd.DataFrame(
+        data={"e": 5},
+        index=pd.MultiIndex.from_tuples([(1, 2, 4)], names=("a", "b", "d")),
+    )
+    right = pd.DataFrame(
+        data={"f": 6}, index=pd.MultiIndex.from_tuples([(2, 3)], names=("b", "c"))
+    )
+    result = left.join(right, how="inner")
+    expected = pd.DataFrame(
+        {"e": [5], "f": [6]},
+        index=pd.MultiIndex.from_tuples([(2, 1, 4, 3)], names=("b", "a", "d", "c")),
+    )
+    tm.assert_frame_equal(result, expected)