BUG: MultiIndex.difference incorrectly raising TypeError when indexes contain non-sortable entries

doc/source/whatsnew/v1.3.0.rst

@@ -1035,6 +1035,7 @@ MultiIndex
 - Bug in :meth:`MultiIndex.intersection` duplicating ``NaN`` in the result (:issue:`38623`)
 - Bug in :meth:`MultiIndex.equals` incorrectly returning ``True`` when the :class:`MultiIndex` contained ``NaN`` even when they are differently ordered (:issue:`38439`)
 - Bug in :meth:`MultiIndex.intersection` always returning an empty result when intersecting with :class:`CategoricalIndex` (:issue:`38653`)
+- Bug in :meth:`MultiIndex.difference` incorrectly raising ``TypeError`` when indexes contain non-sortable entries (:issue:`41915`)
 - Bug in :meth:`MultiIndex.reindex` raising a ``ValueError`` when used on an empty :class:`MultiIndex` and indexing only a specific level (:issue:`41170`)
 - Bug in :meth:`MultiIndex.reindex` raising ``TypeError`` when reindexing against a flat :class:`Index` (:issue:`41707`)
 

pandas/core/indexes/base.py

@@ -3091,7 +3091,7 @@ def intersection(self, other, sort=False):
             return this.intersection(other, sort=sort)
 
         result = self._intersection(other, sort=sort)
-        return self._wrap_setop_result(other, result)
+        return self._wrap_intersection_result(other, result)
 
     def _intersection(self, other: Index, sort=False):
         """
@@ -3113,6 +3113,10 @@ def _intersection(self, other: Index, sort=False):
         res_values = _maybe_try_sort(res_values, sort)
         return res_values
 
+    def _wrap_intersection_result(self, other, result):
+        # We will override for MultiIndex to handle empty results
+        return self._wrap_setop_result(other, result)
+
     def _intersection_via_get_indexer(self, other: Index, sort) -> ArrayLike:
         """
         Find the intersection of two Indexes using get_indexer.

pandas/core/indexes/multi.py

@@ -3588,50 +3588,23 @@ def _maybe_match_names(self, other):
                 names.append(None)
         return names
 
-    def _intersection(self, other, sort=False) -> MultiIndex:
+    def _wrap_intersection_result(self, other, result):
         other, result_names = self._convert_can_do_setop(other)
-        other = other.astype(object, copy=False)
 
-        uniq_tuples = None  # flag whether _inner_indexer was successful
-        if self.is_monotonic and other.is_monotonic:
-            try:
-                inner_tuples = self._inner_indexer(other)[0]
-                sort = False  # inner_tuples is already sorted
-            except TypeError:
-                pass
-            else:
-                uniq_tuples = algos.unique(inner_tuples)
-
-        if uniq_tuples is None:
-            uniq_tuples = self._intersection_via_get_indexer(other, sort)
-
-        if sort is None:
-            uniq_tuples = sorted(uniq_tuples)
-
-        if len(uniq_tuples) == 0:
+        if len(result) == 0:
             return MultiIndex(
                 levels=self.levels,
                 codes=[[]] * self.nlevels,
                 names=result_names,
                 verify_integrity=False,
             )
         else:
-            return MultiIndex.from_arrays(
-                zip(*uniq_tuples), sortorder=0, names=result_names
-            )
+            return MultiIndex.from_arrays(zip(*result), sortorder=0, names=result_names)
 
     def _difference(self, other, sort) -> MultiIndex:
         other, result_names = self._convert_can_do_setop(other)
 
-        this = self._get_unique_index()
-
-        indexer = this.get_indexer(other)
-        indexer = indexer.take((indexer != -1).nonzero()[0])
-
-        label_diff = np.setdiff1d(np.arange(this.size), indexer, assume_unique=True)
-        difference = this._values.take(label_diff)
-        if sort is None:
-            difference = sorted(difference)
+        difference = super()._difference(other, sort)
 
         if len(difference) == 0:
             return MultiIndex(

pandas/tests/indexes/multi/test_setops.py

@@ -216,11 +216,10 @@ def test_difference_sort_incomparable():
 
     other = MultiIndex.from_product([[3, pd.Timestamp("2000"), 4], ["c", "d"]])
     # sort=None, the default
-    # MultiIndex.difference deviates here from other difference
-    # implementations in not catching the TypeError
-    msg = "'<' not supported between instances of 'Timestamp' and 'int'"
-    with pytest.raises(TypeError, match=msg):
+    msg = "sort order is undefined for incomparable objects"
+    with tm.assert_produces_warning(RuntimeWarning, match=msg):
         result = idx.difference(other)
+    tm.assert_index_equal(result, idx)
 
     # sort=False
     result = idx.difference(other, sort=False)