BUG: idxmax raising for arrow strings (pandas-dev#55384)

(cherry picked from commit 68e3c4b)

Author: phofl

pandas/core/arrays/arrow/array.py

@@ -1596,6 +1596,15 @@ def _reduce(
         ------
         TypeError : subclass does not define reductions
         """
+        result = self._reduce_calc(name, skipna=skipna, keepdims=keepdims, **kwargs)
+        if isinstance(result, pa.Array):
+            return type(self)(result)
+        else:
+            return result
+
+    def _reduce_calc(
+        self, name: str, *, skipna: bool = True, keepdims: bool = False, **kwargs
+    ):
         pa_result = self._reduce_pyarrow(name, skipna=skipna, **kwargs)
 
         if keepdims:
@@ -1606,7 +1615,7 @@ def _reduce(
                     [pa_result],
                     type=to_pyarrow_type(infer_dtype_from_scalar(pa_result)[0]),
                 )
-            return type(self)(result)
+            return result
 
         if pc.is_null(pa_result).as_py():
             return self.dtype.na_value

pandas/core/arrays/string_arrow.py

@@ -444,6 +444,17 @@ def _str_rstrip(self, to_strip=None):
             result = pc.utf8_rtrim(self._pa_array, characters=to_strip)
         return type(self)(result)
 
+    def _reduce(
+        self, name: str, *, skipna: bool = True, keepdims: bool = False, **kwargs
+    ):
+        result = self._reduce_calc(name, skipna=skipna, keepdims=keepdims, **kwargs)
+        if name in ("argmin", "argmax") and isinstance(result, pa.Array):
+            return self._convert_int_dtype(result)
+        elif isinstance(result, pa.Array):
+            return type(self)(result)
+        else:
+            return result
+
 
 class ArrowStringArrayNumpySemantics(ArrowStringArray):
     _storage = "pyarrow_numpy"

pandas/tests/frame/test_reductions.py

@@ -1073,6 +1073,15 @@ def test_idxmax_arrow_types(self):
         expected = Series([2, 1], index=["a", "b"])
         tm.assert_series_equal(result, expected)
 
+        df = DataFrame({"a": ["b", "c", "a"]}, dtype="string[pyarrow]")
+        result = df.idxmax(numeric_only=False)
+        expected = Series([1], index=["a"])
+        tm.assert_series_equal(result, expected)
+
+        result = df.idxmin(numeric_only=False)
+        expected = Series([2], index=["a"])
+        tm.assert_series_equal(result, expected)
+
     def test_idxmax_axis_2(self, float_frame):
         frame = float_frame
         msg = "No axis named 2 for object type DataFrame"