BUG: idxmax raises when used with tuples

[helgehatt]

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the master branch of pandas.

Reproducible Example

import pandas as pd

x = pd.Series([(1,3),(2,2),(3,1)])

# This succeeds as the max operation is performed on the first element of a tuple
assert x.max() == (3,1)

# This fails with `TypeError: reduction operation 'argmax' not allowed for this dtype`
assert x.idxmax() == 2

# Using numpy directly works as you'd expect
import numpy as np
assert np.argmax(x.values) == 2

Issue Description

Using max on a series of tuples returns the tuple as if the max operation was performed on the first element of each tuple.

Using idxmax however, raises an operation not allowed TypeError.

Expected Behavior

Even though there are several ways of achieving the desired result, I would expect consistency between the usage of max and idxmax, as it is for max and argmax in numpy.

Installed Versions

INSTALLED VERSIONS

commit : 73c6825
python : 3.8.10.final.0
python-bits : 64
OS : Linux
OS-release : 4.15.0-1113-azure
Version : #126~16.04.1-Ubuntu SMP Tue Apr 13 16:55:24 UTC 2021
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : en_US.UTF-8
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 1.3.3
numpy : 1.20.1
pytz : 2021.1
dateutil : 2.8.2
pip : 21.1.3
setuptools : 52.0.0.post20210125
Cython : 0.29.23
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : 4.6.3
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.0.1
IPython : 7.22.0
pandas_datareader: None
bs4 : 4.9.3
bottleneck : 1.3.2
fsspec : 2021.06.0
fastparquet : None
gcsfs : None
matplotlib : 3.3.4
numexpr : 2.7.3
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pyxlsb : None
s3fs : None
scipy : 1.6.2
sqlalchemy : None
tables : 3.6.1
tabulate : 0.8.9
xarray : None
xlrd : None
xlwt : None
numba : None

[goyodiaz]

The problem actually comes from argmax:

>>> x.argmax()
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/home/goyo/.local/lib/python3.9/site-packages/pandas/core/base.py", line 647, in argmax
    return nanops.nanargmax(  # type: ignore[return-value]
  File "/home/goyo/.local/lib/python3.9/site-packages/pandas/core/nanops.py", line 88, in _f
    raise TypeError(
TypeError: reduction operation 'argmax' not allowed for this dtype

The way it is written it always delegate to nanops.nanargmax for dtype 'O', but nanops.nanargmax explicitly disallows arrays of that dtype.

Here's a hotfix:

import numpy as np
import pandas as pd
from pandas.core.base import nv, nanops, ExtensionArray, IndexOpsMixin

def argmax(self, axis=None, skipna: bool = True, *args, **kwargs) -> int:
    """
    Return int position of the {value} value in the Series.

    If the {op}imum is achieved in multiple locations,
    the first row position is returned.

    Parameters
    ----------
    axis : {{None}}
        Dummy argument for consistency with Series.
    skipna : bool, default True
        Exclude NA/null values when showing the result.
    *args, **kwargs
        Additional arguments and keywords for compatibility with NumPy.

    Returns
    -------
    int
        Row position of the {op}imum value.

    See Also
    --------
    Series.arg{op} : Return position of the {op}imum value.
    Series.arg{oppose} : Return position of the {oppose}imum value.
    numpy.ndarray.arg{op} : Equivalent method for numpy arrays.
    Series.idxmax : Return index label of the maximum values.
    Series.idxmin : Return index label of the minimum values.

    Examples
    --------
    Consider dataset containing cereal calories

    >>> s = pd.Series({{'Corn Flakes': 100.0, 'Almond Delight': 110.0,
    ...                'Cinnamon Toast Crunch': 120.0, 'Cocoa Puff': 110.0}})
    >>> s
    Corn Flakes              100.0
    Almond Delight           110.0
    Cinnamon Toast Crunch    120.0
    Cocoa Puff               110.0
    dtype: float64

    >>> s.argmax()
    2
    >>> s.argmin()
    0

    The maximum cereal calories is the third element and
    the minimum cereal calories is the first element,
    since series is zero-indexed.
    """
    delegate = self._values
    nv.validate_minmax_axis(axis)
    skipna = nv.validate_argmax_with_skipna(skipna, args, kwargs)

    if delegate.dtype is np.dtype('O'):  # This is the part I added to deal with dype('O')
        # Ignoring skipna because I am not sure what it should do here. NA's in
        # series with dtype('O') will cause trouble anyway.
        return delegate.argmax()
    elif isinstance(delegate, ExtensionArray):
        if not skipna and delegate.isna().any():
            return -1
        else:
            return delegate.argmax()
    else:
        # error: Incompatible return value type (got "Union[int, ndarray]", expected
        # "int")
        return nanops.nanargmax(  # type: ignore[return-value]
            delegate, skipna=skipna
        )

IndexOpsMixin.argmax = argmax

x = pd.Series([(1, 3), (2, 2), (3, 1), (3, 0)], index=['zero', 'one', 'two', 'three'])
assert x.idxmax() == 'two'
assert x.argmax() == 2