BUG: Series with same index values, but in different orders, cannot be compared, but can be added

[Dr-Irv]

Pandas version checks

• 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 main branch of pandas.

Reproducible Example

import pandas as pd
s=pd.Series([1,2,3,4,5])
s
t=s[-1::-1]
t
s + t
s <= t

Issue Description

Code above produces

>>> import pandas as pd
>>> s=pd.Series([1,2,3,4,5])
>>> s
0    1
1    2
2    3
3    4
4    5
dtype: int64
>>> t=s[-1::-1]
>>> t
4    5
3    4
2    3
1    2
0    1
dtype: int64
>>> s + t
0     2
1     4
2     6
3     8
4    10
dtype: int64
>>> s <= t
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "C:\Anaconda3\envs\pandasstubs\lib\site-packages\pandas\core\ops\common.py", line 70, in new_method
    return method(self, other)
  File "C:\Anaconda3\envs\pandasstubs\lib\site-packages\pandas\core\arraylike.py", line 52, in __le__
    return self._cmp_method(other, operator.le)
  File "C:\Anaconda3\envs\pandasstubs\lib\site-packages\pandas\core\series.py", line 5617, in _cmp_method
    raise ValueError("Can only compare identically-labeled Series objects")
ValueError: Can only compare identically-labeled Series objects

Expected Behavior

s<=t should produce

0    True
1    True
2    True
3    True
4    True
dtype: bool

Question is why we align the indices in arithmetic, but not in a logical operation. The two series are identically labeled, but just not in the same order, so the error message is misleading.

Installed Versions

INSTALLED VERSIONS ------------------ commit : f4ca4d3 python : 3.8.12.final.0 python-bits : 64 OS : Windows OS-release : 10 Version : 10.0.19043 machine : AMD64 processor : Intel64 Family 6 Model 158 Stepping 13, GenuineIntel byteorder : little LC_ALL : None LANG : None LOCALE : English_United States.1252

pandas : 1.5.0.dev0+1050.gf4ca4d3d0e
numpy : 1.22.4
pytz : 2022.1
dateutil : 2.8.2
setuptools : 60.9.3
pip : 22.0.3
Cython : 0.29.30
pytest : 7.1.2
hypothesis : 6.46.11
sphinx : 4.3.2
blosc : None
feather : None
xlsxwriter : 3.0.3
lxml.etree : 4.8.0
html5lib : 1.1
pymysql : None
psycopg2 : None
jinja2 : 3.1.2
IPython : 8.4.0
pandas_datareader: None
bs4 : 4.11.1
bottleneck : 1.3.4
brotli :
fastparquet : 0.8.1
fsspec : 2021.11.0
gcsfs : 2021.11.0
matplotlib : 3.5.1
numba : 0.53.1
numexpr : 2.8.0
odfpy : None
openpyxl : 3.0.9
pandas_gbq : None
pyarrow : 7.0.0
pyreadstat : 1.1.7
pyxlsb : None
s3fs : 2021.11.0
scipy : 1.8.1
snappy :
sqlalchemy : 1.4.37
tables : 3.7.0
tabulate : 0.8.9
xarray : 2022.3.0
xlrd : 2.0.1
xlwt : 1.3.0
zstandard : None

[CloseChoice]

Please note that

s.le(t)
#0    True
#1    True
#2    True
#3    True
#4    True
#dtype: bool

works fine and gives the expected result. I would naively think that logical comparisons match the behaviour of the overloaded double-underscore methods. The documentation also states this equivalence:

Equivalent to series <= other, but with support to substitute a fill_value for missing data in either one of the inputs.

Edit: This is no regression, at least until v1.1.0

Edit2: Also note that the exact same behaviour appears for <, >, >=, ==, != while their counterparts .lt, .gt, .ge, .eq, .ne all work fine.

[Dr-Irv]

Broadcasting also doesn't work for comparisons and is inconsistent as well:

>>> s = pd.Series([1,2,3,4], index=pd.MultiIndex.from_product([["a", "b"], ["x", "y"]], names=["ab", "xy"]))
>>> s
ab  xy
a   x     1
    y     2
b   x     3
    y     4
dtype: int64
>>> t = pd.Series([0, 5], index=pd.Index(["a", "b"], name="ab"))
>>> t
ab
a    0
b    5
dtype: int64
>>> t < s
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "C:\Anaconda3\envs\pandasstubs\lib\site-packages\pandas\core\ops\common.py", line 70, in new_method
    return method(self, other)
  File "C:\Anaconda3\envs\pandasstubs\lib\site-packages\pandas\core\arraylike.py", line 48, in __lt__
    return self._cmp_method(other, operator.lt)
  File "C:\Anaconda3\envs\pandasstubs\lib\site-packages\pandas\core\series.py", line 5617, in _cmp_method
    raise ValueError("Can only compare identically-labeled Series objects")
ValueError: Can only compare identically-labeled Series objects
>>> t.lt(s)
ab  xy
a   x      True
    y      True
b   x     False
    y     False
dtype: bool

[simonjayhawkins]

somewhat related #36941 (comment) and #20442 (comment)

it maybe that we have tests for the None case that break when sharing code.

since the ValueError("Can only compare identically-labeled Series objects") is explicitly raised, the issue in the OP could be considered not a bug but an enhancement request.

so we could add more logic to do the alignment in the existing code (-1). Or share the working code so that it is consistent (+1).

If the latter, I think can probably close as a duplicate.

[Dr-Irv]

so we could add more logic to do the alignment in the existing code (-1). Or share the working code so that it is consistent (+1).

I think we should do the alignment. As shown in #47554 (comment) , the difference in behavior between Series.le() and Series.__le__() seems inconsistent

[kathryn1229]

take