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Reproducible Example

import pandas as pd
import numpy as np

# On trunk
pd.Series([1], dtype="bool") // np.bool_(0) # => NotImplementedError
pd.Series([1], dtype="bool") // pd.Series([0], dtype="bool") # => NotImplementedError
pd.Series([1, 0], dtype="bool") // pd.Series([0], dtype="bool") # => ZeroDivisionError
pd.Series([1, 0], dtype="bool") // pd.Series([1], dtype="bool") # => pd.Series([1, np.nan], dtype="object")
pd.Series([1, 0], dtype="bool") // pd.Series([0, 0], dtype="bool") # => NotImplementedError
pd.Series([1, 0], dtype="bool") // pd.Series([1, 1], dtype="bool") # => NotImplementedError

Issue Description

If only one operand is a Series, we consistently get a NotImplementedError for pow, truediv, and floordiv if both operands have boolean dtypes.

If both operands are series (with bool dtype) the behaviour is dependent on whether or not the series have matching lengths. When the lengths mismatch, for some reason the NotImplementedError check is bypassed and we just evaluate as normal.

Expected Behavior

If one is going to not allow division or exponentiation of boolean dtypes, it should happen consistently.

Aside: FWIW, I don't really like this choice, why are booleans special in this way? (I see some discussion in https://github.com/pandas-dev/pandas/issues/41165 but with no conclusion).

Installed Versions

INSTALLED VERSIONS ------------------ commit : e41b6d7827720df90a51ff05caa689333d7e02af python : 3.10.6.final.0 python-bits : 64 OS : Darwin OS-release : 21.6.0 Version : Darwin Kernel Version 21.6.0: Mon Aug 22 20:19:52 PDT 2022; root:xnu-8020.140.49~2/RELEASE_ARM64_T6000 machine : arm64 processor : arm byteorder : little LC_ALL : None LANG : en_GB.UTF-8 LOCALE : en_GB.UTF-8 pandas : 2.0.0.dev0+643.ge41b6d7827.dirty numpy : 1.23.4 pytz : 2022.6 dateutil : 2.8.2 setuptools : 65.5.1 pip : 22.3.1 Cython : 0.29.32 pytest : 7.2.0 hypothesis : 6.56.4 sphinx : 4.5.0 blosc : None feather : None xlsxwriter : 3.0.3 lxml.etree : 4.9.1 html5lib : 1.1 pymysql : 1.0.2 psycopg2 : 2.9.3 jinja2 : 3.0.3 IPython : 8.6.0 pandas_datareader: 0.10.0 bs4 : 4.11.1 bottleneck : 1.3.5 brotli : fastparquet : 0.8.3 fsspec : 2021.11.0 gcsfs : 2021.11.0 matplotlib : 3.6.2 numba : 0.56.3 numexpr : 2.8.3 odfpy : None openpyxl : 3.0.10 pandas_gbq : 0.17.9 pyarrow : 9.0.0 pyreadstat : 1.2.0 pyxlsb : 1.0.10 s3fs : 2021.11.0 scipy : 1.9.3 snappy : sqlalchemy : 1.4.43 tables : 3.7.0 tabulate : 0.9.0 xarray : 2022.11.0 xlrd : 2.0.1 zstandard : 0.19.0 tzdata : None qtpy : None pyqt5 : None

Comment From: mroeschke

Almost similar behaviors happen for Index cc @jbrockmendel 

pd.Index([1], dtype="bool") // np.bool_(0) # => NotImplementedError
pd.Index([1], dtype="bool") // pd.Index([0], dtype="bool") # => NotImplementedError
pd.Index([1, 0], dtype="bool") // pd.Index([0], dtype="bool") # => NotImplementedError *different from Series
pd.Index([1, 0], dtype="bool") // pd.Index([1], dtype="bool") # => NotImplementedError *different from Series
pd.Index([1, 0], dtype="bool") // pd.Index([0, 0], dtype="bool") # => NotImplementedError
pd.Index([1, 0], dtype="bool") // pd.Index([1, 1], dtype="bool") # => NotImplementedError

Agreed consistency is an issue here, but discussion whether this should be implemented should probably continue on https://github.com/pandas-dev/pandas/issues/41165

Comment From: jbrockmendel

IIUC the differences vs Series probably occur bc the Series has to reindex with mismatched lengths, so ends up with object dtype.

Comment From: wence-

IIUC the differences vs Series probably occur bc the Series has to reindex with mismatched lengths, so ends up with object dtype.

That seems likely. Since with 

l = pd.Series([1, 0], dtype="bool")
r = pd.Series([1], dtype="bool")

r.reindex_like(l)

Produces an object-dtype series with True, NaN, I suppose because there is no nullable bool series that one can put a pd.NA in.

Comment From: mroeschke

Produces an object-dtype series with True, NaN, I suppose because there is no nullable bool series that one can put a pd.NA in.

There's a nullable bool dtype with the string "boolean"

>>> l = pd.Series([1, 0], dtype="boolean")
>>> r = pd.Series([1], dtype="boolean")
>>> r.reindex_like(l)
0    True
1    <NA>
dtype: boolean