BUG: find_common_type returning incorrect common type

[galipremsagar]

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• 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

In [2]: import pandas as pd
In [3]: from pandas.core.dtypes.cast import find_common_type
In [4]: import numpy as np
In [5]: find_common_type([np.dtype('int32'), np.dtype('bool')])
Out[5]: dtype('O')
In [6]: np.find_common_type([np.dtype('int32'), np.dtype('bool')], [])
Out[6]: dtype('int32')
In [7]: np.find_common_type([], [np.dtype('int32'), np.dtype('bool')])
Out[7]: dtype('int32')
In [8]: pd.__version__
Out[8]: '2.1.0'

Issue Description

I expect the common type for int32 & bool to be int32 rather than object dtype. This results in incorrect behavior of some operations like:

In [9]: idx = pd.Index([0, 1, 2, 3], dtype='int32')
In [10]: bool_idx = pd.Index([True, False, True])
In [11]: idx
Out[11]: Index([0, 1, 2, 3], dtype='int32')
In [12]: bool_idx
Out[12]: Index([True, False, True], dtype='bool')
In [13]: idx.union(bool_idx)
Out[13]: Index([0, 1, 1, 2, 3], dtype='object')

Expected Behavior

In [13]: idx.union(bool_idx)
Out[13]: Index([0, 1, 1, 2, 3], dtype='int32')

Installed Versions

INSTALLED VERSIONS

commit : ba1cccd
python : 3.10.2.final.0
python-bits : 64
OS : Darwin
OS-release : 22.6.0
Version : Darwin Kernel Version 22.6.0: Wed Jul 5 22:22:05 PDT 2023; root:xnu-8796.141.3~6/RELEASE_ARM64_T6000
machine : arm64
processor : arm
byteorder : little
LC_ALL : None
LANG : None
LOCALE : en_US.UTF-8
pandas : 2.1.0
numpy : 1.23.2
pytz : 2022.2.1
dateutil : 2.8.2
setuptools : 60.2.0
pip : 21.3.1
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : None
IPython : 8.5.0
pandas_datareader : None
bs4 : None
bottleneck : None
dataframe-api-compat: None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : None
numba : None
numexpr : 2.8.4
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : 11.0.0
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
zstandard : None
tzdata : 2023.3
qtpy : None
pyqt5 : None

[galipremsagar]

cc: @mroeschke

[mroeschke]

Since bools and ints are meant to be distinct in pandas, I think the expected behavior would be (sort may be incorrect)

In [13]: idx.union(bool_idx)
Out[13]: Index([0, False, 1, True, 2, 3], dtype='object')

[mroeschke]

So the set ops issue is already known in #44000

But I think the find_common_type dtype behavior is intended

[galipremsagar]

Thanks @mroeschke ! Closing in favor of #44000