BUG: Join of DataFrames with MultiIndex does not keep order of index

[rikardn]

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

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

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

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Code Sample, a copy-pastable example

import numpy as np
import pandas as pd

arrays = [np.array(['top', 'top', 'top', 'top', 'bottom', 'bottom', 'bottom', 'bottom']),
          np.array(['bar', 'bar', 'baz', 'baz', 'bar', 'bar', 'baz', 'baz']),
          np.array(['one', 'two', 'one', 'two', 'one', 'two', 'one', 'two'])]

left = pd.DataFrame(np.random.randn(8, 4), index=arrays)
left.index.set_names(['pos', 'vars', 'numbers'], inplace=True)

right = pd.DataFrame({'vars': ['bar', 'bar', 'baz', 'baz'], 'numbers': ['one', 'two', 'one', 'two'], 'value': [1, 2, 3, 4]})
right = right.set_index(['vars', 'numbers'])
joined = left.join(right)

print(left.index.names)
print(joined.index.names)

output

['pos', 'vars', 'numbers']
['vars', 'numbers', 'pos']

Problem description

When two multindexed DataFrames are joined on a subset of the left index the resulting index becomes reordered.

Expected Output

I expect the order of the left dataframe to be kept after the left join.

Output of pd.show_versions()

INSTALLED VERSIONS

commit : None
python : 3.7.5.final.0
python-bits : 64
OS : Linux
OS-release : 5.3.0-51-generic
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 1.0.3
numpy : 1.16.2
pytz : 2019.2
dateutil : 2.7.3
pip : 18.1
setuptools : 41.1.0
Cython : None
pytest : 3.7.4
hypothesis : None
sphinx : 2.4.4
blosc : None
feather : None
xlsxwriter : None
lxml.etree : 4.5.0
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 2.11.2
IPython : 7.10.2
pandas_datareader: None
bs4 : 4.9.0
bottleneck : None
fastparquet : None
gcsfs : None
lxml.etree : 4.5.0
matplotlib : 3.1.2
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pytables : None
pytest : 3.7.4
pyxlsb : None
s3fs : None
scipy : 1.1.0
sqlalchemy : None
tables : None
tabulate : None
xarray : 0.14.1
xlrd : None
xlwt : None
xlsxwriter : None
numba : None

[lukemanley]

When left and right indexes have a different number of levels, the current behavior is to order the output as:

common levels + left levels not in right levels + right levels not in left levels

I agree this behavior seems odd. I would expect a left join to maintain the order of the left index levels. However, changing the behavior would break a few tests.

cc @mroeschke if any thoughts?

[mroeschke]

How many tests break if we change this behavior? Also agreed not sorting would be better behavior here

[lukemanley]

How many tests break if we change this behavior? Also agreed not sorting would be better behavior here

I opened #55370 showing what would need to be updated