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Reproducible Example

import pandas as pd

ind= pd.MultiIndex.from_arrays([['B', 'C', 'A', 'A'],
                                ['H', 'G', 'F', 'G'],
                                ['V', 'U', 'W', 'U']])
ind = ind.set_levels(['B','M','A'], level=0)

ind.sortlevel(0, sort_remaining=True)

Issue Description

Result is not sorted:

(MultiIndex([('B', 'F', 'W'),
             ('B', 'G', 'U'),
             ('M', 'H', 'V'),
             ('A', 'G', 'U')],
            ),
 array([2, 3, 0, 1]))

Expected Behavior

MultiIndex should be sorted. Cryptic phrase in documentation: "The result will respect the original ordering of the associated factor at that level." is not productive. A function called sortlevel should not depend on some mysterious "original ordering of an associated factor at that level".

If anything, please rename the function to: sortlevel_based_on_original_ordering_of_the_associated_factor_at_that_level, otherwise people will be confused that it's not working. Also, what the "original ordering of the associated factor at that level" is, is nowhere discussed. Also, for consistency reasons, the function should be called: sort_level (or sort_levels?) not sortlevel.

Installed Versions

INSTALLED VERSIONS ------------------ commit : 87cfe4e38bafe7300a6003a1d18bd80f3f77c763 python : 3.9.13.final.0 python-bits : 64 OS : Darwin OS-release : 20.6.0 Version : Darwin Kernel Version 20.6.0: Wed Jun 23 00:26:31 PDT 2021; root:xnu-7195.141.2~5/RELEASE_X86_64 machine : x86_64 processor : i386 byteorder : little LC_ALL : None LANG : en_US.UTF-8 LOCALE : en_US.UTF-8 pandas : 1.5.0 numpy : 1.22.4 pytz : 2022.1 dateutil : 2.8.2 setuptools : 63.1.0 pip : 22.1.2 Cython : None pytest : None hypothesis : None sphinx : 5.0.2 blosc : None feather : None xlsxwriter : None lxml.etree : 4.9.0 html5lib : None pymysql : None psycopg2 : None jinja2 : 3.1.2 IPython : 8.4.0 pandas_datareader: None bs4 : 4.11.1 bottleneck : 1.3.4 brotli : 1.0.9 fastparquet : 0.8.1 fsspec : 2022.5.0 gcsfs : None matplotlib : 3.5.2 numba : 0.55.2 numexpr : 2.8.3 odfpy : None openpyxl : 3.0.10 pandas_gbq : None pyarrow : 8.0.0 pyreadstat : None pyxlsb : None s3fs : 2022.5.0 scipy : 1.8.1 snappy : None sqlalchemy : None tables : None tabulate : 0.8.10 xarray : 2022.3.0 xlrd : 2.0.1 xlwt : None zstandard : None tzdata : 2022.1