ENH: make sorting algorithm options to `value_counts` and record it in the docs

[cmp0xff]

Feature Type

• Adding new functionality to pandas

• Changing existing functionality in pandas

• Removing existing functionality in pandas

Problem Description

In the dev documentation, it is not clear which sorting algorithm is used by value_counts, which is also fixed.

It would be helpful to make such an option and record it in the docs.

Feature Description

We can follow the example of sort_values, adding the parameter kind:

import pandas as pd

s = pd.Series([1, 1, 1, 2, 2, 2]).value_counts(kind="stable")

Alternative Solutions

We can just record in the docs that the algo is fixed to quicksort.

Additional Context

Related to #63154 and numpy/numpy#30262. As a user I would like to know that the sorting result is deterministic and optionally stable.

[rhshadrach]

Thanks for the request. I'm positive on switch the sort here to stable and documenting it as such, but negative on adding options.