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There's a 'short circuit' in shutil.which(), described as 'If we're given a full path which matches the mode and it exists, we're done here.'
It also matches if an executable file of the same name is present in the working directory, although on most Unix-y systems you need ./ to execute such files in a shell (i.e. ./foo, not just foo).
This could fool code calling which() into thinking that a program is installed, when it is not.
If we consider this a bug, one simple fix would be to only allow the short circuit with an absolute path, so the line
 if _access_check(cmd, mode):
would become
 if os.path.isabs(cmd) and _access_check(cmd, mode):

I've added a patch with my suggested fix, as well as a test for this.
test_shutil all passes on Linux - I haven't run the tests on Windows.

I think it should be
 if os.path.dirname(cmd) and _access_check(cmd, mode):

No, it should be
 if os.path.dirname(cmd):
 if _access_check(cmd, mode):
 return cmd
 return None

That makes sense - foo/setup.py can be run from the working directory, but you can't refer to subdirectories on $PATH like that.
I've added a revised version of the patch.

I assume that ./script is working just like dir/script (what the tests exercize is not crystal clear to me).

Perhaps the comment in which() is misleading now, if I understand correctly the meaning of the words "short circuit". Native speakers, please correct me if I wrong.

Yes, as far as I know, ./script works in the same way as dir/script - from the current directory, but not from $PATH.
The first test added is for the case I reported - which('script') shouldn't look in the current directory on Unix. The second test would have failed without Serhiy's correction.
Serhiy, I agree that the comment wasn't quite right. I've uploaded a new version of the patch with a modified comment.

LGTM.

I have reorganized tests a little.

New changeset f18d11ab53a0 by Serhiy Storchaka in branch '3.3':
Issue #16957: shutil.which() no longer searches a bare file name in the
http://hg.python.org/cpython/rev/f18d11ab53a0
New changeset 7b51568cfbae by Serhiy Storchaka in branch 'default':
Issue #16957: shutil.which() no longer searches a bare file name in the
http://hg.python.org/cpython/rev/7b51568cfbae 

Committed. Thank you for for the patch.

New changeset 99db73ce8374 by Serhiy Storchaka in branch '3.3':
Fix pathext test for shutil.which() which was
http://hg.python.org/cpython/rev/99db73ce8374
New changeset ab0ff935126c by Serhiy Storchaka in branch 'default':
Fix pathext test for shutil.which() which was
http://hg.python.org/cpython/rev/ab0ff935126c