Ilya Nemenman, an Emory University physics professor, seethed as summer break neared its end.

After a pro-Palestinian demonstration in April had ended with police officers firing chemical irritants, Emory’s president had decided to update the campus’s protest policy. The revisions were not necessarily what angered Dr. Nemenman.

The problem was that the president had not received the University Senate’s feedback first.

“This is not just a corporation,” Dr. Nemenman chided the president, Gregory L. Fenves, during an Aug. 28 meeting, according to interviews and contemporaneous notes that summarized the discussion. “It is also a community that does not operate top-down.”

But Dr. Fenves’s repeated pledges to work with faculty did not reassure every professor.

For more than a century, professors have regularly had vast influence over instruction, personnel and other hallmarks of campus life, sharing sway with presidents and trustees in decisions shaping many parts of campus life — an authority that is unfathomable in many workplaces.