After the annual meeting, CPSI arranged for Mr. Mulherin step down in 2014. “There was a delay because it’s hard to find good directors here; we are not Chicago,” Mr. Douglas said. “We needed some time.” (Mr. Mulherin did not return a call seeking comment.)

This wasn’t enough for I.S.S., and Mr. Douglas said that this year I.S.S. took a run at Mr. Douglas himself, as well as another director. Mr. Douglas immediately called BlackRock, its second-largest shareholder, asking for its support.

“We are trying and we are making changes and we don’t think it was in best interest of shareholders for Austin to come off the board immediately,” Mr. Douglas said he told a member of BlackRock’s governance team. He said the BlackRock staff member listened “respectfully” but didn’t say much. BlackRock declined to comment about CPSI, but Mr. Douglas said he and the other director that I.S.S. targeted this year were re-elected with BlackRock’s support. (The voting history of money managers like BlackRock becomes a matter of public record at the end of August.)

BlackRock has disagreed with the recommendation of the proxy advisory firms in a number of instances. For example, I.S.S. and Glass, Lewis generally support companies splitting the role of chairman and chief executive in order to create stronger, independent boards, which counterbalance management. BlackRock has rarely voted to split the role, believing that if a company has a strong lead director, there is likely no need to sever the roles.

BlackRock holds firm to certain principles when it comes to boards it sees as in need of “refreshment” — directors who have been around too long or serve on too many boards. In 2012, it voted against three directors of Coca-Cola — Ronald W. Allen, Barry Diller and Jacob Wallenberg — because each serves on more than four boards, the tipping point that suggests to BlackRock that a director is “overboarding.”

 Mark Preisinger, director of corporate governance at Coca-Cola, said his company was happy with its board but knew BlackRock’s policy, so that it was no surprise when the firm voted against these directors. Despite its “no” votes, he said BlackRock was engaged with Coke on numerous topics.

BlackRock has also voted against or withheld votes from compensation committee members at companies when it thinks that they pay executives too much. Still, the A.F.L.-C.I.O. said that in 2012, the firm voted against board nominees at just 6 percent of United States companies. In contrast, the federation voted against 42 percent of all board nominees. And BlackRock almost always sides with management in “say on pay” measures.

WHILE BlackRock is more likely than not to side with management, it has been known to vote with more vocal shareholders.

In 2010, it voted against the management of the Dollar Thrifty Automotive Group, which recommended supporting a takeover by Hertz for a $51 a share. Robert Zivnuska, who runs BlackRock’s governance effort for the Americas, said a BlackRock team concluded that company was better off as a stand-alone concern. Other shareholders agreed and rejected the Hertz offer. Two years later, Dollar Thrifty was sold to Hertz for $87.50 a share, almost 60 percent higher than the 2010 offer.

“Since Ms. Edkins took over, we have seen a real change and willingness to dialogue with other investors and we hope she continues on this path,” said Dieter Waizenegger, executive director of the CtW Investment Group, which represents union pension funds.