That’s the most intriguing question ahead of the media giant’s annual shareholders’ meeting, to be held tomorrow in Los Angeles. The country’s two largest public pension funds — the California Public Employees’ Retirement System (Calpers) and the California State Teachers’ Retirement System (CalSTRS)– say that they voted against re-electing CEO Rupert Murdoch and his sons, Deputy COO James Murdoch and Lachlan Murdoch, to the board. (CalSTRS opposed the entire slate.) They’re also lined up to support a resolution by Christian Brothers Investment Services that would require the chairman to be independent of management. The anti-Murdoch efforts probably won’t prevail. The family controls 38.4% of the voting shares of News Corp and a close ally, Prince Alwaleed bin Talal, has 7%. Still, it could be a major embarrassment if half of the independent investors line up against the CEO. Several investors say that his concentrated power contributed to the lax oversight of the UK tabloids at the center of the company’s hacking and bribery scandals.

In addition to the California funds, UK Local Authority Pension Fund Forum Chairman Ian Greenwood plans to speak up for the resolution splitting the CEO and chairman roles, The Telegraph reports. “If we can get 50% [of the non-Murdoch vote], that would be a message to the company,” he told the paper. “This issue is not going to go away.” Shareholder advisory firms ISS and Glass Lewis & Co have supported the independent chairman proposal. Another firm,  Egan-Jones, opposes it saying that the board should have the flexibility to pick whomever it wants to be chairman.