The largest public pension fund in the US, and one of the country's most influential investors, is stepping up the pressure for a drastic overhaul of the way News Corporation is run as the fallout from Rupert Murdoch's appearance before MPs begins.

The California Public Employees' Retirement System, which manages $237bn (£147bn) of assets and prides itself on its tough corporate governance stance, wants the unusual dual share structure of News Corp to end so it will be able to influence the media company more effectively.

Anne Simpson, the Briton who is in charge of corporate governance at Calpers, said that it was time for change at the company, which gives special voting powers to shares held by the Murdoch family.

"News Corp does not have one share one vote. This is a corruption of the governance system. Power should reflect capital at risk. Calpers sees the voting structure in a company as critical. The situation is very serious and we're considering our options. We don't intend to be spectators – we're owners," she said.

While the Murdochs own 12% of the company, their special B shares give them voting rights over 40% of the company. Calpers holds 6.4m shares.

Other investors have also raised this share structure – which is very unusual in the UK – as a concern while this is not the first time that Calpers has had concerns about the Murdoch family.

In 2003, Calpers had attempted to oppose the appointment of James Murdoch as chief executive of BSkyB, 39% owned by News Corp.

"This is a very unsatisfactory situation with a father and son chairman and chief executive at the head of a major FTSE company," Daniel Somerfield of US investors USS and Calpers said at the time.

James Murdoch has since become chairman of BSkyB and his position is causing concern to some investors, given the amount of time he will have to devote to the investigations into phone hacking as he is also a senior executive of News Corp.

BSkyB investors are considering whether it might be sensible for him to step aside or more non-executive directors to be appointed to ensure that the cash generated by the satellite broadcaster every year is distributed to them.

Rupert Murdoch's position at News Corp, where he is both chairman and chief executive, is also being questioned. The small shareholder Christian Brothers Investment Services Global Funds is planning to call for him to split those roles.

Simpson indicated that Calpers was continuing to review the situation, in light of the range of inquiries into phone hacking at News of The World, the Sunday newspaper that News International - the UK arm of News Corp - shut down this month after the Guardian reported its journalists had listened to voice messages of the missing teenager Milly Dowler.

"The serious situation is the hacking scandal, and the market reaction shows how seriously this is being taken. I can't say what the options are at the moment, but we have strong experience in governance reform," Simpson said.

Calpers is already known for its successes is provoking changes in US boardrooms. In 2004 it led the shareholder revolt that forced Michael Eisner to give up the chairman's role at Walt Disney and when the head of the New York Stock Exchange, Dick Grasso, was handed a $188m pay deal, it was Calpers that was involved in the charge that led to his departure.

Public sector pension funds are well known in the US as the protagonists for change at major companies, and regarded as more influential that more typical institutional investors.

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