The compensation committee of the board of directors at Twenty-First Century Fox Inc.  (FOXA) - Get Report  needs a shake-up, according to Institutional Shareholder Services Inc.

The proxy advisory firm on Monday, Oct. 30, called for Fox shareholders to vote against the re-election of four independent Fox directors who serve on its compensation committee: Roderick Eddington, James Breyer, Jacques Nasser and Robert Silberman. The vote, ISS said, is necessary to push the company to better address the issue of executive compensation. Fox is set to hold its annual meeting in two weeks.

The governance group also recommended that shareholders vote against the election of a fifth independent board member, Delphine Arnault, an executive at clothing manufacturer Louis Vuitton Malletier, for serving on the boards of more than five publicly traded companies. ISS and other corporate governance monitors have cracked down in recent years on directors who serve on a multitude of boards, arguing that they're unable to adequately attend to the demands of so many different companies.

Arnault and James Breyer attended less than 75% of the total board and committee meetings on which they served last year, ISS said.

But Fox, in a statement Tuesday, countered that ISS's own report made clear that Fox "CEO pay and company performance are aligned for the year under review." The recommendation to vote against members of the compensation committee comes a year after the four board members obtained just 69% of shareholder support, a comparatively low mark given that U.S. board elections rarely meet with shareholder disapproval.

Fox shares at midday Tuesday were down 1% to $26.12, extending their decline this year to 6.8%.

While ISS said that Fox board members were responsive in speaking with shareholders following that vote, it was nonetheless dismayed that "no changes appear to have been made in response to the most recent vote and subsequent engagement. As such, the committee does not appear to have adequately responded to shareholder concerns voiced through the low say-on-pay support," ISS said. 

The lower-than-usual vote last year (the vote in 2015 was 93.5% in favor) was due in part to an ISS analysis of Fox executive compensation in which the company was compared with retailers such as Home Depot Inc. (HD) - Get Report and Target Corp. (TGT) - Get Report . Executives at media companies historically have been among the highest paid in the country; retailers are more in the middle of the pack.

In its statement, Fox said, "This year ISS changed the peer group it uses in its analysis to more accurately reflect the company's peers, and, as a result, ISS has indicated that executive pay is an area of 'low concern.'"

Yet ISS also contended that Fox isn't giving independent directors on its board more of a say on matters of compensation. Only 61.5% of the board's directors are independent, ISS pointed out, proclaiming that "investors generally prefer that independent directors be a substantial majority of the company's board." Nonetheless, it did acknowledge that independent directors serve on key committees.

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