Institutional Shareholder Services is concerned that bribery allegations arose and that Wal-Mart's board may not be structured to handle the investigation properly, Pat McGurn, special counsel to the advisory firm, said in a telephone interview today. Some of same board members who are involved in the investigation were executives or on the board when the alleged bribes took place, he said.

A senior Wal-Mart lawyer received bribery allegations in September 2005 and a cover-up may have occurred later, according to the Times article. Scott was CEO from 2000 to 2009. Duke became vice chairman, overseeing Wal-Mart's international operations, in September 2005. Williams has been on the board since 2004 and Walton has been chairman since 1992.

"You don't want the same people serving as witness and juror," McGurn said. "You want to make sure you have independent directors. We are really concerned with board oversight vis a vis senior management."

Wal-Mart was founded in by Sam Walton. His heirs control Walton Enterprises Inc., which owns 47 percent of Wal-Mart stock, according to data compiled by Bloomberg.

Voting Power

Calstrs is concerned that the Walton family has effective voting control of proxy issues, Mike Sicilia, a Calstrs spokesman, said in an interview.

"That makes it difficult for unaffiliated shareholders to nominate directors to the board," Sicilia said.

On May 1, New York City Comptroller John Liu said the New York City Pension Fund would vote against five Wal-Mart directors because of the bribery allegations.

Liu said the funds will vote against Rob Walton, Duke, Scott, Williams and Arne Sorenson, president and CEO of Marriott International Inc.

New York Pension Funds said in a statement that Marriott "has a multimillion dollar vendor relationship with Wal-Mart," so Sorenson shouldn't be on a board overseeing the allegations.