Buffett was not immediately available for comment.
His $58.2 billion net worth makes him the world's fourth-richest person, Forbes magazine said this month.
In opposing Witt's proposal, Berkshire's board said it already considers annually whether the Omaha, Nebraska-based company should retain all earnings.
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Buffett, 83, has long maintained that he can generate better returns through acquisitions such as the BNSF railroad and investments such as Wells Fargo.
He told shareholders in 2011 that Berkshire's share price ought to fall if the company decided to pay a dividend. Buffett also wants to keep a $20 billion cash cushion.
"Our shareholders are far wealthier today than they would be if the funds we used for acquisitions had instead been devoted to share repurchases or dividends," he said in his March 2013 annual letter.
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"Though large transactions of the BNSF kind will be rare, there are still some whales in the ocean."
Berkshire also urged shareholders to vote against a proposal that it set goals for its energy businesses to reduce greenhouse gas and other emissions. Similar proposals failed in 2011 and 2013.
Buffett controls one-third of Berkshire's voting power. Shareholder proposals that Berkshire opposes typically fail by overwhelming margins.
Berkshire also disclosed that Buffett's compensation rose 15 percent last year to $485,606. That includes his usual $100,000 salary, plus $385,606 for personal and home security.
The company also said it paid most directors an extra $300 last year. That meant Bill Gates, the Microsoft co-founder and world's richest person, was awarded $2,100 last year for his work as a Berkshire director.
Gates is worth $76 billion, Forbes said.