GameStop Corp. shareholders vote this week to resolve a fight over the embattled videogame retailer’s board. But the company’s largest investors won’t cast much of a vote.

The three biggest money managers in GameStop reported that their funds held some 40% of shares in the first quarter. When it was time to commit to voting, they controlled roughly 5% of ballots, according to count estimates reviewed by The Wall Street Journal. Each share of GameStop normally grants an investor one vote.