Two weeks ago, I argued that it was hard to imagine a more compelling case for ousting directors than the one posed by Hewlett-Packard.

It turns out there are many stronger cases — 41.

That’s the number of publicly traded companies where directors actually lost their elections last year, meaning that more than 50 percent of the shareholders withheld their votes of approval. Yet despite these resounding votes of no confidence, they remained in their posts.

At least at H.P., all the directors got a majority of the votes cast, and even then, two resigned and a third gave up his post as chairman. But at Cablevision Systems, the New York cable and media company controlled by the Dolan family, three directors lost shareholder elections twice in the last three years — in 2010 and 2012 — and received only tepid support in 2011. Nonetheless, the three remain on the board.

“As fiduciaries, we can’t sit by and let the board make a mockery of our fundamental right to elect directors,” said New York City’s comptroller, John Liu, who oversees the city’s pension funds, which own more than 532,000 Cablevision shares. “Share owners need accountable directors who will ensure the company isn’t being run for the benefit of insiders at our expense.”