THE involvement of the Rockefeller family gives added piquancy to one of the two most significant shareholders-versus-board battles of this year's proxy season. (Carl Icahn's proposal to replace the board of Yahoo! is the other.) Of the 78 adult direct descendants of John D. Rockefeller Jr, 72 have endorsed a resolution to split the jobs of chairman and chief executive at Exxon Mobil, which eventually emerged from the antitrust break-up of the family oil monopoly, Standard Oil. Exxon strongly opposes the resolution and has tried to stem growing enthusiasm for it ahead of its annual meeting on May 28th by writing for a second time to shareholders urging them to vote no.

Last year the resolution won 40% of the vote, up from 34% in 2006. The endorsement of the Rockefellers (who nowadays own only a tiny slice of Exxon, though it is the family's biggest shareholding) is raising hopes of breaking through the 50% ceiling, as does the support of three of the leading firms that advise institutional shareholders on how to vote their proxies. Particularly significant is the support of Proxy Governance Inc, a firm that has previously opposed resolutions to split the jobs of chairman and chief executive. It gave warning that if Exxon continued its “my way or the highway” approach, it risked a “shareholder revolt”.

Even if it attracts over 50%, the resolution is non-binding. Yet it would be a hugely important result, says Robert Monks, a veteran corporate-governance activist who has proposed the resolution in each of the past six years. (Oddly, in two of those years, the Securities and Exchange Commission backed Exxon's decision to throw out the resolution, though the regulator has since realised that such pandering to management is out of step with today's corporate-governance climate.)

Not only is Exxon America's largest public company, with a stockmarket value of over $500 billion, it is also the most consistently hostile to shareholders, says Mr Monks. As he describes in his entertaining new book, “Corpocracy”, its annual meeting is a vigorous exercise in doing the minimum required by the law. Yet this year's vote could be a “turning-point in American corporate governance,” he says, revelling in the prospect of America's most important board “facing a majority, or powerful minority of shareholders saying they want something—and not doing it.”

Exxon says that its board is better placed than shareholders to determine its leadership structure, and that it wants Rex Tillerson to continue as both chairman and chief executive. This is in keeping with general practice among big American public companies. Over 60% of the firms in the S&P 500 have a combined chairman and chief executive. Around 25% have a “lead director” who chairs the compensation and audit committees (but Exxon does not). Only 16% have an independent director as chairman. Contrast that with Britain, where over 95% of public companies now split the two jobs, a shift that is generally agreed to have improved corporate governance and performance.

The involvement of the Rockefellers highlights the nonsensical nature of the complaint often made by opponents of shareholder rights—namely that shareholder resolutions tend to be the politically motivated work of activists and trade unions. They are generous philanthropists, but the Rockefellers are no bleeding hearts. Their support for the resolution is driven by a desire to maximise the long-term value of their Exxon shares.

“Rex Tillerson is a good manager, the board is good, but too often when times are good, shareholders and management don't look hard enough at their vulnerabilities,” says Peter O'Neill, speaking for the family. The Rockefellers worry that Exxon does not spend enough time analysing risks to the business, such as climate change and the need to replace reserves as countries are becoming more nationalistic about their natural resources. “The best way to ensure that all the scenarios are properly tested, to enhance Rex Tillerson's ability to do his job, is to appoint an independent chairman.”