Over the next few weeks, American companies will engage in a quaint ritual: the shareholder meeting. Investors will have a chance to vent about performance and to offer resolutions on corporate policy. Many will also get to do something relatively novel: cast an advisory vote on the pay packages of C.E.O.s and other top executives. This power, known as “say-on-pay,” became law in 2010, as part of the Dodd-Frank bill. In the wake of the financial crisis, which amplified anger about exorbitant C.E.O. salaries, reformers looking for ways to rein in the practice seized on say-on-pay, which the United Kingdom adopted in 2002. The hope was that the practice would, as Barack Obama once put it, help in “restoring common sense to executive pay.”

Say-on-pay is the latest in a series of reforms that, in the past couple of decades, have tried to change the mores of the executive suite. For most of the twentieth century, directors were paid largely in cash. Now, so that their interests will be aligned with those of shareholders, much of their pay is in stock. Boards of directors were once populated by corporate insiders, family members, and cronies of the C.E.O. Today, boards have many more independent directors, and C.E.O.s typically have less influence over how boards run. And S.E.C. reforms since the early nineteen-nineties have forced companies to be transparent about executive compensation.

These reforms were all well-intentioned. But their effect on the general level of C.E.O. salaries has been approximately zero. Executive compensation dipped during the financial crisis, but it has risen briskly since, and is now higher than it’s ever been. Median C.E.O. pay among companies in the S. & P. 500 was $10.5 million in 2013; total compensation is up more than seven hundred per cent since the late seventies. There’s little doubt that the data for 2014, once compiled, will show that C.E.O. compensation has risen yet again. And shareholders, it turns out, rather than balking at big pay packages, approve most of them by margins that would satisfy your average tinpot dictator. Last year, all but two per cent of compensation packages got majority approval, and seventy-four per cent of them received more than ninety per cent approval.

Why have the reforms been so ineffective? Simply put, they targeted the wrong things. People are justifiably indignant about cronyism and corruption in the executive suite, but these aren’t the main reasons that C.E.O. pay has soared. If they were, leaving salary decisions up to independent directors or shareholders would have made a greater difference. As it is, studies find that when companies hire outside C.E.O.s—people who have no relationship with the board—they get paid more than inside hires and more than their predecessors, too. Four years of say-on-pay have shown us that ordinary shareholders are pretty much as generous as boards are. And even companies with a single controlling shareholder, who ought to be able to dictate terms, don’t seem to pay their C.E.O.s any less than other companies.

At root, the unstoppable rise of C.E.O. pay involves an ideological shift. Just about everyone involved now assumes that talent is rarer than ever, and that only outsize rewards can lure suitable candidates and insure stellar performance. Yet the evidence for these propositions is sketchy at best, as Michael Dorff, a professor of corporate law at Southwestern Law School, shows in his new book, “Indispensable and Other Myths.” Dorff told me that, with large, established companies, “it’s very hard to show that picking one well-qualified C.E.O. over another has a major impact on corporate performance.” Indeed, a major study by the economists Xavier Gabaix and Augustin Landier, who happen to believe that current compensation levels are economically efficient, found that if the company with the two-hundred-and-fiftieth-most-talented C.E.O. suddenly managed to hire the most talented C.E.O. its value would increase by a mere 0.016 per cent.

Dorff also makes a persuasive case that performance pay is overrated. For a start, it’s often tied to things that C.E.O.s have very limited control over, like stock price. Furthermore, as he put it, “performance pay works great for mechanical tasks like soldering a circuit but works poorly for tasks that are deeply analytic or creative.” After all, paying someone ten million dollars isn’t going to make that person more creative or smarter. One recent study, by Philippe Jacquart and J. Scott Armstrong, puts it bluntly: “Higher pay fails to promote better performance.”

So the situation is a strange one. The evidence suggests that paying a C.E.O. less won’t dent the bottom line, and can even boost it. Yet the failure of say-on-pay suggests that shareholders and boards genuinely believe that outsized C.E.O. remuneration holds the key to corporate success. Some of this can be put down to the powerful mystique of a few truly transformative C.E.O.s (like Steve Jobs, at Apple). But, more fundamentally, there’s little economic pressure to change: big as the amounts involved are, they tend to be dwarfed by today’s corporate profits. Big companies now have such gargantuan market caps that a small increase in performance is worth billions. So whether or not the people who sit on compensation committees can accurately predict C.E.O. performance—Dorff argues that they can’t—they’re happy to spend an extra five or ten million dollars in order to get the person they want. That means C.E.O. pay is likely to keep going in only one direction: up.