Manzi argues that they do:

I picked the median company on the most recent Fortune 500 (i.e., number 250), Smith International.  It has about $11 billion in sales and $1.6 billion in operating income.  A 1% swing in $1.6 billion is $16 million.  As context the median Fortune 500 CEO recently had total annual comp of about $6 million.  So as a shareholder of Smith International going into the market to hire a CEO, the question I would ask myself if presented with the choice of paying $6 million per year or, say, doubling this to $12 million per year, is not "Will the CEO I get for $12 million fundamentally transform my business?" or whatever; instead, I'd rationally ask myself, "Can the $12 million dollar CEO drive about 0.6% more operating profit than the person I would hire at $6 million?".

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