Artistic directors and managers come and go. But the power behind them is in boards that oversee arts organizations. “Their numbers include hard-charging entrepreneurs, top executives, retired moguls, heiresses and the occasional full-blown celebrity, and they operate in a chandelier-lighted, by-invitation-only realm full of fiduciary responsibility and social opportunity. In this largely white and mostly over-50 world, lunches with Frank Gehry and cocktails with David Hockney are entirely possible and getting tickets is never a problem. But it’s likely to cost a five-figure donation, maybe six, every year, just to get a foot in the door. And the price of admission is rising fast.”