The knock on multi-class share structures is that they render shareholders mute. By controlling the company, the minority shareholders (usually the founders sometimes combined with pre-IPO investors) elect the board and effectively make all major corporate decisions. From a corporate governance perspective, it's certainly not good for shareholders. On the other hand, it is precisely because these founders have been able to execute on a strategic vision that these companies are able to go public. In this sense, the multi-class structures lock in the founders and their vision for the company.
Recent IPOs that have dual or multi-class share structures include Facebook (two classes of common stock), Zynga (three), Groupon (two), Kayak (two), Yelp! (two), Zillow (two) and LinkedIn (two). Of these, LinkedIn, Zillow, Yelp, Kayak are trading above their IPO prices and Facebook, Zynga and Groupon are trading below their IPO prices.
In my view, whether a company can list with a multi-class share structure is really about demand for the IPO and the marketing of the IPO. If the IPO is in strong demand, then the underwriters may be able to structure an IPO that enables multi-tier structures, selling shareholders in the IPO, a larger number of shares sold, or a higher IPO price, or some combination of the above. The marketing of an IPO is both art and science, and the underwriters develop the structure of an IPO based upon market factors.
If CalPERS boycotts IPOs with multi-class structures that enable minority shareholders to control the company, AND if other large IPO investors join the boycott, then this might make it more difficult for IPOs to have these structures. Also, if the post-IPO performance of companies with multi-class share structures is poor, then IPO investors may shy away from these structures and they may fade away.
Link to SmartMoney article: http://www.smartmoney.com/news/on/?story=ON-20120820-000058