In a new paper, Alex Brill and James Glassman propose imposing standards for membership in the G20. They note correctly that the economic steering group's membership was determined without explicit criteria and that members aren't held to any binding standard of conduct.  The authors claim that the murkiness surrounding members' qualifications fatally undermines the group's legitimacy:

Remarkably, since its founding thirteen years ago, the G20 has lacked transparent rules governing its membership. As a result, there has been an erosion of trust among the nearly two hundred nations that are not part of the group but are affected by its decisions. Without legitimacy, the G20 cannot lead. 

Instead, they propose using World Bank and IMF data to rank countries by their economic size and strength, record on abiding by international laws and regulations, and by the centrality of the national financial sector. Applying these standards, they find that four current members wouldn't make the cut: Russia, Mexico, Argentina and Indonesia. They would be replaced by Malaysia, Norway, Singapore and Switzerland.

The full paper is well worth a read, although I think the authors significantly overstate the degree to which clear standards would boost the body's legitimacy; reams of World Bank data won't convince those outside the charmed circle that the circle isn't defective. What's more, the authors don't make clear how improved legitimacy, even if it could be attained, would produce results. The G20's problems, it seems to me, have less to do with global standing than with its own inability to form a meaningful consensus.