The G-20 heads of state gather this week in Los Cabos, Mexico, for what may be their most important meeting since their first summit in November 2008. The Group of 20 set three objectives at that meeting: restore global growth, strengthen the international financial system, and reform financial institutions.

That work is far from complete. Another recession has begun in Europe, and the U.S. economy remains sluggish. Developing economies are weakening. And the problem of what to do about too-big-to-fail financial institutions is still unresolved.

The G-20 is well situated to help meet some of these challenges. Free of the stultifying bureaucracy and pomposity of many multilaterals, the group has the advantage of flexibility and informality.

Yet now it's facing a crisis of legitimacy. When the G-20 was established in 1999, membership was decided without any definitive, objective standards. It was based loosely on country size, but politics were clearly a factor too. The arbitrary selection process has been a sore point for nations that weren't anointed. Many observers have noted that the lack of membership criteria has diminished international trust in the G-20's decisions and activities.

The G-20 needs clear admission standards, and in a study sponsored by the National Taxpayers Union, we propose a set of seven criteria that correspond to the group's stated policy objectives. These criteria measure: 1) a nation's economic size and global economic importance, 2) its adherence to the rule of law and other principles consistent with market-based economics, and 3) the scope of its financial interconnectedness with other nations."Under our proposed criteria, the four countries that would accede to the G-20 are Switzerland, Singapore, Norway and Malaysia."

By these criteria, two of the current G-20 members-Argentina and Indonesia-fall far short of qualifying for membership. Not only is Argentina the smallest of the 20 by gross domestic product (GDP), it has the lowest global financial interconnectedness score and an abysmal rule-of-law ranking. In the largest sovereign default in history, the country renounced its debt in 2001. It ranked last in compliance with the priority commitments that G-20 members set at their 2010 Seoul summit. Sen. Richard Lugar, among many others, wants Argentina booted out of the G-20 for its record as a bad economic actor.

While Indonesia's economy and its financial sector are larger than Argentina's, its scores are still very low. If Indonesia had carried out promised economic reforms, it might have remained in the G-20 under our criteria.

Two other current G-20 members, Mexico and Russia, also fail to keep their seats according to our metrics, but only by a hair. That highlights the importance of solid criteria for making a determination in the case of a close call. Mexico's aggregate score is 38.3 and Russia's is 39, both just behind Saudi Arabia, which qualified with 39.4. By comparison, the U.S., the highest-ranked country, had a score of 95.2. Argentina scored just 18.1.

Under our proposed criteria, the four countries that would accede to the G-20 are Switzerland, Singapore, Norway and Malaysia. All four illustrate the value of employing mission-based criteria rather than relying only on GDP or perceived geopolitical importance. If they do join the G-20, they will provide a powerful example for other smaller nations which aspire to become members.

The process of applying precise, transparent standards to membership will help the G-20 strengthen its legitimacy. Using these criteria has only a modest impact on the existing composition of the G-20 and thus would not be disruptive to the organization's activities. Periodic re-evaluation, every five to 10 years, will keep the membership contemporary as the global economy evolves.

With the global economy again weakening, we need a strong G-20 now more than ever. The leaders of the world should take the opportunity of their meeting in Los Cabos to put aside political incentives and do what is best to ignite the global economy. By setting real membership standards, world leaders could build a better G-20, one capable of facing the challenges ahead.

Click here to read the full National Taxpayers Union study.

Alex M. Brill is a research fellow at AEI.  James K. Glassman is the executive director of the George W. Bush Institute and a member of the Investor Advisory Committee of the Securities and Exchange Commission.