Even as they address these legacy tasks, the G20 leaders should expand their horizons. So far, the G20 has focused overwhelmingly on financial and economic issues, and its members have resisted mission creep. But if the G8 experience is any guide, the G20 will inevitably be drawn into a broader global agenda, encompassing issues like development, climate, and - eventually - peace and security. Instead of resisting this trend, the G20 leaders should embrace it. An expanding G20 remit promises to shake up world politics in at least three healthy ways.

First, an expanding G20 will inject fresh air into global negotiations, which too often are split along outdated lines. As US President Barack Obama observed at the United Nations last September, effective multilateral diplomacy is often stifled by obsolete bloc politics inherited from the Cold War.

The G20, however, includes not only the advanced market democracies, but also prominent members of the Group of 77 (G77). By placing leaders of major developed and developing countries side by side at the same high table, the G20 increases the possibilities for diplomatic breakthroughs.

Such informal settings allow statesmen to strike up a personal rapport with their counterparts and bargain pragmatically across issue areas, rather than just playing to the galleries. Over time, obsolete alignments may yield to a more dynamic diplomacy, in which shifting coalitions of interest form to advance practical cooperation against global challenges.

Second, the G20 can encourage rising powers to assume greater global leadership in return for a bigger voice in shaping the world order. Today, the world expects China and other emerging players to help solve shared problems from climate change to financial instability to nuclear proliferation. But today's emerging powers rightly insist on being "rule-makers", not simply "rule-takers". The G20 provides a setting to advance both goals. It can anchor emerging powers as pillars of world order, while giving them a platform to influence the direction of global rules and institutions.

Third, the G20 can give tired international organizations - and particularly the United Nations - some healthy competition. Certainly, the G20 will never replace the UN, which has unequalled universality, legitimacy and technical capacity.