Global Rule of Law perfered by most people.

“A global system based on the rule of law?” American and international polls suggest most people now support it. Unfortunately, fear of world government will rule it out. Conservatives will fear having it and liberals will fear talking about it. And most people will remain oblivious to our need for it. And, need means need. Without it, maximum freedom or security will remain elusive and increasingly difficult for all people and all nations.
The Council on Foreign Relation’s Program on International Institutions and Global Governance is seeking to identify the institutional requirements for effective multilateral cooperation in the twenty-first century. Unfortunately, unenforceable cooperation and international treaties will continue to excite such intellectuals but they will continue to fail to deliver.
The polls on global and American attitudes on international institutions and an array of global issues suggest significant overlap between global and U.S. opinion -- and a few noteworthy differences. Public polls in both the US and abroad indicate most citizen views on world order are strongly internationalist in orientation. They believe that global challenges are simply too complex and daunting to be addressed by unilateral or even regional means. In every country polled, most people support a global system based on the rule of law, international treaties, and robust multilateral institutions. They believe their own government is obliged to abide by international law, even when doing so is at odds with its perceived national interest. Large majorities, including among Americans, reject a hegemonic role for the United States, but do want the United States to participate in multilateral efforts to address international issues.
http://www.cfr.org/thinktank/iigg/pop/about.html\
Regarding UN: Most Americans favor a world order that is multipolar or led by the United Nations, rather than based on U.S. hegemony or a bipolar balance. They believe that all nations must abide by international law even when doing so is at odds with their national interest. A large majority of Americans express support for U.S. participation in the International Criminal Court, even after hearing past U.S. government objections. And most Americans believe that the United Nations plays a necessary role in the world, including in legitimating the use of armed force. They also favor giving the United Nations stronger powers to investigate human rights violations and to regulate the international arms trade (though not, significantly, to impose any taxes). At the same time, surveys show significant dissatisfaction with the UN's actual performance in fulfilling its missions, contributing to erratic overall evaluations of the UN as an institution.