An argument in favor of the League of Nations would be that international cooperation in such an association would be a way of preventing and limiting wars and conflict.
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An organization such as the League of Nations was the signature idea of US President Woodrow Wilson. He had laid out 14 Points for establishing and maintaining world peace following the Great War (World War I). Point #14 was the establishment of an international peacekeeping association. The Treaty of Versailles adopted that idea, and the League of Nations was established in 1920. [Notably, the United States never joined the League, because the US Senate did not ratify the Treaty of Versailles.]
The League of Nations had set out clear goals for what it intended to do. The main aims of the League were disarmament across nations, preventing war through collective security of the international community, settling disputes between countries through negotiation, and improving welfare of people around the globe. But it proved unable to meet those goals. The United Nations, formed after World War II, has similar goals, and has been more effective in its efforts -- though there are still plenty of people who criticize the UN's effectiveness.
