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big stick policy refers to U.S. President Theodore Roosevelt's foreign policy: "speak softly, and carry a big stick."
President Theodore Roosevelt’s big stick policy was used by the United States to negotiate an agreement for an American-led canal through Panama, spread American influence in Cuba, and broker a peace treaty between Russia and Japan. Big Stick diplomacy is the policy which refers to a carefully mediated negotiation "speak softly, and carry a big stick." and Roosevelt won the Nobel Peace Prize for it in 1906.