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Gibbard was born on April 7, 1942. He received his BA in mathematics from Swarthmore College in 1963 with minors in physics and philosophy. After teaching mathematics and physics in Ghana with the Peace Corps (1963–1965), Gibbard studied philosophy at Harvard University, participating in the seminar on social and political philosophy with John Rawls, Kenneth J. Arrow, Amartya K. Sen, and Robert Nozick. In 1971 Gibbard earned his PhD, writing a dissertation under the direction of John Rawls.