Anderson was born in Rockford, Illinois, where he grew up. He then attended University of Illinois at Urbana, but his education was interrupted by World War II, when he enlisted in the Army in 1943. He served as a staff sergeant in the U.S. Field Artillery until the end of the war. After the war, returned to complete his degree, graduating in 1946, and commenced the practice of law in Rockford, Ill.
Soon after, he moved east to attend Harvard, obtaining an LL.M. degree from Harvard Law School in 1949. While at Harvard, he served on the faculty of Northeastern University School of Law in Boston, Mass. Between 1952 and 1955, he served as the Economic Reporting Officer in the Eastern Affairs Division, as an adviser on the staff of the United States High Commissioner for Germany. In 1956, he was elected State's Attorney in Winnebago County, Illinois.
Anderson remained State's Attorney until 1960, when he ran for the House of Representatives in the 16th District of Illinois. He won the election, serving in Congress from 1961-1981. In 1969, he became Chairman of the House Republican Conference.
In 1980, Anderson entered the Republican primary for the U.S. presidential election, in a crowded field that included Ronald Reagan and George H. W. Bush. That spring, he dropped out of the primary race to run as an independent candidate for the fall general election. His poll numbers surged early, but waned before the election, and Anderson received only 7% of the vote in the election. His inability to overcome the spoiler effect in that election would later lead him to become an advocate for Instant Runoff Voting.
He then became a visiting professor at series of universities: Stanford University, University of Illinois College of Law, Brandeis University, Bryn Mawr College, Oregon State University, University of Massachusetts, and Nova Southeastern University (his most recent post). He has also served as Chair of the Center for Voting and Democracy from 1996 to the present day (as of this writing in 2002), and as President of the World Federalist Association.