Anderson was born to a Swedish American family in Rockford, Illinois, where he grew up. He then attended University of Illinois, 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, receiving a Juris Doctor (J.D.) degree from the University of Illinois College of Law in 1946. He was admitted to the Illinois bar the same year, and commenced the practice of law in Rockford.

Soon after, he moved east to attend Harvard Law School, obtaining an LL.M. degree in 1949. While at Harvard, he served on the faculty of Northeastern University School of Law in Boston, Massachusetts. 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 U.S. Congress from 1961-1981. In 1969, he became Chairman of the House Republican Conference. He was one of the most articulate of the liberal Rockefeller Republicans.

In the 1980 presidential election, 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 campaign manager was New York media strategist David Garth. Anderson started out very well in the polls--over 25àBut as a top advisor reported, "Instead of rising to something on the order of 30 percent, he fell, steadily, about 1 percentage point every week and a half, down to 22 percent, then 20 percent, then 18 percent, and progressively worse." Most of Anderson's original support came from Rockefeller Republicans who were more liberal than Reagan, but it bled away. Many prominent intellectuals, including the author and activist Gore Vidal, also endorsed the Anderson campaign. He also had the support of many independents. The hope that Anderson would score when the Democrats split faded when Ted Kennedy endorsed Jimmy Carter and the Democrats held together. The choice of little-known Democrat Patrick Joseph Lucey, a former governor of Wisconsin, as his running mate signaled that Anderson was unable to win over any prominent Democrat. His poll numbers kept falling, despite a spirited debate with Reagan. He stayed in the race because he would receive federal election subsidies only if he received 5f the vote, and millions of unpaid debts had been accumulated. In the end he barely made the 5 nd received 7f the vote in the election, with a total of about 6 million votes. He did not carry a single precinct in the country. See Reagan Coalition for vote details. His inability to achieve the spoiler effect in that election would later lead him to become an advocate for Instant Runoff Voting. Four years later in 1984 he supported the Democratic candidate Walter Mondale.

By the end Anderson's support was on college campuses, and he capitalized on that by becoming 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 served as Chair of the Center for Voting and Democracy from 1996 to the present (as of 2006), as President of the World Federalist Association, on the advisory board of the Electronic Privacy Information Center and is of counsel to the Law Offices of Greenberg & Lieberman, LLC.

In the 2000 U.S. presidential election, he endorsed Ralph Nader.