Addressing a small audience last night in a talk titled "Power, Law and Order," Mathematics Professor Bob Norman discussed the accuracy of different voting systems and advocated the "approval system," which allows voters to choose as many candidates as they wish in any given race.
Norman said most elections in the United States are either decided by the plurality method, in which the highest vote-getter wins, or by the plurality with run-off method, in which the top two candidates compete in a second election and the winner is the one with the greatest number of votes.
But in his studies of election outcomes, Norman found these two methods often fail to accurately reflect the will of the voters. He established criteria to determine which system is better and concluded that the approval system best fits these criteria, while conceding that no system meets all of them.
The most important criteria, according to Norman, is called the Condorcet winner. If a candidate is preferred when matched head to head with all other candidates, they are the Condorcet winner, and a good voting system should almost always select the Condorcet winner, he said.
Sincerity in voting was another of the criteria Norman considered in selecting the "fairest" voting system. "I would like people to vote sincerely," he said, "so that we're getting a truer reflection of the populous view."
Insincere voting occurs when voters do not choose their favorite candidate because they believe their interests would be better served by voting for another.
He cited the 1980 U.S. presidential election as an example, asserting that many voters preferred Socialist John Anderson to Jimmy Carter or Ronald Reagan but, instead, voted for Carter because they thought Anderson had little chance of winning and preferred Carter to Reagan.
Norman's final criteria was monotonicity. Violations of monotonicity occur when voters change their preference in favor of a candidate and consequently hurt the candidate in the election.
The approval system is used by the American Mathematical Society, the American Psychiatric Society and other groups, including the College Alumni's selection of Board of Trustees members. "They're very happy with the results," Norman said.
At Stanford University in Palo Alto, Calif., the approval system is used for student elections.
