V. Vitols, Anaheim Hills, Calif. posed this question to Scientific American Magazine:

"Has there been any progress in developing fairer ways for people to vote in elections? I recall reading some time back about a system in which people would get one vote per candidate, not transferable between candidates; such a system was said to be fairer overall than one vote per voter."

Several mathematicians responded to the above question. Here are a couple of those responses.

Lawrence Ford, the chair of the mathematics department at Idaho State University, notes that the goal of fairness is more elusive than it may appear:

"There has been lots of activity over the past 30 to 40 years on mathematical applications in political science. One problem that has been studied extensively seems similar to the problem you describe: Given a set of candidates (at least 3) and a number of voters, select the 'fairest' winner.

"Many solutions have been proposed, but all were shown to exhibit flaws in some cases. Then, in the early 1960s, Kenneth Arrow proved his famous Impossibility Theorem, which essentially states that no system can exist without these flaws, that is, no perfect voting system exists. So 'fairer' is a subjective measure; any voting system can be made to look 'unfair' under the right set of circumstances.

". . . In it [approval voting], a voter votes for all candidates he or she approves of. The candidate with the most votes wins. In it, the candidate with the broadest approval base wins (centrists, not extremists, get elected--which is often not the case in a one person/one vote election). One big flaw here is that most voters are fairly positive of their favorites and fairly positive of those they hate, but wishy-washy in the middle. If they choose randomly for or against approval in that middle range, the whole election can become random."

Sam Merrill in the department of mathematics and computer science at Wilkes University in Wilkes-Barre, Penn., provides more details:

"The method of voting in multicandidate elections referred to in the question is, I believe, Approval Voting. Under this procedure, each voter can vote for one, two, three or any number of candidates. In effect, the voter considers each candidate one by one and casts a vote for those whom she (or he) approves but not for those whom she does not approve. The winner is the one approved by the most voters.

"Approval Voting is now used by several national and international professional societies in their election of officers. These include the Institute of Electrical and Electronics Engineers, the American Statistical Association, the Mathematical Association of America and the Institute for Management Science. Some of the approval-voting elections in these societies have led to winners who would not have won under single-vote plurality (the more common method used in the U.S.) or have enhanced the standing in the voting outcome of candidates who had broad support throughout the profession. Generally speaking, however, the candidate who has won under Approval Voting did well among bullet voters (those who voted for only one candidate), as well as among those who voted for more than one candidate."

"Although bills have been introduced in New Hampshire, New York and North Dakota to institute Approval Voting in public elections, I am not aware of any recent progress on that front.

"In a recent study [Steven J. Brams and Samuel Merrill III, 'Would Ross Perot Have Won the 1992 Presidential Election under Approval Voting?' in PS: Political Science and Politics, Vol. 27, No. 1, pages 39-44; March, 1994, we projected the likely outcome had Approval Voting been used in the three-cornered 1992 presidential election. Based on polling data from the American National Election Study, which asks voters to score each candidate on a scale from 0 to 100, we projected approval-voting totals using three different assumptions. The results consistently indicate that Bill Clinton would have received approvals from about 55 percent, George Bush from about 50 percent, and Ross Perot from about 40 percent. Hence, Clinton would have attained majority support--enhancing his mandate--but his margin over Bush would have been unchanged.

"Perot would have doubled the 19 percent he received under plurality because some Bush and especially Clinton supporters also approved Perot but opted to cast their vote for one of the main contenders. Under Approval Voting, Perot's total would therefore have more accurately reflected his true support. Yet his chances of actually winning might have been reduced, because voters deciding to cast a vote for Perot would not have had to switch away from Clinton or Bush but could support both. In light of the high disapproval rate that Perot faced, he would have been hard-pressed to climb past Clinton's 55 percent approval.

"It has been argued that Approval Voting benefits centrist candidates, who tend to have a broader appeal, while not denying voters the opportunity to express support for more extreme candidates, and that it should reduce infighting between like-minded candidates because they need to share support from the same voters. Approval Voting could be implemented on existing voting machines, and it could be done without a Constitutional amendment."