Participants 141
There is no valid way to design a good voting method or to select one from those already proposed without having a clear, concise, objective and correct definition for the “best” choice of candidates. For inexplicable reasons, this crucial step is often glossed over or skipped completely. Without it, the cases for or against this method or that method are reduced to just “hand-waving arguments.” Sometimes, the capabilities or characteristics of a particular voting method are themselves tacitly considered to be the definition, which of course, is completely backward.
Since it is voters who will, through their ballots, choose the best candidates, there is no alternative but to lightheartedly assume that voters, collectively, do possess the knowledge and wisdom to make good decisions.
Each voter, when about to mark a ballot for a particular race, has an “opinion” in their brain about each of the candidates in that race. Sometimes that opinion will be strongly positive for a candidate they consider to be “very good;” the voter would be very happy and satisfied if that candidate wins. Sometimes the opinion will be strongly negative for a candidate and the voter would be very dissatisfied if that candidate should win. Of course, a voter’s satisfaction regarding a candidate might be anywhere between strongly positive and strongly negative, including zero. It also happens quite often that a voter’s opinion of a candidate is zero (no opinion) because s/he is not informed and simply does not know anything about that candidate.
There are many voters, each with their own set of opinions about each of the candidates in the race. It is possible (virtually certain with large numbers of voters) that, for any particular candidate, some voters will have positive opinions and some will have negative ones. Which of the candidates, then, would be the “best” one to win this race?
Assuming (because there is no other reasonable assumption) that positive opinions are indicative of good choices and the reverse for negative opinions, the only logical conclusion we can reach is that the best candidate is the one which has the highest (or most positive) net total of all opinions (that is, positive opinions minus negative ones).
Definition: The best possible choice is that result (chosen candidate) which maximizes voter satisfaction, net of dissatisfaction, when summed over all voters who voted.
There is no better way to translate the collective knowledge, judgement and wisdom of the voters into the best choice. This is the only objective that a voting method should have.
The remaining challenge is to find a voting method which determines voters’ sincere opinions as accurately as possible, calculates the net satisfaction for each candidate and selects the one with the highest net total. If only that were as easy and straightforward as it sounds!
A Perfect “Voting Method” – Voters’ opinions of candidates will range from strongly positive (meaning the voter would be very satisfied if the candidate were to be elected) to strongly negative (meaning the voter would be very dissatisfied if the candidate were elected). Of course, voters might hold an opinion of any value in between, including zero. Suppose that we have a wonderful machine, call it a “satometer,” which is able to detect a person’s brain waves and accurately measure the sincere opinion or satisfaction that a voter holds for each candidate. Our satometer is able to measure voter satisfactions for candidates on a scale of “Sats” with +Sats of varying magnitudes corresponding to positive satisfactions and negative satisfactions mapping to –Sats. The scale doesn’t matter as we already must assume that the satometer has the correct conversion factor to map satisfactions onto the chosen scale. We simply have the satometer grab a quick reading of the satisfactions each voter has for each of the candidates; then when the polls close, add up the satisfactions for each candidate to obtain the net satisfaction for each. It is then a simple matter to identify the best candidate as the one with the highest (or most positive) net total.
Unfortunately, no such “satometer” yet exists. However, the fictional satometer serves to crystalize the meaning of the definition and to illustrate specifically what a good voting method must achieve as closely as may be possible.
Much ado has been made over the years regarding the “fairness” of elections and/or of voting methods. Note that the definitions for the primary purpose of elections and for the best choice of candidates say absolutely nothing about fairness. What is “fair” depends completely on what the user of the term thinks is fair, so the term cannot be used in any rigorous argument without the accompanying detailed criteria for what the user of the term considers to be fair. However, if one were attempting to define the “fairest” result, it would be difficult to think of anything more fair than maximizing the satisfaction for the result when totaled over all those who voted.
There is an important ramification of the above definition that needs to be addressed head on in order to avoid later confusion. Adoption of this definition requires abandonment of the majoritarian principle. There will be some cases for which the majority does not rule and this is perfectly OK. It is already widely agreed that the power of the majority must be limited. The fundamental rights of an individual cannot be abrogated just by a majority vote. The definition is related to that concept. A majority is still a powerful indicator that is usually correct, but some narrow exceptions do exist. Because of pervasive inculcation from the cradle that “the majority rules,” this may induce heartburn for some. A hypothetical example may help.
Suppose there is an organization which has 100 active members. Fifty-two of the members live in town A and 48 live in town B. The two towns are 200 miles apart. The organization is voting to choose the best location for a meeting that is expected to last 4 hours. The 52 town A members have proposed a location in town A. The town B members, knowing that a location in town B could never win approval, have proposed a location in town C which is at the half-way point on the shortest route between towns A and B. There are 52 votes (a majority) for the location in town A and 48 votes to hold the meeting in town C. By the “majoritarian rule,” the town A location would be chosen; but is that really the best choice?
Naturally, the 52 members prefer the location that is right in their town. The town C location would require them to drive 2 hours each way; they are mildly dissatisfied with that choice, but can easily do it in one day. However, the 48 town B members prefer the town C location since they, too, can easily drive there and back in one day. The town B members are very dissatisfied with the town A location since it would not only require double the driving for them, but also would add another day and considerable additional expense for an overnight stay.
Very clearly, in terms of the total cost, inconvenience and burden totaled for all 100 members, the town C location actually is the best choice. A satometer reading of the sincere satisfaction or dissatisfaction of each member for each location would determine that location C has decisively the highest net satisfaction. Most people would also consider C to be clearly the fairest decision, even though the majority does not rule in this case. Note that the occurrence of cases in which the majority does not rule are likely to occur only when majorities are only slightly larger than the minority.
