Majority Rule Problems Revisited

By  Lee, Cho Sik

emeritus professor of philosophy

Korea University.

Translated by Dr. Rim, Byonggap

  Prof. Han Soon-goo, at Chosun Ilbo (Nov. 29. 2007), pointed out problems lurking in the election system based upon 'majority rule.' He doubts that the majority rule of our existing presidential election system reflects the public opinion properly. It is well known that the outcomes of majority rule could distort rather than reflect the truth or justice. So we always have to be wary of the tyranny of majority. It is also true, however, that we have no choice but to adopt the majority rule. Especially when the truth or justice cannot be determined unanimously within a community, we cannot help following the decisions made by the community members through majority rule.

  In democratic countries election systems are a matter of great concern not only to voters but also to political scientists and economists. How about philosophers? The issue cannot evade philosophers' interest, since it is one of their biggest jobs to struggle with the fundamental problems facing societies. That is why I, as a philosopher, got to take interest in Prof. Han's article where he made suggestions on how to reflect voters' preferences with more integrity.

  Han raised a hypothetical case ; voters have three candidates A, B, C. Now 34 % of voters give A a strong support, while the rest of voters have an intense dislike against A . In this situation, if voters had only two candidates A and B, A would get 34% of votes and B would get 66% of votes. Again, if voters had only two candidates A and C, A would get 34% of votes and C would get 66% of votes. After all, the majority of voters dislike A. However, if voters have three candidates at once, the outcome could be 34% of votes for A, 33% for B, and 33% for C respectively. This hypothetical situation shows that, despite the majority's dislike against A, A could be a winner.

  This case could hardly be actualized, but is plausible enough to remind us that majority rule could distort people's preferences. As an alternative, Han proposed a new voting method invented by Eric Maskin, the 2007 Nobel prize winner in economics. Maskin's idea is as follows ; instead of having voters choose one out of three candidates as we do now, it is possible to put them to three 'one-to-one' matches, like A to B, B to C and C to A, and let voters show their order of preferences. Then the candidate who will get the most preferences at three 'one to one' matches will be chosen. Voting method is also not complex. Voters could rank three candidates beside the name of candidates on the ballet paper just in order of their preferences. It must be an easy job for computers to calculate those overall preferences shown on the ballot.

  This alternative is worthy of our deep consideration. But it also has to be deeply examined, since it has been proposed as a solution to the problems with the existing voting system.

  It occurs to me that it may have two problems. One is whether it is more reasonable than the existing election method in extracting collective preferences with more integrity. The other is that the result could be dependent upon how computer operators process data from the ballots.

  First, let me examine how reasonable the proposed method is in reflecting collective preferences. Suppose that I told you that, among three candidates, I prefer A to B, B to C. Then you may infer that I must prefer A to C. It does not follow, however, that I prefer A to C. It is possible that, comparing A to C, I actually prefer C to A, unreasonable as it may sound. Let me take another example. I know that you prefer apples to persimmons, and persimmons to pears. Then how about comparing apples to pears? Isn't it possible that you actually prefer pears to apples?

  This unreasonable choice is known as so-called 'non-transitivity of preferences.' In case that voters' preferences could be transitive or non-transitive, we first have to decide which method will reflect people's preferences with more integrity.

  Second, it could happen that the election outcomes are varied, depending upon how computers process data. Suppose, for instance, that voter P, Q, R's preferences for A, B, C are the same and that voter P's preference is A>B>C, voter Q's is B>C>A, and R's is C>A>B. In this case, when A is matched against B, A is chosen. And when A is matched against C, C is chosen. If the order of matches is to be changed, however, the winner will also be changed. If you are to choose A, then put 'B to C match' first, which will make B a winner at the first match. Then put the second match between A and B and the outcome will be A's victory.

  Even if the alternative proposed by Han, as I pointed out in the above, remains to be examined,  still I believe that we have to take into account the objections raised by Han against the existing election system.