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Majority judgment: a better way to vote By Bob Sleeuwenhoek, mathematics student
Voting is incorporated into our daily lives in more ways that we usually realise. From electing national leaders and parliaments to selecting a group leader of a collaboration project and from electing the winner of an Olympic sport event to choosing the best date for a group meeting, we use voting as a solution of many problems, some of which are daily, some of which only turn up every few years. But how do we decide on the result, and what voting system do we use to select a winner? Different competitions require different ways of voting, but are all possible ways equally good? As Kenneth Arrow states in his classic, Social Choice and Individual Values, “The methods of voting and the market…are methods of amalgamating the tastes of many individuals in the making of social choices… Any individual can be rational in his choices. Can such consistency be attributed to collective modes of choice, where the wills of many people are involved?”. A few years ago, French mathematicians Rida Laraki and Michel Balinski developed a new way of voting and counting votes, the majority judgment, which they believed to be superior to all other traditional ways of voting. But does that statement hold?
voter to cast one vote for their favorite candidate. The winner would be the candidate that received the highest number of votes. This system is most often used within small groups and in informal settings, but the national elections of the United Kingdom and Canada also apply this system. A modified version of this system is the two-past-the-post system in which voting takes place in the same way, but the winner requires to have received an absolute majority of the votes. If no such winner exists, the two top competitors face off in a second round. This second system is used in the French presidential election. The problem with these systems is that, although the winner might receive a majority of the votes, if the number of competitors is large enough it is possible that a large majority of the population actually wished another competitor to win. Let us assume there are 10 competitors and the winner receives 11 percent of the votes. In the case of the two-past-the-post system, let us assume he won the second round. This would mean that even though the winner received the highest per-
Different competitions require different ways of voting
Traditional voting systems
First, let us look at some of the more traditional ways of voting. The most often used variant would be the first-past-the-post system, which simply allows each 12
Eureka! nummer 49 – juni 2015