The "voter's paradox" is another model which has been used and studied to understand inefficiencies which exist in voting and democracies. Democratic societies use ballot procedures to determine aggregate preferences and to make the social decisions that follow them. If all votes could be unanimous, efficient decisions would be guaranteed. Unfortunately, unanimity is virtually impossible to achieve when hundreds of millions of people, each with his or her own different preferences, are involved.

      The most common social decision-making mechanism is majority rule. However, this system is far from perfect. In a well-known work published in 1951, Kenneth Arrow proved what has been called the "impossibility theorem." With this he showed that it is impossible to devise a voting scheme that respects individual preferences and gives consistent, definite results.

    The voting paradox is an example of irrational results that can result from majority-rule voting. Consider the following example: Suppose that, faced with a decision about the future of a firm, the president of the company decides to let her three top administrators vote on the following options: A) increase the number of employees and hire more monitors (supervisors), B) maintain the current size of the supervisors and employees, or C) cut back on supervisors and reduce the number of employees. The Vice President of finance (VP1) prefers A to B and B to C. The Vice President of hiring and firing (VP2) doesn't want to rock the boat. She prefers keeping the current size of the firm (option B) to either of the others, although she prefers C to A. The 3rd in command does believe in changes and doesn't really care if it means decreases or increases in things. He prefers C to A and A to B.

      When the three vote on A vs B, they vote in favor of A-to increase the university size because VP1 and the 3rd in command outvote VP2. Voting on B and C gives B a victory over C. But then they all vote on A vs C. Here a problem arises because C wins. But if A beats B, and B beats C, how can C beat A? The results seem to be a bit inconsistent don't you agree?!?

      What this voting paradox illustrates is that when preferences for public goods differ for individuals, any system for adding up those preferences can often lead to inconsistencies and results which just don't seem to make much sense. The voter's paradox also shows us that when there are more than 2 alternatives, we should not make paired comparisons, to avoid mistakenly assuming that a chosen alternative is preferred to one that is not chosen. We need to consider all the alternatives together, because if we do this we might discover that the collective may have no clear preference. What this also shows is that people may then be able to sway the outcome of an election to their advantage; specifically related to 1) agenda setting (on the part of the candidates) and to 2) strategic voting (on the part of the voters); which are both inefficiencies and do occur. Much of the work that has been done in these areas is very mathematical and complex, but let me just give you an outline of the conclusions that have been drawn.

      The idea of agenda setting refers to the means of making decisions based on the order in which issues or candidates will be compared. Clever people will be assigned the task of setting the agenda for the elections or meetings where incomplete pairwise comparisons are held. If the preferences are such that a voters' paradox is present, they can manipulate the agenda to obtain their preferred outcome.

      Strategic voting refers to voting in a way which is different from your preferences in order to cause a preferred alternative to be chosen. In other words, you are treating the vote as a kind of game in which you adopt the best strategy to win. It can be a big threat to a system in which there are party primary elections. In such elections, people may chose to vote for a candidate that they know is most likely to be defeated in the general election so that that party can win. When people can act in these ways, it is obviously not efficient.

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