Voting Paradox

Imagine that a Political Science class studying the American presidential process holds a mock election. Members of the class are asked to rank, from most preferred to least preferred, the nominees from the Democratic Party, the Republican Party, and the Third Party. There are six possible ways to vote:

ABCDEF
1. Democrat
2. Republican
3. Third		 1. Republican
2. Democrat
3. Third		 1. Democrat
2. Third
3. Republican		 1. Republican
2. Third
3. Democrat		 1. Third
2. Democrat
3. Republican		 1. Third
2. Republican
3. Democrat

Let's assume the results of the mock election are as follows:

VotesPreference Order
8   E  :  Third > Democrat > Republican   
8   D  :  Republican > Third > Democrat   
5   A  :  Democrat > Republican > Third   
4   C  :  Democrat > Third > Republican   
2   F  :  Third > Republican > Democrat   
2   B  :  Republican > Democrat > Third   
29Total Votes

What is the preference of the group as a whole?

Answer: This is an example of a voting paradox, specifically a majority circle.

Voting paradoxes are also studied in part because of their implications for practical politics. For instance, the instructor can manipulate the class to choose between the Republican and the Third, and then ask the class to choose between the winner of that contest (the Republican) and the Democrat. By similar manipulations, any of the other two candidates can be made to come out as the winner.

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