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Method of Majority Voting

In class, we saw how the method of majority voting can fail with more than two alternatives to chose from. This system seems simple because the winning option is determined by whichever is most favorable for the greatest number of people. However, this ranking system gets tricker with more options. This is known as the Condorcet Paradox, or voting paradox, in social choice theory. What this means is that when people have to vote for their preferred option but are given more than two to choose from, majority rules doesn’t always work because it’s difficult to turn individual preferences into social preferences.

To see why, suppose there are 3 people (a, b, c) and 3 alternatives (x, y, z). Then, we ask people a, b, and c to rank these 3 alternatives from best to worst, but we know that individuals have different preferences. Suppose the rankings are as followed:

a: x > y > z

b: z > x > y

c: y > z > x

When applying majority rules we see:

x vs y => x wins

x vs z => z wins

y vs z => y wins

So, the ranking is x > y > z > x

This issue can appear in elections relating to politics as described in the 2016 article, “Unusual Flavor of G.O.P. Primary Illustrates a Famous Paradox.”  The author highlights that “the failure of democracy to provide a coherent ranking of political hopefuls” during the 2016 Republican presidential primaries is related to the Condorcet Paradox. As mentioned in the article, the same paradox shown above appears when voting between conservatives, moderates, and populists (conservatives > moderates > populists > conservatives). In this situation, the social raking system of majority rules proves to be ineffective since it does not produce a social ordering of alternatives that is optimal for society. Again, this is because people have different preferences, so in order to determine social preferences and avoid the Condorcet Paradox you would need to use another ranking system.


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November 2018