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# Plurality Rule and U.S. Presidential Elections

What is wrong with casting a single vote for our most-preferred candidate and the candidate with the most votes wins the election?  When each voter casts a vote for a single candidate in which the candidate with the most votes wins, then the election procedure is called plurality rule.  Many people in the United States think of plurality rule when they think about voting, because they cast a vote for a single candidate in many of the governmental elections, including the U.S. presidential election.  But, the election for U.S. president is more complicated than plurality rule, as a candidate becomes the next president of the United States when he or she wins a majority, or 270 of the 538 electoral votes.

For example, Maine has four electoral votes and two congressional districts. It awards one electoral vote per congressional district and two by the state-wide, "at-large" vote. It is possible for candidate A to win the first district and receive one electoral vote, candidate B to win the second district and receive one electoral vote, and candidate C, who finished a close second in both the first and second districts, to win the two at-large electoral votes.

Maine’s four electoral votes and Nebraska’s five electoral votes are small compared to the 270 majority needed to win the presidency.  For that reason, the discussion will consider the elections held in these states to conform to the winner-take-all method of the other 48 states and the District of Columbia.

Hence, the U.S. presidential election is (close) to 51 separate plurality elections in the 50 states and the District of Columbia.  The plurality winner of a state receives all of the electoral votes for that state.  Although the U.S. presidential election is based on plurality rule, it is possible for a candidate to win the election, but not be the plurality winner of the popular election.  This has occurred three times since 1872, as noted below.  Note that in the 1876 and 1888 elections, the total number of electoral votes was less than 538, as the number of electoral votes has changed over time.  Because one elector (Barbara Lett-Simmons, from the District of Columbia) cast a blank ballot for president and vice president, there were only 537 electoral votes cast in the 2000 election.  More information about how electors and the voting process can be found at http://www.archives.gov/federal-register/electoral-college/.

Tables: From 1872 to 2004, three U.S. Presidents won a majority of electoral votes but did not win a plurality of popular votes.

The reliance on plurality rule is not the source of the apparent contradiction that we see when the majority winner of electoral votes does not win a plurality of the popular vote.  Instead, it is occurs because the electoral college combines or aggregates each state’s election outcome to arrive at the outcome for the country.  Any election procedure could be used at the state level for which the winner of the majority of electoral votes would not be the popular vote winner.

Consider a simple three state example.  Assume that states X, Y, and Z have six, four, and four electoral votes, respectively.  Each state receives two votes for their senators and the other votes are derived from the population.  The same apportionment method used to allocate representatives (and hence electoral votes) in the U.S. House of Representatives, the Hill-Huntington Method, can be used to divide an additional eight electoral votes among the states according to their population.  Assume that the census population of states X, Y, and Z is 101, 50, and 50, respectively.  Under the following election results, candidate A wins a majority of the popular vote, but candidate B wins eight, a majority, of the electoral votes.

This election outcome persists regardless of how elections at the state level are determined.  This follows because only candidate A can win the electoral votes of state X as he or she receives all of the popular votes.  Similarly, only candidate B can win the electoral votes for states Y and Z because he or she receives all of the popular votes in these states.