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 WHY THE WINNER OF THE NATIONAL POPLAR VOTE SOMETIMES LOSES

To win the presidency, a candidate must win a majority in the electoral college – 270 votes.
The Electoral College provides a great illustration of the way the choice of institution or rule can change political outcomes. Periodically in U.S. political history, the Electoral College has selected as president a candidate who received fewer votes nationwide than some other candidate. In 2016, for instance, Hillary Clinton received roughly 2.8 million more votes than Donald Trump nationwide. But Trump received 304 Electoral College votes versus 227 for Clinton.
To illustrate how this sort of thing happens, I’ve created a simplified set of ‘states’ below – a US with only five equal-sized states. Each has the same number of voters (5 per state) and to keep things simple, let’s assume that each has three electoral votes which will be allocated to the winner of the state-wide plurality. In each state in which Clinton (C) voters make up a plurality of the voters in the state (as in States 4 and 5), then Clinton will win all three electoral votes per state. On the other hand, if Trump (T) voters are more numerous than supporters of other candidates in a state, then Trump will win all three electoral votes (as in States 1, 2 and 3) from each state.
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In the example above, Clinton has a majority of the popular vote (14 of 25 votes) but she loses in the Electoral College because Trump wins three of five states, giving him a 9 to 6 majority.
The key point involves how efficiently a candidate’s supporters are distributed across states. Here Clinton has many wasted votes in State 5. This puts her over the top in terms of the nationwide popular vote, but these voters are not there to help her win in key states.
In the table below, I have reallocated Clinton’s votes to distribute them more efficiently. Now, while receiving the same 14 nationwide votes, she wins a solid majority in the Electoral College.
To illustrate how this sort of thing happens, I’ve created a simplified set of ‘states’ below – a US with only five equal-sized states. Each has the same number of voters (5 per state) and to keep things simple, let’s assume that each has three electoral votes which will be allocated to the winner of the state-wide plurality. In each state in which Clinton (C) voters make up a plurality of the voters in the state (as in States 4 and 5), then Clinton will win all three electoral votes per state. On the other hand, if Trump (T) voters are more numerous than supporters of other candidates in a state, then Trump will win all three electoral votes (as in States 1, 2 and 3) from each state. 
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