## Minimum Democracy

A few weeks ago, I pointed out that Barack Obama (or John McCain) could win the upcoming Presidential Election with a tiny fraction of the popular vote.  I wrote:

It is possible to win the election for President of the United States with .00001% of the vote. For instance, suppose only one voter shows up in 49 states, and those voters vote for Obama, and 10,000,000 Republicans vote for McCain in New York, then Obama would lose the national popular vote 10,000,000 to 49 but he would have an overwhelming majority in the electoral college. While the results would never be that extreme, it is certainly possible (and has happened) to win the national popular vote and lose the electoral vote.

The current issue of OR/MS Today has a neat article by Winston Yang (University of Wisconsin-Stout) who takes the problem much more seriously.  Rather than allow my extreme variance in turnout, he works with population numbers (which is equivalent to assuming the same turnout rate in every state).  In this case, the minimum popular vote for a winner must be at least 22% or so.  This occurs when a candidate just wins enough states to get 270 electoral votes, and loses (completely) all other states.  Yang then analyzes a number of different ways of allocating electoral votes from the states.  For instance, Maine and Nebraska both use a system where there are electoral districts allocating all but two of the electoral votes, with the two electoral votes then be allocated to the candidate who wins the most popular votes.   Many political thinkers have proposed a number of approaches to allocating the electoral votes.  Yang has a nice graph illustrating the minimum fraction of votes necessary to win for the past elections: