Democracy in the United States?

L. David Roper


U.S. citizens and media ofter describe the U.S. as being a "democratic" country. This article is an attempt to quantify the degree to which the U.S. is democratic.

Congress Representation

The question to ask here is how democratic is the states per capita representation in the U.S. Congress. Each state has two Senators and a number of Representatives allowcated every ten years proportional to the states' population. The last date for this representation calculation was in 2010 after the decadal census.

The senatorial and representation data are given in Here is a graph constructed from those data.

Of course, states with small population have much greater representation in Congress than do more populous states. For example, Wyoming has more than 3.59 times the per capita representation than does California. And the District of Columbia has zero representation.

A way to make the Congress representation more democratic would be to change the Constitution such that the number of senators for each state is determined by the percentage of the population in those states according to:

Then the following graph shows the increased degree of representation of the states in the Congress according to this scheme:

Of course, the number of senators could be apportioned according to population the same way as the House of Representation to get even closer to democracy.

Since Black citizens have always been underrepresented in Congress, here is a graph of Congress representation by Black population of states:

Electoral College Representation

Presidential elections every year are largely based on Electoral College votes from each states determined by the number of senators and representatives for the states on a winner-take-all vote. There are three exceptions:

Here is a graph constructed from the congressional data plus the three extra Electors for DC:

So, DC has no representation in Congress and is second highest behind Wyoming in Electoral College representation.

Maine and Nebraska do not assign Electoral College votes by winner-take-all as other states do. Instead, they use the Congressional District Method in which the winner of each district is awarded one electroral vote, and the winner of the state-wide vote is awarded the two remaining electoral votes. This makes the electoral vote closer to the popular vote within the state, thus making it more democratic within the state, but does not make it more democratic amoung the states.

Of course, presidential elections could be totally democratic by using the total vote instead of the Electoral College to select a president.

Four presidential elections that were decided by the Electoral College contrary to the popular vote:

  1. 1876: Rutherford B Hayes over Samuel J. Tilden by 1 Electoral vote but lost popular vote by >250,000.
  2. 1888: Benjamin Harrison over Grover Cleveland by 65 Electoral votes but lost popular vote by >90,000.
  3. 2000: George W. Bush over Al Gore by 5 Electoral votes but lost popular vote by >540,000.
  4. 2016: Donald J. Trump over Hillary R. Clinton by 62 Electoral votes but lost popular vote by >1,800,000.


Gerrymandering is a process used by state governments to reduce the representation of certain groups (blacks, political parties, etc.) in Congress. Here is a graph that shows an index that measures the deviation of congressional districts from a circle for states that have more than one congressional district. The lower the index, the greater the deviation.

My state of Virginia is one of the worst.

Examples of Gerymandering:

Mathematics should be used in defining congressional districts. Here are some references that describe possible ways to use mathematics to define districts: