I have been working on a choropleth display of 48 continuous states where the political bias of the state is encoded in its background color, and the population is encoded in the size of a circle with a center on the geometric center of the state. The Bokeh library interface for a circle uses its diameter to specify the circle size. So, it is natural to make the diameter proportional to population size. When doing this, the following plot results. Notice the extreme range in size between the most populous states and the least. Mousing over a state will render the state's name, level of political bias, and population. 

Is plotting the circle with diameter proportional to populations a fair representation of the states' relative sizes? Does a viewer intuit the circle's diameter or the circle's area as a representation of population size? Note that plotting the size of the circle based on diameter causes a quadratic relation between population size and circle area. Is this fair? Montana's area is roughly a quarter of that of Oregon. But the circle representation for Montana is minuscule.

Circle diameter varies linearly with population.

So, I made the population proportional to the circle area. This means that the diameter will vary by the square root of the area:

area = (pi x radius)2

radius = (area)1/2/pi

diameter =  2(area)1/2/pi

 I show the result below. Now note the significantly attenuated variation in the circle area. Montana's area, like its population, is roughly a quarter of that of Oregon. 

I think this demonstrates that representing data as proportional to the circle diameter subtly misguided the reader. It is more honest to use area.

 Circle area varies linearly with population.