If someone asks, Do you live in a democracy?, then you'd think about how your country is governed and give an answer. For example, say I lived in the USA (in Humboldt County, California to be precise) and someone asked me that question, I'd say that with some shortcomings, yes I do live in a democracy. Now imagine if the USA broke up into individual states, and each state became a democratic country in its own right. Then someone asked me the same question, Do you live in a democracy?, then again I'd say yes I do. But in going from the USA to a collection of states, hasn't democracy in some way been lessened?

What if every state broke up into its counties, so that each county was a sovereign democratic country in its own right. Again I'm asked, Do you live in a democracy?, and since my country (formerly my county) is democratic I reply yes, since I live in the sovereign democratic country of Humboldt, I do live in a democracy. But again, isn't this county-level democracy somehow less than the previous state-level one?

I feel that with each break-up described above, democracy is in some way diminished. Is it somehow possible to put a number on this degree of democracy? Then we can compare numbers for different people in the world and have some way of improving the degree of democracy (assuming democracy is a good thing). The Democratic Magnitude is such a measure and is defined for a person as:

Democratic Magnitude = (number of citizens in your democracy) / (world population)

Assuming that the world population is 7.8 bn, then working out the Democratic Magnitude for each of the scenarios above gives:

Democratic Magnitude if you live in the USA = 330 m / 7.8 bn = 0.042308 = 4.2%

If the USA were broken up into individual states:

Democratic Magnitude if you live in California = 39.5 m / 7.8 bn = 0.0051 = 0.5%

If California were broken up into individual counties:

Democratic Magnitude if you live in Humboldt = 135 k / 7.8 bn = 0.000017308 = 0.00173%

Photo by Rama - CC BY-SA 2.0 fr

To give another example, say you're a UK citizen. Then:

Democratic Magnitude of a UK citizen = 63 m / 7.8 bn = 0.0081 = 0.81%

But before the UK left the EU the it was:

Democratic Magnitude of a UK citizen (in EU) = 501 m / 7.8 bn = 0.0642 = 6.42%

Surely the citizens of India have the highest Democratic Magnitude:

Democratic Magnitude of an Indian citizen = 1.3 bn / 7.8 bn = 0.1667 = 16.67%

What would it take to acheive a Democratic Magnitude of 100%? A world government I suppose.

What's the Democratic Magnitude if you live in an anarchy? In that case the individual is sovereign, and so:

Democratic Magnitude in an anarchy = 1 / 7.8 bn = very small