(thanks to Yoram Gat, statistician)
Margin of error is not exactly the right term. 'Margin of error' is used when using a proportion in a sample to estimate the proportion in the population. In our case the proportion in the population is known (50.8% women; 49.2% men), and we wish to bound the proportion in a sample. I would use something like “random fluctuation”.
To simplify, let us say the proportion is exactly 50-50. So in the case of a sample of 500, you will have at least 239–261 about 70% of the time, at least 227–273 about 95% of the time, and at least 216–284 about 99.5% of the time.
The chance of having a split that is worse than 200/300 is about 1:100,000.
The chance that either there would be more than 350 men or more than 350 women in the group of 500 is less than 0.2 millionth of a millionth of a millionth (2 x 10^-19)
In making these calculations, the size of the population doesn’t matter unless it is tiny – the statements are as true for a city of 100,000 as they are for a country of hundreds of millions. It is only the size of the sample that matters. As a rule of thumb, on each particular issue the sampling error is about 1 / (2 sqrt(n)), where n is the size of the sample.
This means, further, that if any group makes less than 40% of the population, then the chance that it will form a majority in a group of 500 randomly selected people is less than 3 in a million.
Sortitional selection was a central and defining feature of the first Athenian democracy. It was used to select both legislative and administrative functions. There were also a small number of meritocratic elective offices, particularly for the military and the treasury.
Sortitional selection was also used in Florence and Venice in the late medieval period. The system was instituted in order to break the power of political factions. Sortition was also used during the French Revolution.
Sortition is also used by the Amish to choose their bishops.
Jury selection in U.S. courts is initially through sortition.
Sortition has been widely used in military drafts; in choosing recipients of organ transplants; in allotting places for children in magnet or charter schools; in dispensing tickets to entertainment or sporting events.
A long list of examples can be found in Wikipedia's entry: http://en.wikipedia.org/wiki/Sortition#Examples
the common lot
No, definitely not.
The executive and judicial branches must be chosen meritocratically, based on skills.
The executive is charged to carry out the will expressed by the legislature and therefore requires management expertise.
Similarly, judicial appointments require extensive training in the law and jurisprudence.
The primary purpose of sortitional selection of the legislative branch is to insure that the decision-making body can be as close to proportionally representative of the entire population as possible. It is intended to insure that the government is 'by' the people as well as 'for' and 'of' them.
"The Common Lot: Next Step for Democracy" advocates that sortition (random selection) be used to select among qualified citizens who are willing to serve in the legislature.
In order to be entered into the pool for random selection a citizen would be required to do two things.
First: register (just as one registers now to vote). Placing oneself in the lottery pool should be voluntary.
Second: pass a civics test in order to demonstrate basic understanding of the legislative process. This test should be no more difficult than the one required to obtain a driver's license in the U.S.
Accomplishing those two requirements, the citizen's name would be placed in the pool for random selection to serve in the legislature.
'Sortition' means 'choice by lot; random selection'.
Random selection in a large population will automatically produce, with small deviations, a proportional representation of that population. This is 'automatic' because of probability theorem: 'The Law of Large Numbers'.
A random selection of, say, 1,000 people from the U.S. population would produce a body that would contain approximately 492-496 men and 504-508 women (since men are 49.4% and women are 50.6% of the national population).
Unlike selection by competitive balloting, sortition is immune to the sway of political faction, economic privilege or any other factor besides citizenship.
[Note, however, that our proposal also suggests one other qualifier: a base-level understanding of the legislative process.]