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This simple simulation was originally produced over 20 years ago to demonstrate the potential impact of cultural preferences on gender componsition of children if people acted on these by favouring contraception once the ideal balance of children had been reached, and kept trying if it had not. It has since been used in teaching. So I won't make my point just yet, but rather let it be demonstrated.
Don't stop indicates no strategy, women will each have their 4 children. Stop at 2 boys will cause all women to start contraception as soon as they have achieved two boys. The Stop at 1 boy and 1 girl will result in contraceptive practices when this number has been achieved. Stop at 1 boy ditto. Note that 1000 women is small enough that there will be a random error in the result, so you may need to run this several times to identify the trend.
Assumptions: To keep it simple and explicable I have made a number of assumptions, which I do not think detract from the final conclusions that can be drawn from the simulation. First, I assume that women will end up with a maximum of 4 live children each if they place no restrictions on their fertility. Second, I assume that both genders have an equal chance of being born and surviving at each birth, although we know that this ration is adjusted in some circumstances in living populations. Third, I assume that they will be successful in their contraceptive endevours. It would not be hard to modify the simulation to make each of these more complex, but this would not change the trend of the outcome.
The simulation is written in javascript, and is entirely contained in the source of this page. If you want to modify it, simply do a "Save" from the File menu, making sure you choose "source" or "html" from the save menu, thus not selecting so called 'archive' formats or pdf format. Then you can edit the page in the program of your choice and run it directly in a browser.
It runs in Firefox and Safari, and should work in recent versions of Internet Explorer and others.