Mathematics-free Explanation By Analogy
Assume the human species is a car driver. The driver has encountered some bumps but no catastrophes, and the car (Earth) is still road-worthy. However, insurance is required. The cosmic insurer has not dealt with humanity before, and needs some basis on which to calculate the premium. According to the Doomsday Argument, the insurer merely need ask how long the car and driver have been on the road—currently at least 40,000 years without an "accident"—and use the response to calculate insurance based on a 50% chance that a fatal "accident" will occur inside that time period.
Consider a hypothetical insurance company that tries to attract drivers with long accident-free histories not because they necessarily drive more safely than newly qualified drivers, but for statistical reasons: the hypothetical insurer estimates that each driver looks for insurance quotes every year, so that the time since the last accident is an evenly distributed random sample between accidents. The chance of being more than halfway through an evenly distributed random sample is one-half, and (ignoring old-age effects) if the driver is more than half way between accidents then they are closer to their next accident than their previous one. A driver who was accident-free for 10 years would be quoted a very low premium for this reason, but someone should not expect cheap insurance if they only passed their test two hours ago (equivalent to the accident-free record of the human species in relation to 40,000 years of geological time.)
Read more about this topic: Doomsday Argument
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