The reason is the same as in the example with the lottery balls: The relatively low number of 8 (or 80 billion) suggests that there aren't many balls (human names) in the machine.
Here's another slightly different example. Let's assume that Al receives about 20 e-mails per day, whereas Bob averages about 2,000 per day. Someone picks one of their accounts, chooses an e-mail at random from it, and notes that the e-mail is the 14th one received in the account that day. From whose account is the e-mail more likely to have come?
There are many other examples devised to shore up the numerous weak points in the Doomsday Argument. Surprisingly, many of them can be remedied, but a few of them, in my opinion, cannot be.
That a prehistoric man (who happened to understand Bayes theorem in probability) could make the same argument about a relatively imminent extinction is an objection that can be nicely addressed. Appealing to some so-called anthropic principle whereby inferences are drawn from the mere fact that there are observers to draw them is much more problematic.
In any case, there's probably still time to learn more about the Doomsday Argument and the use of the so-called anthropic principle in philosophy, cosmology and even everyday life. A good place to begin is Nick Bostrom's work, particularly his book, Anthropic Bias.
Professor of mathematics at Temple University and winner of the 2003 American Association for the Advancement of Science award for the promotion of public understanding of science, John Allen Paulos is the author of several best-selling books, including Innumeracy and A Mathematician Plays the Stock Market. His Who’s Counting? column on ABCNEWS.com appears the first weekend of every month.