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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]

Still, the one-number-per-year thing is a real bummer of the current system.[/quote]

Imagine there was only one other person in the lottery, but only one seat. How would you rather settle it: a single coin toss, or each of you flips a coin 100 times and whoever gets the most heads wins?

You do realize that having more flips doesn't change your chances of winning right? And it certainly doesn't change the fact that there is only one seat for two people. [/quote]

In this hypothetical, you are correct.  Only one flip is the best procedure.

But your hypothetical is flawed.  The true situation is that there are many schools.  So imagine 100 kids and 100 schools, each with one seat.
Now roll a 100-sided die.  Would you rather have one roll, and if it turned up badly you got shut out of all your choices?  Or would you rather have 1 roll for each school so that even if you were unlucky for your top choice you’d have another shot at other schools instead of being shut out at all of them?

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The downside in your scenario is "being shut out at all of them." So let me tweak your game a little: say you get to rank as many schools as you want, and then roll the 100-sided die once.  Is that better or worse than picking the same number of schools, and rolling the 100-sided die for each of them? I say it's the same, it just doesn't take as long. (It can be shown using induction that if everyone picks the same number the odds are exactly the same in both scenarios). In each scenario you run the risk of being shut out, which decreases as the number of picks increases.

In the real world, n=12. Most people don't use all twelve picks. The reason people get shut out is not because twelve is too small, or because they don't get enough rolls of the dice, but because they get poor lottery numbers and there aren't enough good seats in the system.

What seems to underlie your argument is a belief that somehow the current system over-rewards people with good lottery numbers, that a fairer system would spread the wealth more equitably. You've repeatedly referred to people with good numbers getting into "all" of their choices. But people with good numbers get into exactly [i]one[/i] school. There is no way to divide that one seat more finely and spread the wealth.

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