Reply to Common Lottery Algorithm

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[quote=Anonymous]The description of the New Orleans lottery is maddeningly imprecise, but it doesn't sound like DC. They describe a scenario where "the top ranked student for school B... has selected school C as his number one choice." That would never happen in DC.

There are two fundamentally different ways of running a multi-choice lottery like this. The difference stems from what happens when someone doesn't get into their number one choice. Do you:
A. Try their number two, then number three, and so on, all the way to number twelve; or
B. Skip over that person, and try to get the next person into their number one choice. Once you have placed as many people as possible in their number one choice, then you go back and try to put as many as possible in their number two choice, then number three, and so on all the way through number 12.

Some notes:
Method A is the way DC does it.

In Method A, the optimum strategy is to rank your choices in your actual preference.

In Method B, it makes a great deal of difference whether you get into your number one choice or a lower choice. If you don't get into your number one you get put to the end of the list. So the optimal strategy is not to rank in your actual order of preference, but instead to take into consideration your chances of being accepted.

In Method B, it is possible that three-way (or more) exchanges will exist where every participant improves their outcome by trading. This is not possible under Method A.

Since this article (imprecisely) seems to be talking about three-way switches, I suspect that New Orleans uses method B, which is not the same as DC.[/quote]

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