<p>Apparently it's far from a straight up lottery and it's constantly being tweaked. If I had to guess, the algorithm maximizes the number who get their top 2 or 3 choices, consistent with filling all dorms. This is from a 2001 RIST meeting proposing changes:</p>
<p>"Some notes on the lottery algorithm</p>
<p>Broadly speaking, there are two basic strategies one might take to running the lottery: call them filling up dorms, or satisfying preferences. The Filling Up Dorms strategy begins, predictably, with the first dorm in some predecided order and filling up all its available slots with people who identified it as their first preference; conflicts are decided by some form of random selection process. Those people who do not succeed in getting their first choice are returned to the candidate pool, and the process goes to the next dorm. Many variations on this theme are possible, but that's the basic idea. The Satisfying Preferences strategy begins by looking at the people's various preferences and trying to best accommodate those in the available residence spaces. It is important, for both strategies, to have quantitative means to decide which of two competing results is the better one. </p>
<p>The Filling Up Dorms (by lottery and then preference) strategy has the virtue of being relatively straight forward and computationally light. (There is some evidence that this method resides in the current black box.) But it has the drawback of compounding lottery losses by the unlucky, making the unlucky increasing unlucky, and widening the disparity between those who are lucky early and those who are unlucky late. This is less fair than certain alternatives. </p>
<p>The Satisfying Preferences strategy seems the more logical approach, given the lottery's goals, anyhow. It has the virtue of being more fair than the FIlling Up Dorms strategy -- it is unlikely to compound lottery losses -- and it is flexible enough to accommodate the sorts of tweaks and changes that Denise needs to be able to make (during the actual running of the Housing Selection Lottery and for the execution of the other lotteries, the Orientation Adjustment Lottery and the spring and fall lotteries). The Filling Up Dorms approach could also satisfy these requirements, but with greater rewriting and at some cost, once again, to its fairness. The Satisfying Preferences strategy is, however, more complicated and computationally heavy than some of its rivals. </p>
<p>One Preference Satisfying approach is to use a monte carlo style algorithm to arrive at some equilibrium state which can be tweaked depending on how the algorithm is weighted. In the summer, the weighting -- say, whether to maximize 1st and 2nd choices, or to minimize 5th and 6th choices, or whatever -- can be fiddled with between runs in order to produce the best result. (How exactly to measure the 'best' result needs a little thought, but at first glance, anyway, a the old preference/value system seems like a good start.) In the Orientation Adjustment Lottery (and the Spring lottery) it makes some sense to maximize on people's 1st and 2nd choices given that, at worst, they ought to be in at least their 4th or 5th choice as a result of the origina Housing Selection Lottery already. "</p>