Many people have misconceptions about the proposed revision to the housing lottery, called "Enhanced Choice." Some of these surfaced in Hillary Anger's editorial of December 4; some have appeared previously in The Crimson.

Because these misunderstandings extend to much of the Harvard community, we feel that we can and should clarify some of these ideas. Using example statistics on housing choice, we wish to show the differences that each system will have on the composition of each house and on a student's choice.

Before proceeding further, we'll briefly summarize the proposed system. Enhanced choice simply adds an additional round to the current system. The first round enables each block to designate one of four houses as their first choice house (FCH).

Up to 25 percent of each house can be filled by individuals in the first round. If a block's first choice has already reached its quota, that block will be set aside until the second round, and the FCH will be returned to the same status as the other three choices.

In the second round, each block will be placed in one of their four choices, exactly as in the current system, except that there are potentially only 75 percent of the spaces in each house remaining.

Finally, if a block was not placed in the first two rounds it will then be randomized into a house that still has space. Students can also elect not to designate a first choice, which does not affect their probability of getting into one of their four choices.

This proposal has been seen as a compromise between the old system of ordered choice, and the current system of non-ordered choice.

But how much of a compromise? Some have said that an individual has between a 42 to 44 percent chance of getting into their first choice house; some have said that 43 percent of each house will be filled by people who put it down as their first choice. Both are incorrect.

Under "enhanced choice," both the chance of a person getting into his/her first-choice house and the percentage of the house that is filled by people who chose it as a first choice depend on two factors: the number of people who put down a particular house as a first choice, and the number of people who put down that house as any one of their four choices.

Because of these two factors, anywhere from zero to 100 percent of a house may ultimately be filled by people who put it down as their first choice.

WHAT?!?

Obviously, we need an example. Try to read through the following explanation, and please be patient with the confusing statistics.

Let us create a fictional scenario involving an enormously popular house and resulting in an unfortunately homogeneous population to illustrate the beauty of enhanced choice. We will call this imaginary house "Bok House" after former president Bok.

Out of an imaginary First-year class of 1620 people, we will say one-third of the students (540 people) put down Bok House. Of these 540, two-thirds (360 people) designate Bok House as their first choice.

Assume there are only 100 places available in Bok House, and that blocking groups are only one person large since individuals cases are easier to understand.