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.

Under enhanced choice, 25 percent of the spots, or 25 people, will enter the house in the first round. The chance of a student getting his first choice in this round is 25 out of 360 first-choice students, or 6.94 percent. In the second round, 335 people remain who chose Bok House first, and 180 remain who chose Bok House as one of their four.

Therefore, the remaining 75 spaces in Bok House will go by random chance to students in the ratio 335/180 of first-choices. In other words, 65 percent of the remaining Bok House slots will be filled by students who chose it as first-choice. That means 49 more people who chose Bok House first will get in. Your chance of getting in through the second round is 49/335, or 14.6 percent. Finally, one's chances for the two rounds are additive, so if you designated Bok House as a first choice, your total chance of getting into Bok House is 21.5 percent.

This does NOT mean 21.5 percent of the house will be filled with students who chose Bok House first!

As mentioned above, 25 percent of the house is filled by the first round. 75 percent of the house remains to be filled. Of this 75 percent, we said 65 percent will go to those who chose Bok House as a first choice. Therefore, 65 percent of 75 percent of the house, or 48.8 percent of Bok House, will be filled by students who chose it as a first choice in the second round.

IN TOTAL, 48.8 percent plus 25 percent, or 73.8 percent of Bok House will be filled by what people will call a "homogeneous" population, that is, those people who designated Bok House first choice. The remaining 26.2 percent of Bok House will be filled by people who put Bok House down, but not as a first choice.

Sounds terrible.

But let us not forget to compare enhanced choice with the current system, non-ordered choice, and with old system, ordered choice.

Under the current system of non-ordered choice, a person's chance of getting into Bok House is still dependent on how many people designate it as one of their four choices. There are 100 slots available.

Remember, 540 people designated it. Of those, 360 still want Bok House first, even though that desire is hidden by the system. Only 100 people out of 540 people will get into Bok House, or 18.5 percent. Since 360/540, or 66.7 percent of those 18.5 percent will want Bok House as a first choice, your chance of getting Bok House, it if is your first choice, is 12.3 percent.

Remember, the percentage of first-choice people to non-first choice people will be 360/180 as before. Therefore, Bok House will have 66.7 percent people who wanted it first; it will be 66.7 percent "homogeneous."

Consider ordered choice. Assuming 360 people designate Bok House first, your chances of getting in are 100/360. You have a 22.7 percent chance of getting into your first-choice house. Of course, the house will be 100 percent "homogeneous."

FINALLY, consider this comparison. Ordered choice stinks. You have some chance of getting into Bok House if it is a popular house. But the house masters will hate it because they believe, with some apparent credence, that the houses will be too homogeneous. Non-ordered choice stinks, too. You have a miserable chance of getting into Bok House, and the house will not really be that diverse after all.

Enhanced choice is the ideal solution. You raise your chance of getting into your favorite house in this scenario by 9.2 percent, up to 21.5 percent from 12.3 percent.

However, the houses' diversity will not be compromised. In the extreme scenario described above, enhanced choice only raises the final population of people who wanted the house as a first choice by 7.1 percent, up from 66.7 percent to 73.8 percent.

In truth, most real-life scenarios will not be as extreme as they are above, even in immensely popular houses such as Eliot.

Using the same calculations as above, if only one-fourth of the first-years put down Eliot, and of those half designate it as their first choice, Eliot will end up about 60 percent first-choice students, only 10 percent higher than the 50 percent first-choice designators under non-ordered choice. However, enhanced choice would also increase your chances of getting into Eliot House by 7.5 percent.

Less popular houses will be even more diverse, and the different systems do not change this diversity that significantly; however, the few students who actually DO want these houses can get into them by designating them with a first choice.

Blocking groups who don't care which of their four houses they get can still elect not to designate a first choice without hurting their overall chances.

Some students, masters and members of the administration want choice. Some want diversity. Enhanced choice is a sensible, workable and fair compromise; it enhances the chance of getting into the House of Your Dreams without making it the House of Exclusivity. Adam Hertzman '95   Victor Chiu '95   Dunster House U.C. Reps