grades and size

People do graduate. Also chapters that are below chapter total can take quota additions and can also COB.

Quota additions have nothing to do with chapter size. They are new members added to your bid list in the process of RFM in the bid matching process. If a PNM attends all her pref parties and ranks all her choices, she is guaranteed a bid from one of those choices even if she ends up not being high enough on any of their bid lists. That's what a quota addition is. No one knows who the quota additions are, including the new member herself.

COB is an informal recruitment process that allows chapters to extend bids in order to get them up to total. Total is essentially the average number of members in each chapter. It is reset every year after formal recruitment ends. Some chapters will always be above total because they do a great job of retention and have the higher membership numbers that figure into the equations used to recalculate total. Each year, some chapters are able to add COB bids after total is reset because they fall belowc the new total. Others get to COB a few new members here and there because they lose a few due to things like graduation, quitting, transferring etc. which puts them a few spots under total.

One other thing. Those chapters that start out each year as larger get to take the same quota as everyone else during formal recruitment. So if they continue to have strong member retention, they will continue to be one of the larger chapters.

Yeah but they way they place QA's is based off of a mix of chapter size and how the PNM ranked the houses. If 12 PNMs were cross cut but they all put ABC as number one they're not going to give them all to ABC, they're going to spread them out. It sounds unfair that someone can just pick what house you're going to be in based on need but no one ever knows if it's them so it doesn't matter.

But you're right in that houses don't "take" QA's they just get them

Right, but the PNM's pref chapters are of the same relative strength, which happens frequently in QA/crosscut situations, the PNM will go to her #1 ranked chapter. Or if the PNM only had one option at pref, she gets that one as long as she ranks it.

The point is, every sorority takes the same baseline quota. The OP was claiming differently.

This is not true at all. Larger houses get to take the same quota as everyone else does during formal and also get quota additions assigned to them as part of the RFM process. That is how they stay larger, as long as they do a good job at membership retention.

This is an explanation of what happens in the bid matching process in the RFM system and how quota additions happen when PNMs maximize their options. I lifted this from another school's GR page because it's so good at explaining a very complex process:

It means that you list all the chapters you were invited to a preference party to on the bid card you hand in afterwards. If you were invited to three parties, you list all three in order of your preference. If you were invited to two parties, then you list both parties in order of preference. If you were invited to one party, you list that party. When you list all the parties you were invited to, then you are agreeing that you will accept a bid to any of those sororities. If you do this, you will be guaranteed a bid from one of those sororities (although it may be your second or last choice.)

If you do not list all the parties you went to for preference, if the sorority or sororities you did list do not have you high enough on their bid list, you will not receive a bid from anyone.

Listing all the sororities keeps you in a kind of "holding pool" and makes you eligible for a bid even if one, two or all three of your selections did not list you high enough to get a bid from any of them. If this happens, the computer uses a formula to place you in one of those sororities anyway. So you are guaranteed to receive a bid from one of those sororities if you maximized your options, but you won't have any control over which one you end up in. No one will know you would have ended up bidless if it weren't for maximizing your options.

The only time you shouldn't list all the sororities on your bid card is if you would rather not be Greek at all than belong to that chapter(s).

Alpha chi didn't take quota last year though, and they're still the biggest house. It's super frowned upon but I guess you can do it if you don't care and you trust that your girls won't drop

That's not exactly true. Quota last year was 134 plus 12 sophomores and above, so chapters could take up to 146 but 12 couldn't be freshmen. AXO took at total of 142. They didn't take all the upperclassmen they could have which is totally ok. There are a lot of reasons this can happen. Sometimes it's just a matter of not having enough upperclassmen at your pref parties to fully maximize that separate quota, especially if some of them list someone else as their #1 and match to it. AXO could also have snapped a few more upperclassmen up to that extra quota but they chose not to. PBP and DDD also chose not to fully use this optional quota as well. Not using a couple of extra optional quota spots (upperclassman quota was only 12 last year after all) will not get your total lower by any significant amount. And the point once again is that everyone gets the same quota.