Set the bar for admission as you described. Have two options for admissions for those who meet the bar. You can choose one and only one of the two systems per admissions cycle.
Option 1: Lottery. Every student is entered into a drawing.
Option 2: Auction. The highest bidders get admitted.
The proportion of slots available for auction or lottery is the same as the proportion of students choosing auction vs lottery.
This allows the rich to buy their way into the school while keeping the majority of the slots available for everyone without extreme wealth.
Now I know what you are thinking, "why should the rich get to buy their way in?" To which I reply, why not? We only sell a small percentage of the slots, only to otherwise qualified applicants, and only to the highest bidders (meaning they necessarily overpay per the winners curse).
I'd argue that it's not the current system, and also not how the power-brokers who designed the current system want it.
One of the important functions of the current university system is to cherry-pick the smartest, most charismatic, most driven, and most ambitious poor children and give them a seat at the table, indoctrinating them in the ways of the well-to-do and providing them opportunities within polite society. Basically, take anyone who rolled an 18 on one of their D&D attribute scores and make them a lord. By doing this, you decapitate the leadership of any potential revolution. Anyone who has enough charisma, intelligence, ambition to organize the poors into a movement that actually has a chance of success instead has a much easier pathway of going to university, getting a degree and a middle-class job, and enjoying a comfortable existence without the risk of being killed in the revolution. Keep your friends close and your (potential) enemies closer.
Pure lottery admissions doesn't have this property. The biggest threat is that you miss someone talented, who then gets pissed off and overthrows the system. You want to have humans looking over the application packets of everybody, and you want lots of competing admissions departments so that if one of them screws up, that person gets snatched up by another university.
I think the crucial part of OP's proposal is that the number of slots allocated to each system is proportional to the total number of students who have applied for that system. In practice this would mean that most slots would be allocated through lottery, because the bidding game would be too expensive for most.
> Legacy admissions at private universities are not blind auction
Donor admissions. I’ve literally heard Hamptons parents timing pregnancies to not overlap with billionaires’ kids, the theory being a million can buy a seat in an “off” year that would cost far more in an “on.”
Harvard takes about 2,000 kids a year. The Dean's or director's list is about 200 of those [1]. If a few more kids come from families giving tens of millions, that will absolutely reduce the odds of a family giving high hundreds of thousands making the cut.
Set the bar for admission as you described. Have two options for admissions for those who meet the bar. You can choose one and only one of the two systems per admissions cycle.
Option 1: Lottery. Every student is entered into a drawing.
Option 2: Auction. The highest bidders get admitted.
The proportion of slots available for auction or lottery is the same as the proportion of students choosing auction vs lottery.
This allows the rich to buy their way into the school while keeping the majority of the slots available for everyone without extreme wealth.
Now I know what you are thinking, "why should the rich get to buy their way in?" To which I reply, why not? We only sell a small percentage of the slots, only to otherwise qualified applicants, and only to the highest bidders (meaning they necessarily overpay per the winners curse).