This does NOT matter.
As long as this selection method was NOT known, it does NOT matter.
Nobody knew that the first applicants would be selected. This is why it is called an "ERROR" and not "FRAUD". Consequently, nobody tried to apply first.
The system could have chosen the 2nd 100,000 or last 100,000.
Do you see that as long as nobody knows of this, the selection is still RANDOM?
Applicants applied at RANDOM and a group was chosen. As long as nobody knows the method these applicants are chosen, the selection is still RANDOM.
1- Assume that a program will choose 2 balls out of 10 balls at RANDOM and you ask me to order 10 balls next to each other for this program to choose from.
2- I order 10 balls that I have next to each other.
3- Then the program goes ahead and chooses the first 2.
4- The choice is still RANDOM.
5- I did NOT know that the program would take the first 2 balls. Consequently, I did not put the balls in any specific order.
6- The probability of any of these 2 balls to be chosen is still unchanged.
Nobody knew of the "ERROR" and NOBODY got an unfair advantage.
The program (and error) resulted in a certain group to be chosen. The people in this group are still RANDOM.
The "ERROR" could have made the program choose every 100th applicant. Or the first 50,000 and last 50,000.
All these choices are the internal workings of the BLACKBOX selection program.
As applicants we had no way of knowing this and we could not affect the selection process.
Therefore, the RANDOMNESS is NOT effected.
I think you are mistaking "random selection" to mean "uniformly distributed".
The program took as input ALL applicants and then, according to whatever its internal logic, selected a certain group.
The resulting group is a random selection from among ALL applicants.
The group selected does Not need to be "uniformly distributed" according to their application date & time.
The important point in randomness is that all applicants should have the same chance of being selected.
This was definitely the case, as long as all this was an "error" as declared.
If all this was planned to give someone an advantage over others, then someone could apply at a certain time to increase his/her chance to being selected.
Then only would the selection not be random anymore.
However, in that case it could not be called an "error" anyway.
To reiterate, an "error" indicates that noone knew of the programming details. Therefore noone had an advantage over others.
Consequently, everybody applied without knowledge of being able to manipulating the selection system.
Hence the selection is still RANDOM.
Without knowing how the system would make the selection, would you have been able to gain an unfair advantage? Would you know when or when not to apply?
No, you would not.
As a result the selection was still RANDOM from amongst ALL applicants.
It all comes back to the crucial point which I have repeated many times. As long as noone had any prior knowledge of the details of how the system would behave while selecting the "winners", nobody had an unfair advantage. And as this situation is an "error", this is definitely the case.
Simple question: Without knowing how the system would make its selection, could you have made anything to increase your chances of being selected. Simple Answer: NO.
I believe that cancelling the "winners" based on the statement that this was an unfair and non random selection is wrong.
Let aside human factors, it is wrong even mathematically.
Assume that there are 1000 tiny balls in a toy train which has 10 seperate wagons.
Each wagon has 100 balls in it.
Someone tells you to randomly choose 100 balls.
It is not necessary for you to choose 10 balls from each seperate wagon.
You can randomly choose 50 from some wagons and 5 from others. You only need to make sure you choose 100 balls.
Or you might just randomly pick up a whole wagon...
And you still have chosen 100 random balls.
Nobody new that you would choose this particular wagon.
Noone had any unfair advantage.
The selection has taken into account ALL Wagons and ALL Balls and it is still RANDOM.
In our case the balls are the applications and the wagons correspond to the Application Dates.
Unless you can prove that any one applicant had any chance to manipulate the outcome of he system and gain any unfair advantage, I can not agree to the fact that this selection was not random.
In any case this discussion is probably nothing but a mind game