Thank you to all of you, including a Mathematics Ph.D., who have educated me on the randomness issue. My initial reaction that the results were not random was based on the unusual skewing of the results and the possibility that the results were manipulated, warranting further investigation. I now see that while the results were not uniform, they are random.
Here is my own simplistic 2 step analysis:
1. Mathematically speaking, these results certainly could have have occurred naturally. As such, the results are random.
2. Even if the results did not occur naturally because of a “computer glitch”, the results are still random because no one in advance knew how to increase one’s chances. Thus there was a level playing field. Example: Lotto – 6 numbers drawn 1-40. Computer glitch causes a drawing in which the 6 numbers drawn are 1-6. But no one knew about it in advance. It would seem to be a strange result, but it is still random because no one knew about the glitch in advance, thus they were unable to modify behavior accordingly (buy tickets with those 6 numbers).
In retrospect, one can always see how to have improved one’s chances. In retrospect, a Lottery never seems random; one can always find a pattern. But the determination of randomness is based on equal probability: whether an individual was able to take advantage in advance, thereby increasing his or her chances. Here the answer is undoubtedly no. There is no evidence of anyone knowing in advance that the results would be skewed in such a manner; there is no evidence of people modifying their behavior to gain an advantage.
There are other reasons that this Lottery was conducted randomly, but as made clear in my May 17th letter to Mr. Donahue, no matter one’s view on the randomness issue, NOTHING could justify destroying the hopes and dreams of 22,000 people who played by the rules, as DOS has done by invalidating these results. NOTHING could justify this decision to break the honored commitment of the US government to these people. NOBODY, not even the non-winners, called for invalidating the 22,000 winning notifications.
There is an appropriate, fair, and reasonable way of going forward in this matter – and that would be to recognize the 22,000 winners and hold a new selection event in which an additional 78-100,000 individuals are selected. To not take this way going forward is an insult to these 22,000 individuals and flatly contravenes American principles of fairness and justice.