0x668143c4…385fsent to0xb1038d97…281f·#12,789,252·view on Etherscan
The random number generation in Online Pseudonym Parties relies on that every person submits random entropy, and that every person votes (in a way they cannot predict or control) for the entropy submitted by a random person. This is made possible by that the list of registered people one month (who have pre-committed their entropy, but not yet revealed it) is randomised using the random number generated by the registered people the previous month.
The probability that a candidate gets k points is 1/k! (multiplied by 1/e) i.e., the probability of 2 points is /=2 less than 1 point. The probability of 3 points is /=3 less than 2 points. The probability of 4 points is /=4 less than 3 points. The highest score should on average be the value of k where k!*e is closest to population.
If it is a draw, the person who had the most points first is selected. If the person who won did not reveal a number, it goes to the person with the second highest score.
For example, the highest score with 8*10^9 people, will be 12.7 points. This is not possible to get, so, it will be 12 points, with the occasional 13 point score. It can be calculated that on average 6 people will get 12 points, (1/(12!*e))*(8*10^9) = 6. If the colluders control either of the accounts that hold the "winning votes", they will at best be able to throw their vote as fast as they can (to be the first to get to 12 points), but, without knowing if that value is better than any of the others that will be revealed.