The new board of the Fun-and-Nonsense-Club is to be elected. The voting procedure itself is fairly simple: The club has 24 members, and every pair of (distinct) members announces to the public whether they are close friends or not. Then every member receives one vote for every close friend, and the composition of the board depends on these numbers of votes in a horribly complicated fashion; in our puzzle this luckily is of no concern to us.
In the week before the election, the club hired Professor Halfbrain to carry out an opinion poll. Halfbrain briefly spoke to every pair of club members and asked them whether they are close friends or not. Then he summarized his data and announced his prediction on the number of votes that each club member is going to receive.
Scenario 1: During the poll, all club members answered truthfully to the professor's questions. But once they hear Halfbrain's prediction, they change their mind and decide to have their fun with the professor. They plot up and at the actual election not a single one of Professor Halfbrain's 24 predicted numbers turns out to be correct.
Question 1: Was it just a lucky coincidence that the original (truthful) data allowed the club members to shatter Halfbrain's predictions? Or is there always a way of doing this?
Scenario 2: At the end of his interviewing work with the club members, Professor Halfbrain realized that he had accidentally erased all the collected data. As he could not remember a single number and as he was unwilling to admit his mistake, he decided to simply use 24 random numbers (from the range $0,1,\ldots,23$) in his prediction. Once the club members hear Halfbrain's prediction, they decide to have their fun with the professor. They plot up and at the actual election not a single one of Professor Halfbrain's 24 predicted numbers turns out to be correct.
Question 2: Was it just a lucky coincidence that the club members were able to shatter Halfbrain's random predictions? Or is there always a way of doing this?