*I am using "charisma" here to sum up all of the aspects of force of personality and authority over those evaluating the data.
This thought just came to me now, so I do not think I can explain the reasoning as to why that might be so. I will try any way. It seems possible that the necessity of having to explain to one's peers the reason one made a choice which was unpopular with them might offset the amount which the individual charisma of the candidate (or the candidate's representatives) influenced the decision. The other way in which eliminating the secret ballot would influence the outcome is that it would make it harder to manufacture votes for a particular candidate, since everyone would have some idea how everyone else voted.
The wisdom of crowds works doesn't have anything to do with having experts.
You are right that the wisdom of crowds does not come from having experts. The wisdom of crowds comes from having a lot of people who all have a little bit of knowledge relevant to the subject. Some of that knowledge might be something that you would not necessarily think was relevant, but when applied as a filter on the other knowledge present produces a result much more accurate than an expert on the subject would ever produce.
The results of this study are not new. Back in the lat 70s, early 80s, there was a study which showed that a group of people with no particular expertise on the subject will reach a better decision than an individual expert on the subject as long as certain criteria are met in the group discussion. The most important criteria that needs to be met is that the groups deliberations must be such that the individual charisma of each person must not be allowed to influence the group discussion. My understanding is that they accomplished this by having all of the discussion occur in anonymous text (such as if all of the comments on slashdot were from Anonymous Coward).
Constitution clearly states that the arbiters of what is and what is not constitutional is the supreme court
Actually, the Constitution at NO place states, clearly, or otherwise, that the Supreme Court is the arbiter of what is and is not constitutional. That is a role which the Supreme Court assigned to itself.
I tend to think that it should be, both in this case and in those other cases. All too many people forget that blacks were not forced to sit in the back of the bus because the bus companies wanted it that way. They were forced to sit in the back of the bus because the government passed laws mandating it. There is evidence that if those "Jim Crow" laws had not existed, segregation would have gone away on its own.