Man, you really like the Big 5 model
Since you've posted so many threads on it, I think it's worthwhile to explicate the well known problems on interpreting what these "factors" actually represent in terms of psychological traits. And these problems become exponential when you go from merely using the measure as a predictor of some outcome where what the scale measured doesn't actually matter to using it to make claims about how any particular individuals or groups differ in conceptually meaningful psychological traits.
It's critical to keep in mind that their is little scientific validity to the actual conceptual labels given to these factors. They are not grounded in psychological theory, but are just items that happen to cluster together for countless possible reasons, then someone slapped a label on the clusters of correlated items, where the labels sometimes do not even conceptually map onto many of the items in that cluster. Plus, those labels make implausible assumptions that people are trying to and are able to accurately report what they sincerely think, feel, and do. That assumption presumes not only honesty but an ability to have accurate self knowledge about these things.
For example, some items that supposedly measure "Openness" include "I have excellent ideas." "I am quick to understand things." "I am full of ideas." Not only is it questionable how those statements would ever indicate "openness", but those sound like things Trump and most other highly arrogant people would say, including people close-mindedly dogmatic about the possibility that they might be ever be wrong. Likewise there are many other items across the scales that for many people can reflect something other than what the factor label implies.
And those are just the problems in conceptual meaning of the factors, even when people respond honestly to the survey and report what they sincerely feel and think is true about themselves. Even if people are honest, people differ in how self aware they are and whether they have enough accurate knowledge about themselves or the world to give accurate responses to these items. For example, suppose two people are of average intellect as most are, and they are not close mindedly arrogant. However, one person happened to be put into a social context where there were many intelligent or well educated people while the other was put into a context of mostly unintelligent or poorly educated people (doesn't matter whether it's ability or schooling). Even if the two people are objectively equal average intellect and both not particular arrogant and trying to be honest, the person raised around dullards is more likely to think that "are quick to understand ideas", b/c such judgments are relative to who you are around. Similar for many of the items which implicitly depend upon relative social comparisons with other people one has experienced. So, some of the variance in how people respond is just difference in who else happened to be around that person not difference in those persons themselves.
Another whole set of interpretation problems is caused by the fact that a huge % of the items on the survey refer to traits that most people view positively or negatively. Which means that many people will respond not with their sincere belief about themselves, but by giving the response they think makes them look good to other or even just appear to be the kind of person they wish they were rather than actually are.
So, if you have one person who scores high and one person who score low an some items of a factor, what does that mean? The promoters of the Big 5 want us to assume it means that one person has more of the quality indicated by the general factor label they made up. But it could just as likely mean any of the following or any combination of them:
1) They have more of the quality that some items on the factor reflect, but those qualities have nothing to do or even the conceptual opposite of the made-up Factor label (such as close minded arrogance rather than "openness",
2) one person wants to be liked so they lie and the other person doesn't care, so they are honest,
3) They both want to be liked, but they differ in what response they think will make them more likable, 4) They differ in what qualities they personally aspire to (which is different than being liked),
5) They differ in how self aware they are about their own qualities,
6) They don't differ in any psychological way, only in who is in their environment that they are using a reference points to judge where they fall on the scale.
So, all that applies to all uses and applications of the Big 5 Factor, which doesn't change that the items cluster together in factor or that some factors predict other things. It just changes what the factors actually mean conceptually and psychologically and therefore why they might be predicting other things. Because most of these other differences between people that have nothing to do with the factor labels would also correlated with many other things. So, none of the research showing these scales predict things addresses these problems "why?" and "what do the factors mean?"
As for this specific context of trying score the presidents, they didn't event take the BIG 5 measure, rather a group of selected "experts" rated the Presidents on each item. IOW, these results are essentially an opinion poll about the Presidents using a highly selective sample, very few of whom actually knew any of the presidents and none who knew most of the Presidents beyond what those presidents said or did in public, while playing the role of President.
On the one hand this does eliminate the person filling out the survey trying to make themselves look good or not having self awareness. On the other hand it just replaces those problems with the biased subjective opinion of how these 125 "experts" viewed these presidents or want to make these presidents appear to others, compounded by the lack of any accurate knowledge of what the person thought, said or did in their private lives when not playing a role to get elected.
I'm not saying that none of the scores are accurate, just that a priori there is little reason to think they are accurate for any particular case, or at most only reflect the kind of person that president portrayed in office rather than who they sincerely were. Granted, that could be even more interesting, b/c then it would say something about the voters who supported the character that president played.
