Tautology implies that the definition we give is redundant, but none of these things were defined in this way. This is because none of the research relies on this kind of dictionary definition.

Instead, they literally ask people hundreds of questions of the type:

"To what extent would you consider yourself to be [adjective]?" (0 - 'not at all' to 5 - 'complete')

Then they factor analyze the results to see which adjectives tend to be highly related to each other. Factor analysis builds on correlation to find shared variation among large groups of indicator variables.

So it is related to how people think of the adjectives and what they mean, but it is not the case that we are just lumping definitions together or "saying the same thing in different words" in the way of a tautology. Instead, what we're saying is that "Most of these personality adjectives mostly mean the same thing. Here's the thing they all mostly mean. If humans in all languages have tons of words that mostly mean this common thing, maybe this common thing is significant and worthy of study."

Regarding life satisfaction, the sense that one finds their life satisfactory and "would change nothing" (one of the items in the Satisfaction with Life Scale that was most likely used to measure it) doesn't show up in those other traits in any major way. In fact, to the extent that a description of the self is related to a world-view, belief or other external factor, it will never be a tautology, because a self-view and other-view or world-view will never share a common definition or tautology by virtue of the self-other distinction.

> Then they factor analyze the results to see which adjectives tend to be highly related to each other. Factor analysis builds on correlation to find shared variation among large groups of indicator variables.

The big problem with these results (and god knows I've analysed enough of them) is that the extent that they map to other characteristics measured without surveys is pretty much unknown.

If you want to create a new measure of extraversion, then you use the older methods (i.e. other surveys), and this only really tells you that the new measure correlates with the old.

I vaguely recall Eysenck doing physiological tests for extraversion/introversion which would avoid this problem, but I'm not aware of any more recent research in this area (mind you, I've been out of the field for a decade now).

I suppose they asked 1000s of different questions, each representing a different personality characteristic. After factor analysis, some arbitrary number of factors were found to account for most of the variance. Why did they settle for 5 vs 8 vs 12?

There are a number of metrics that are commonly used to settle on a number of factors to extract. There's some judgment in it to be sure, but you are looking at data-driven phenomena as well like percentage of variance explained, a precipitous drop in new added value, and etc.

Essentially you come to a point where extracting another value isn't explaining much more variance or producing a factor that's meaningful (e.g., two items of conscientiousness with negative wording are the entire new "factor" and only take variance explained from 80% to 82%).

https://www.theanalysisfactor.com/factor-analysis-how-many-f...

Like pretty much every unsupervised learning problem, there is no data which can tell you what N should be. If there was, you could trivially use that measure to convert it to a supervised learning problem.

More generally, all of those metrics are pretty fluffy (the scree plot is probably the best, as it doesn't give you a p-value).

In order to actually do this right, you need multiple studies and CFA, but the standard in the field is to refit your exploratory model as a CFA on the original dataset, which is almost certainly causing overfitting in most cases.

Other models actually did settle for higher numbers of factors, but higher numbers were usually found to have categories that could be reasonably collapsed into one of the Big 5.

Fwiw, my understanding is that most psychologists believe that with further study, these categories will map to actual functioning of the brain and nerve systems. For example, "Neuroticism" will somehow map to the excitability of certain nerve systems and "Agreeableness" will somehow map to functioning of our mirror and mentalizing systems. "Conscientiousness" will map to inhibiting functions, "Openness" will map to approach/flee type emotional functions, and "Extraversion" will map to systems like dopamine release on securing rewards for behavior.

That's a belief that's a long way from being testable though.