GreyMamba

On the back of the now well-known YouTube video of the 'Gotcha' Jordan Peterson interview by Channel 4s Kathy Newman (https://youtu.be/iEJ1QHu-KEQ), I thought I'd look further into some of ) Peterson's ideas. He seems to be considered a bit of a misogynistic, racist, alt-right apologist by large swathes of the chattering classes but I have to say, having looked at quite a lot of his stuff, I think this is just not entirely accurate - which, I suppose in many eyes, probably makes me a misogynistic, racist, alt-right sympathiser too. Funny, because I don't think that's correct either.

Anyway, one of the things he talks about is the concept that whereas equality of opportunity is good, equality of outcome could be bad. This flies in the face of much of what current liberal thinkers hold dear. But, his arguments are, at least according to him, based on scientific ideas. I thought I'd have a look at some of this.

A couple of months ago a Google engineer (James Damore, just, errr.. Google it :-)) was sacked because he circulated a discussion document where he suggested that it isn't surprising that more of the Google top engineers are male because men have intrinsic personality traits that make them more liable to succeed in a technical world - and, lets be honest, we all know most uber-geeks are male don't we? This is, of course, sacrilege if you think that everyone is equal and Google should obviously have as many girl engineers as boys.

But this is the crux of the matter - if we assume that, for the good of the organisation (or society), we should employ the best suited candidate for the role, then the only way we would get a 50/50 split of male/female operatives would be if there is no difference in any trait that makes the candidate suitable, regardless of sex. We might like to believe that there is no (or very little) differences between traits in men and women (other than the obvious physical ones - and of course the 'fact' that women are much better at 'multi-tasking' than men). My gut feeling is that this belief is probably about right BUT, the kicker is in the 'or very little' modifier. This can - as I hope I'll demonstrate shortly - make a huge difference when we start to look for the very 'best' candidate for a role.

From what I can determine (references later) if we measure any personality traits in men and women, the mean values for each sex appear to be pretty close with a very large overlap. Hence we might think there will, on average, be no real difference in ability. And, around the average that is demonstrably true. However, when we look at the extremes - far from the average where the 'best' exist, the small difference in the 'mean' position of male/female can result in considerable differences in the relative numbers of male/female in this zone. So let's stop hand waving and get to the nitty-gritty.

Psychologist often use 5 measurable personality traits:


Now, just for the sake of argument, let's assume that some form of 'caring' role (doctor, nurse, companion, ...) would ideally be suited to someone with a high Agreeableness score. It sort of doesn't matter if this assumption is correct or not as far as the principle I'm trying to get at is concerned - the only thing that needs to be 'true' is that certain personality traits are useful in specific roles. I really can't prove this so it might be the giant flaw in my argument, but please bear with me and let's crack on.

I tried to find some kind of definitive paper with universal personality trait scores for the 2 sexes but couldn't - it would be nice to do so at some point. However, I did find a number of papers where these traits were measured and I've used these here. These are the data (for Agreeableness) I've extracted.


M F
mean SD mean SD
1 34.22 4.91 35.99 4.83
2 4.291 0.803 4.546 0.762
3 3.89 0.69 4.2 0.63
4 3.37 0.48 3.49 0.51

These values are taken from these articles:

[1] I've lost this reference :-(
[2] H. Saleem, A. Beaudry, and A.-M. Croteau, “Antecedents of computer self-efficacy: A study of the role of personality traits and gender,” Comput. Hum. Behav., vol. 27, no. 5, pp. 1922–1936, Sep. 2011.
[3] M. Vecchione, G. Alessandri, C. Barbaranelli, and G. Caprara, “Gender differences in the Big Five personality development: A longitudinal investigation from late adolescence to emerging adulthood,” Personal. Individ. Differ., vol. 53, no. 6, pp. 740–746, Oct. 2012.
[4] M. Vianello, K. Schnabel, N. Sriram, and B. Nosek, “Gender differences in implicit and explicit personality traits,” Personal. Individ. Differ., vol. 55, no. 8, pp. 994–999, Nov. 2013.

A few observations - In all three, females score higher. The units are, I suppose, arbitrary. There really isn't a huge difference in scores. Do note line 4 - This applies to 20 year olds and of interest is the 'flatter' curve (bigger SD) for females - it has big effect on the results.

So what does this mean? I thought I'd use this protocol to do some sums. Assume the distribution of traits are gaussian (Normal distribution) about the mean. For each of the data rows, look at the relative numbers of female and males in an interval +/- I 'average SD' about an 'average mean' and the same ratio in the extreme 'right' tail of the distribution above 3 SDs from the mean. A bit clunky but should be good enough. I wrote a Python program to do this using 'scipy.norm.cde' package (download the program here). An these are the results:

female/male ratio
Average right tail
1 1.01 2.8
2 1.04 1.7
3 1.06 1.9
4 0.96 4.04

What does this tell us? Well near the mean where most of the population lie there really is no meaningful difference in the personality trait 'agreeableness' for the 'average' male and female. However, if we are looking for the most 'agreeable' persons (3 SDs from the mean) we might expect to find twice as many females (very roughly) as males. So, If a role needed to employ very 'agreeable' people it would be very wrong to expect to see an equal number of men and women - you'd expect to see twice as many women as men.

So, to force an 'equal outcome' (50/50 men/women) would give a sub-optimal mix of people (you'd either need to try twice as hard to recruit men or accept less able men). On the other hand 'equal opportunity' (employ the best candidate) must lead to an unequal outcome.

I guess this isn't really a particularly rigorous analysis but it just might point to an underlying 'truth'. If so then striving for equal outcomes (men only shortlists, positive discrimination, naming and shaming employers etc.) just might lead to a dysfunctional or at least sub-optimal organisation or society. I really don't mean for this to be read as a justification for keeping the status-quo. I just think that we need to be clear about where we are going and why before we start to force changes in our societies.