Unlike other social species, we trust selectively; we choose who we cooperate with. We have exerted evolutionary pressure on each other to to judge well who is worthy of our trust, as well as evolutionary pressure to be (selectively) trustworthy. For more detail, see The biological function of love for non-kin is to gain the trust of people we cannot deceive.

This is not true for our closest primate relatives, so it is an evolutionarily recent phenomenon. We can therefore expect it is not mature and stable across the entire population. I believe this is indeed observable, and propose that most personality disorders are how we perceive people in whom this ability is malfunctioning.

Perso-nality
disor-der
Phenotype (summary)Malfunction of trust cognition
Anti-socialA long-term pattern of manipulating, exploiting, or violating the rights of othersInability or near-inability to care and therefore be trustworthy.
Avoi-dantVery shy; feels inferior a lot; usually avoids people due to fear of rejectionToo low expectation of trust from others.
Bor-der-lineLots of trouble managing emotions; impulsive; uncertain self-image; very troubled relationships.Randomness in computation of trust and trustworthiness.
De-pen-dentOver-dependence on others; may let others treat them badly out of fear of losing the relationship.Too high expectation others will care and therefore be trustworthy.
Hist-rionicDramatic, strong emotions, always wanting attention from others.Too low expectation others will care and therefore be trustworthy.
Nar-cissis-ticLacks empathy, wants to be admired by others, expects special treatment.Too high expectation of trust from others.
Para-noidExtreme fear and distrust of others.Inability or near-inability to trust.
Schiz-oidPrefers to be alone; disinterest in having relationships with others.Understanding trust is too effortful, so often not worth the trouble.

However, depressive, obsessive-compulsive and schizotypal personality disorder do not fit neatly into this frame. I propose these are different things, namely persistent forms of depression, OCD and schizophrenia respectively, that are mild enough not to have been weeded out of the gene pool despite their persistence.

So why consider this hypothesis of the pathogenesis of these disorders? Because it takes eight problems currently considered tied up with personal identy and essentially unsolvable (although talk therapy is sometimes claimed to do some good around the edges) and turns them into deficiencies in a skill that could be learnable and teachable. So this is a set of eight testable predictions. It claims that patients suffering from these eight disorders could be helped through focused training in how to handle trust correctly.

Until we know whether there is any truth to this at all, it is probably too early to know whether eight different trainings are usefully more effective than a general one, or at what age of cognitive development an intervention would be most effective.

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I mean, personality disorders are all about problems in close interpersonal relationships (or lack of interest in such relationships, in schizoid personality disorder), and trust is always really relevant in such relationships, so I think this could be a helpful lens of looking at things. At the same time, I'd be very surprised if you could derive new helpful treatment approaches from this sort of armchair reasoning (even just at the level of hypothesis generation to be subjected to further testing).

Also, some of these seem a bit strained: 

  • Narcissistic personality disorder seems to be more about superiority and entitlement than expecting others to be trusting. And narcissism is correlated with Machiavellianism, where a feature of that is having a cynical worldview (i.e., thinking people in general aren't trustworthy). If I had to frame narcissism in trust terms, I'd maybe say it's an inability to value or appreciate trust?
  • Histrionic personality disorder has a symptom criterion of "considers relationships to be more intimate than they actually are." I guess maybe you could say "since (by your hypothesis) they expect people to not care, once someone cares, a person with histrionic personality disorder is so surprised that they infer that the relationship must be deeper than it is." A bit strained, but maybe can be made to fit.
  • Borderline: I think there's more of pattern to splitting than randomness (e.g., you rarely have splitting in the early honeymoon stage of a relationship), so maybe something like "fluctuating" would fit better. But also, I'm not sure what fluctuates is always about trust. Sure, sometimes splitting manifests in accusing the partner of cheating out of nowhere, but in other cases, the person may feel really annoyed at the partner in a way that isn't related to trust. (Or it could be related to trust, but going in a different direction: they may resent the partner for trusting them because they have such a low view of themselves that anyone who trusts them must be unworthy.)
  • Dependent: To me the two things you write under it seem to be in tension with each other.

Edit:

Because it takes eight problems currently considered tied up with personal identy and essentially unsolvable [...]

I think treatment success probabilities differ between personality disorders. For some, calling them "currently considered essentially unsolvable" seems wrong.

And not sure how much of OCPD is explained by calling it a persistent form of OCD – they seem very different. You'd expect "persistent" to make something worse, but OCPD tends to be less of an issue for the person who has it (but can be difficult for others around them). Also, some symptoms seem to be non-overlapping, like with OCPD I don't think intrusive thoughts play a role (I might be wrong?), whereas intrusive thoughts are a distinct and telling feature of some presentations of OCD.

Unlike other social species, we trust selectively; we choose who we cooperate with...This is not true for our closest primate relatives, so it is an evolutionarily recent phenomenon.

I would like to see some references for this claim. This seems like a big claim which is core to the premise that 'trust' ought to be especially fragile & poorly evolved and so plausibly at the root of many problems, and one that seems to contract animal research I am aware of - even just outside the primates like chimpanzees, you have eg. vampire bats tracking & gradually building up histories of interaction in food sharing & grooming, and many mutualistic interactions (down to 'markets' in plants & microbes).

"The Social Leap" by William von Hippel. He basically says we diverged from chimps when we left the forests for the savannah not only by becoming more cooperative (standard example: sclera that make our focus of attention common knowledge) but also by becoming much more flexible in our social behaviors, cooperating or competing much more dependent on context, over the last six million years.

I have tried and failed to find a short quote in it to paste here. It's a long and occasionally meandering book, much more alike the anthropological than the rationalist literature.

I just want to note here that I think this is an interesting framing. It might also be useful to think about self-trust (trust of oneself to actually do something, trust of one's future self to do what one's past self wants, etc.). I think it's probably also worth seeing what happens if you taboo trust in each of these situations and break down the specific mechanisms that lead to whatever trust is, since that might point the way to interventions that could help with each disorder (or maybe with multiple disorders via the same method!).