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Chapter 1 Internal Working Models: From the Strange Situation to Two Dimensions
Bowlby and Ainsworth
The British psychiatrist John Bowlby proposed that the attachment between an infant and a caregiver is an evolved behavioural system: when threatened, tired or distressed, the infant seeks closeness to the caregiver, who becomes a “safe haven”; once calm, the caregiver becomes a “secure base” from which to explore. Bowlby held that from repeated interactions the child forms internal working models of whether others are available and whether the self is worth caring for, and uses them to anticipate later relationships (Bowlby 1969).
Evidence
The Strange Situation. Ainsworth and colleagues devised a laboratory procedure of about 20 minutes: an infant of about one year, in an unfamiliar room, goes through two brief separations from and reunions with the mother, with a stranger coming and going. The researchers looked above all at the infant’s response at reunion. Most infants were somewhat upset by the separation and at reunion actively sought the mother, were soon comforted and returned to play (secure); some avoided the mother at reunion and seemed unconcerned (avoidant); others both sought closeness and angrily resisted it, and were hard to comfort (ambivalent or resistant). In their Baltimore sample, the mother’s sensitivity to the infant’s signals at home was related to the infant’s classification in the Strange Situation (Ainsworth et al. 1978).
From infants to adults: types or dimensions
Hazan and Shaver carried the idea of attachment over to adult romantic relationships, asking readers to choose which of three descriptions fitted them best, corresponding to secure, avoidant and anxious–ambivalent “styles” (Hazan and Shaver 1987). Bartholomew and Horowitz then proposed a four-category model: according to whether one’s view of the self and of others is positive or negative, people are secure, preoccupied, dismissing or fearful (Bartholomew and Horowitz 1991).
Evidence
Two dimensions. Brennan, Clark and Shaver pooled the 323 items of the adult-attachment self-report measures then available (about 60 subscales), gave them to more than a thousand students, and found that the items fell mainly along two roughly independent dimensions: attachment anxiety (fear of abandonment, need for constant reassurance, high sensitivity to signs of coolness in the relationship) and attachment avoidance (discomfort with closeness and dependence, a preference for handling things alone, pulling away under stress). From this they built the Experiences in Close Relationships scale (ECR), 18 items for each dimension (Brennan et al. 1998). Fraley and colleagues improved the scale with item response theory (Fraley et al. 2000). Fraley and colleagues later tested large samples with taxometric methods and concluded that individual differences in adult attachment fit continuous dimensions better than separate categories (Fraley et al. 2015).
This matters for the whole book. “Anxious type” and “avoidant type” are only shorthand for positions on dimensions, just as “tall” is only a range of height. Cutting continuous scores into four boxes means that people near a boundary are given different labels on two occasions, even though nothing about them has changed.
Calculation
2,000 simulated people, each with true anxiety and avoidance scores, measured by a questionnaire with reliability 0.90. Each scale is cut at its midpoint to make four “styles”; then the same people answer again a few weeks later.
# Attachment as two dimensions, not four boxes. Simulated questionnaire data in the style of the
# ECR (Brennan, Clark & Shaver 1998): each person has true anxiety and avoidance scores; the
# questionnaire measures them with error (reliability about 0.90 per scale). "Styles" are then made
# by cutting each scale at its midpoint (secure = low/low, preoccupied = high anxiety only,
# dismissing = high avoidance only, fearful = high/high). How often does the label change when the
# same people answer again a few weeks later, although nothing about them has changed?
import math, random
rng = random.Random(1)
N, REL = 2000, 0.90
err_sd = math.sqrt((1 - REL) / REL) # error SD relative to true-score SD 1
def label(anx, avo):
return {(0, 0): "secure", (1, 0): "preoccupied", (0, 1): "dismissing", (1, 1): "fearful"}[(anx > 0, avo > 0)]
people = [(rng.gauss(0, 1), rng.gauss(0, 1)) for _ in range(N)]
flips, near, near_flips = 0, 0, 0
counts, a1s, a2s = {}, [], []
for anx, avo in people:
a1, a2 = anx + rng.gauss(0, err_sd), anx + rng.gauss(0, err_sd)
a1s.append(a1); a2s.append(a2)
t1 = label(a1, avo + rng.gauss(0, err_sd))
t2 = label(a2, avo + rng.gauss(0, err_sd))
counts[t1] = counts.get(t1, 0) + 1
if t1 != t2: flips += 1
if min(abs(anx), abs(avo)) < 0.5:
near += 1; near_flips += t1 != t2
print("labels at time 1:", ", ".join(f"{k} {v / N:.0%}" for k, v in sorted(counts.items())))
print(f"same people, same true scores, re-tested: label changes for {flips / N:.0%}")
print(f"among people within 0.5 SD of a cut-off on either scale ({near / N:.0%} of all): {near_flips / near:.0%} change")
def corr(x, y):
mx, my = sum(x) / len(x), sum(y) / len(y)
sxy = sum((a - mx) * (b - my) for a, b in zip(x, y))
return sxy / math.sqrt(sum((a - mx) ** 2 for a in x) * sum((b - my) ** 2 for b in y))
print(f"yet the continuous anxiety score correlates r = {corr(a1s, a2s):.2f} between the two occasions")
# labels at time 1: dismissing 25%, fearful 25%, preoccupied 26%, secure 25%
# same people, same true scores, re-tested: label changes for 26%
# among people within 0.5 SD of a cut-off on either scale (62% of all): 41% change
# yet the continuous anxiety score correlates r = 0.90 between the two occasionsThe continuous score correlates 0.90 between occasions, yet about a quarter of people change “style”; among those within half a standard deviation of either cut-off (more than 60 % of everyone), four in ten change. The people have not changed; the boxes have thrown information away. So when this book speaks of “anxiety” and “avoidance”, it means degree.
Note
Attachment is not a diagnosis. Attachment anxiety and avoidance are dimensions of individual difference in personality and social psychology, not mental disorders. Medicine does have diagnoses related to severe early neglect (reactive attachment disorder, for example), but they have nothing to do with the everyday “I have an anxious attachment style”. Most online “attachment style tests” are not validated scales, and their results should not be used to reach conclusions about oneself or a partner.
Anxiety and avoidance under stress
Evidence
Seeking and giving support under stress. Simpson, Rholes and Nelligan brought dating couples into the laboratory, told the woman she was about to undergo an anxiety-provoking procedure, and video-recorded the couple during five minutes alone in a waiting room. The more avoidant women sought less support from their partner the more anxious they were; the more avoidant men gave less support the more anxious their girlfriend was. More secure people did the opposite: the more anxious, the more they sought support, and the more anxious the partner, the more support they gave (Simpson et al. 1992).
The study shows that avoidance is not “not needing” but a tendency to close the channels of seeking and giving at the very moment they are most needed. Anxiety is the reverse: heightened vigilance to relationship cues and stronger seeking. Reviews of adult attachment research describe anxiety and avoidance as two regulation strategies of the attachment system: anxiety corresponds to “hyperactivation”, avoidance to “deactivation” (Mikulincer and Shaver 2016).
Writing the working model as a prior
The “internal working model” can be put in the language of Bayesian inference: a person has a prior belief about “if I reach out, will the other respond?”, and each interaction supplies new evidence. Cittern, Nolte, Friston and Edalat built a fairly complete computational model of attachment within the active-inference framework, in which an infant’s expectation of the caregiver’s availability is learned from experience and shapes later exploration and seeking (Cittern et al. 2018). A much simpler model below illustrates three possible mechanisms.
Calculation
Write the probability that “the other responds to me” as , and the belief as a beta distribution with mean . Each response adds 1 to ; each missed bid adds to . Three illustrative leanings: secure (prior mean 0.8, , reaches out often); anxious (uncertain prior with mean 0.5, a miss counts double, ); avoidant (prior mean 0.25, rarely reaches out, trying on only a quarter of occasions). All three face the same partner, who responds 80 % of the time.
# Internal working model as a prior belief about a partner's availability. theta = probability that
# the partner responds when one reaches out ("makes a bid"). Belief = Beta(a, b); each bid that is
# answered adds 1 to a, each one that is missed adds w_neg to b. A toy version of the idea, worked
# out far more fully with active inference by Cittern et al. (2018); all parameters illustrative.
# secure-leaning : expects availability (prior mean 0.8), counts misses at face value, bids often
# anxiety-leaning: unsure prior (mean 0.5), a missed bid weighs twice as much (w_neg = 2)
# avoidance-leaning: expects unavailability (prior mean 0.25), and rarely bids, so learns little
# The partner is the same for all three: answers 80 % of bids.
import random
PROFILES = {"secure-leaning": (8, 2, 1.0, 1.0), "anxiety-leaning": (2, 2, 2.0, 1.0),
"avoidance-leaning": (2, 6, 1.0, 0.25)} # a0, b0, weight of a miss, P(bid)
TRUE_P = 0.8
def run(a, b, w_neg, p_bid, n_occasions, rng):
for _ in range(n_occasions):
if rng.random() < p_bid:
if rng.random() < TRUE_P: a += 1
else: b += w_neg
return a / (a + b)
rng = random.Random(3)
print("belief that the partner will respond (true value 0.80), mean over 2,000 simulated histories")
print("profile | start | after 10 occasions | after 50 | after 200")
for name, (a0, b0, w, pb) in PROFILES.items():
row = [sum(run(a0, b0, w, pb, n, rng) for _ in range(2000)) / 2000 for n in (10, 50, 200)]
print(f"{name:18s} | {a0 / (a0 + b0):5.2f} | {row[0]:18.2f} | {row[1]:8.2f} | {row[2]:9.2f}")
# The asymmetric weight does not wash out: with w_neg = 2 the belief settles near
# p / (p + 2(1 - p)) = 0.8 / 1.2 = 0.67, however long the relationship lasts.
print(f"long-run belief with misses counted double: {TRUE_P / (TRUE_P + 2 * (1 - TRUE_P)):.2f}")
# Avoidance learns slowly because it collects little evidence, not because evidence is ignored.
# belief that the partner will respond (true value 0.80), mean over 2,000 simulated histories
# profile | start | after 10 occasions | after 50 | after 200
# secure-leaning | 0.80 | 0.80 | 0.80 | 0.80
# anxiety-leaning | 0.50 | 0.63 | 0.66 | 0.67
# avoidance-leaning | 0.25 | 0.37 | 0.58 | 0.73
# long-run belief with misses counted double: 0.67This toy model shows three different mechanisms. The secure-leaning belief is accurate and stays accurate. The anxiety-leaning belief rises but settles at about 0.67 and never reaches 0.8: not for lack of evidence, but because every miss is counted twice, and the bias does not fade with time. The avoidance-leaning belief starts lowest but eventually approaches the true value; it learns slowly not because it ignores evidence but because it collects little of it.
Hypothesis · not established
Two kinds of “slow learning” (not yet established). Attachment anxiety shows mainly as a weighting bias toward negative evidence; attachment avoidance shows mainly as too little sampling of evidence. Testable prediction: in a repeated “reach out–response” laboratory task (for example a virtual partner who responds with a fixed probability), people higher in anxiety will consistently underestimate the response probability even over many trials; people higher in avoidance will initiate fewer trials, but when required to initiate as many as others their bias will shrink markedly. If the two groups’ biases do not differ after forced sampling, or if the anxious group’s bias vanishes as trials accumulate, the hypothesis is weakened.
Note
Limits of the model. A real working model is not a single number but a whole set of expectations, memories, emotions and strategies about the self, others and relationships; people also hold different models for different relationships (parents, partner, friends). The model above only shows that the “prior” and the “way of updating” are two different things.
Chapter summary
Attachment theory holds that early interactions form internal working models of others’ availability and the self’s worth. Mainstream adult attachment research describes individual differences as two continuous dimensions, anxiety and avoidance; cutting them into types loses information. Under stress, more avoidant people tend to close the channels of seeking and giving support, more anxious people to intensify seeking. Writing the working model as a prior shows that bias can come from the prior itself, from how evidence is weighted, or from collecting too little evidence. The next chapter asks what happens when one person’s “seeking” meets another’s “closing”.
References
Fan, Y. (2026). Computational Attachment Theory and Couple Interaction Dynamics: From Anxious-Avoidant Coupled Oscillators and Gottman's Nonlinear Difference Equations to Updating Early Relational Priors [依恋理论的计算模型与伴侣互动动力学] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23754715 · Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0).