The core claims of self-determination theory

The framework gives a single explanation of the previous chapter’s results: expected rewards contingent on completion are readily experienced as control and so weaken autonomy; verbal feedback affirming ability satisfies competence; an unexpected reward neither controls behaviour nor conveys competence, and so has almost no effect.

Additive or multiplicative?

The author’s framework wanted the three needs written as a multiplicative dynamical equation, so that if any one need approached zero, sustained engagement would collapse. It must first be said plainly that this is the author’s modelling assumption. Self-determination theory holds that all three needs are basic and all need satisfying, but it does not specify the functional form in which they combine; published studies mostly examine the needs through correlation or regression, some combining them into a total score, others testing them separately.

# Engagement E and need satisfactions A, C, R (0..1). Functional forms are the AUTHOR'S assumption:
#   additive T = (A + C + R)/3; multiplicative T = (A*C*R)**(1/3);  dE/dt = (T - E)/4 weeks.
# A threat q adds compliance 0.5*q while it lasts and lowers felt autonomy by 0.3*q.
def target(A, C, R, form):
    return (A + C + R) / 3 if form == "add" else (A * C * R) ** (1 / 3)

def run(A, C, R, form, weeks=16, threat=0.0, threat_weeks=0):
    # returns total engagement = autonomous part E (lagged) + compliance 0.5*q (only while q > 0)
    E, T, q = 0.3, 4.0, 0.0
    for w in range(weeks):
        q = threat if w < threat_weeks else 0.0
        a = max(0.0, A - 0.3 * q)
        E += (target(a, C, R, form) - E) / T
    return E + 0.5 * q

print("needs (A, C, R)        | additive E after 16 wk | multiplicative E after 16 wk")
for needs in ((0.7, 0.7, 0.7), (0.9, 0.9, 0.1), (0.9, 0.9, 0.0), (0.4, 0.9, 0.9)):
    print(f"{str(needs):22s} | {run(*needs, 'add'):22.2f} | {run(*needs, 'mul'):29.2f}")
print("gain from raising autonomy 0.4 -> 0.8, at two levels of competence (relatedness 0.8):")
for C in (0.3, 0.9):
    ga = run(0.8, C, 0.8, "add") - run(0.4, C, 0.8, "add")
    gm = run(0.8, C, 0.8, "mul") - run(0.4, C, 0.8, "mul")
    print(f"  competence {C}: additive +{ga:.2f}, multiplicative +{gm:.2f}")
print("threat-based control (q = 0.6) for weeks 1-8, then removed; A = C = R = 0.6, additive:")
for wk in (8, 9, 12, 16):
    th = run(0.6, 0.6, 0.6, "add", weeks=wk, threat=0.6, threat_weeks=8)
    no = run(0.6, 0.6, 0.6, "add", weeks=wk)
    print(f"  week {wk:2d}: with threat {th:.2f}, never threatened {no:.2f}")
# needs (A, C, R)        | additive E after 16 wk | multiplicative E after 16 wk
# (0.7, 0.7, 0.7)        |                   0.70 |                          0.70
# (0.9, 0.9, 0.1)        |                   0.63 |                          0.43
# (0.9, 0.9, 0.0)        |                   0.60 |                          0.00
# (0.4, 0.9, 0.9)        |                   0.73 |                          0.68
# gain from raising autonomy 0.4 -> 0.8, at two levels of competence (relatedness 0.8):
#   competence 0.3: additive +0.13, multiplicative +0.12
#   competence 0.9: additive +0.13, multiplicative +0.17
# threat-based control (q = 0.6) for weeks 1-8, then removed; A = C = R = 0.6, additive:
#   week  8: with threat 0.82, never threatened 0.57
#   week  9: with threat 0.54, never threatened 0.58
#   week 12: with threat 0.57, never threatened 0.59
#   week 16: with threat 0.59, never threatened 0.60

When all three needs are at a middling level (0.7 each), the two versions make exactly the same prediction (0.70); they part when the needs are unbalanced. First, when one need is almost zero: with autonomy and competence at 0.9 and relatedness at 0.1, the additive model gives 0.63 and the multiplicative 0.43; at zero relatedness the multiplicative model’s engagement falls to 0, the additive model’s stays at 0.60. Second, whether the needs interact: in the additive model, raising autonomy from 0.4 to 0.8 adds 0.13 whatever the level of competence; in the multiplicative model the gain is 0.12 when competence is 0.3 and 0.17 when it is 0.9, so the effect of one need depends on the others. This is testable: if the multiplicative version is closer to the truth, regression analyses should find a significant positive interaction term.

The last part of the program shows that under 8 weeks of control by threat, engagement in week 8 (0.82) exceeds that of someone never threatened (0.57), but is mostly compliance; once the threat is removed it drops in week 9 to 0.54, below the never-threatened 0.58. This follows directly from the model’s assumption (threat lowers felt autonomy) and is not independent evidence, but it gives a shape worth testing: controlling measures may have a negative effect once withdrawn.

Team design: evidence and limits

The author’s framework wanted to replace controlling punishment with “autonomous choice + competence feedback + peer connection”. Here is the main evidence for that direction, and its limits.

Together these support a cautious conclusion: in work and health settings, autonomy support goes with better quality of motivation and better outcomes, and interventions based on self-determination theory have small-to-medium effects. But there are limits. First, the workplace evidence is mainly cross-sectional correlation, and “autonomy support produces good results” and “well-performing teams are more readily given autonomy” would produce the same correlation. Second, intervention effects are mostly small to medium, and outcomes mostly self-reported. Third, “removing punishment” is not “removing structure”: clear goals, timely feedback and necessary rules are themselves part of the need for competence. Autonomy support is not laissez-faire.

Chapter summary

Self-determination theory holds that how an external event affects intrinsic motivation depends on whether it is controlling or informational, and behind this lie three basic psychological needs: autonomy, competence and relatedness. The theory does not specify how the needs combine; the author’s multiplicative version is a modelling assumption that makes different predictions from an additive version when the needs are unbalanced, and the most direct test is the interaction between needs. Evidence from workplaces and health supports a link between autonomy support and better quality of motivation, but it is mainly correlational and intervention effects are small to medium. The next chapter discusses an extreme form of intrinsic motivation: flow.