Why argument rarely changes deep priors

The models of Chapters 1 and 2 give two reasons. First, a very precise prior needs a great deal of contrary evidence to shift, and an argument usually counts as a single piece of evidence, often given very low precision. Second, under active inference a system need not cancel prediction error by revising its belief; when changing its circumstances is cheaper than changing its view, it changes its circumstances. A person who nods at an argument and then carries on as before is, in this framework, not being inconsistent: the belief has received too little new evidence, and behaviour keeps producing evidence that fits the old belief.

To change a prior, then, what is needed is not more argument but new experience, and specifically experience that the old pattern of behaviour would never have produced. The trouble is that in real life trying a new pattern can be costly: a failed job application, a failed relationship, embarrassment in front of colleagues. The higher the cost, the harder it is to try.

Low-stakes simulation

A sandbox here means a simulated environment with clear rules and limited consequences: role play, tabletop exercises, card games, mock negotiations. Its role can be stated in the language of the previous chapters.

First, it lowers the cost of exploration. In Chapter 4’s bandit, exploration is hard because every pull of a worse machine costs a real loss; when the loss shrinks, exploration becomes cheap.

Second, it lowers ambiguity. Chapter 2’s model showed that the ambiguity term in expected free energy on its own favours actions whose outcomes are more predictable, so in uncertain surroundings people lean toward familiar outcomes, even bad ones. A sandbox with clear rules makes the outcomes of new actions predictable and so removes part of the pressure toward the old action.

Third, it lowers threat. The evidence below suggests that stress and threat make people exploit more and explore less.

The temperature parameter

In reinforcement learning the softmax choice rule controls exploration with an inverse temperature $\beta$: option $i$ is chosen with probability proportional to $\exp(\beta Q_i)$. With small $\beta$ choice is nearly random and exploration is high; with large $\beta$ the currently best-valued option is almost always chosen. The program below makes a simplifying assumption: the greater the threat, the larger $\beta$.

# Threat, inverse temperature and the discovery of a better option (a simplified model).
# Four options. The learner starts with a pessimistic prior: the familiar option is worth 0.5,
# new ones 0.2. In truth option 3 pays 0.8 on average. Choice is softmax with inverse temperature
# beta; the model's assumption is that perceived threat raises beta (more exploitation).
import math, random
TRUE = [0.5, 0.3, 0.4, 0.8]

def run(beta, trials=100, alpha=0.2, seed=0):
    rng = random.Random(seed)
    q = [0.5, 0.2, 0.2, 0.2]
    found = None
    total = 0.0
    for t in range(trials):
        z = [math.exp(beta * v) for v in q]
        u, acc, a = rng.random() * sum(z), 0.0, 0
        for i, zi in enumerate(z):
            acc += zi
            if u <= acc:
                a = i; break
        r = TRUE[a] + rng.gauss(0, 0.2)
        q[a] += alpha * (r - q[a])
        total += TRUE[a]
        if found is None and q[3] > max(q[:3]):
            found = t + 1
    return found, total / trials

print("inverse temperature | discovered within 100 trials | median trials to discovery | mean payoff per trial")
for beta in (2, 5, 10, 20, 40):
    out = [run(beta, seed=s) for s in range(500)]
    res = [o[0] for o in out]
    pay = sum(o[1] for o in out) / len(out)
    hits = sorted(r for r in res if r is not None)
    med = hits[len(hits) // 2] if hits else None
    print(f"{beta:19d} | {len(hits) / len(res):28.0%} | {med if med else '-':>26} | {pay:21.2f}")
# inverse temperature | discovered within 100 trials | median trials to discovery | mean payoff per trial
#                   2 |                         100% |                         13 |                  0.56
#                   5 |                         100% |                         15 |                  0.66
#                  10 |                          98% |                         26 |                  0.68
#                  20 |                          36% |                         56 |                  0.55
#                  40 |                           1% |                         74 |                  0.50

With inverse temperatures from 2 to 10 the better option is found within 100 trials almost every time; at 20 only 36 % of the time, at 40 only 1 %. The last column is a reminder of the other side: the learner with the lowest inverse temperature finds the better option fastest but explores too much, keeps trying options it knows are worse, and earns less on average than a learner with a moderate inverse temperature. In this model the best is not unlimited exploration but thorough exploration in a low-stakes phase, followed by exploitation once good estimates are in hand. That is exactly the sequence a good sandbox can offer: “hot” in the sandbox, “cooler” back in life.

Card-based simulation

In his community courses the author uses a structured card-based simulation: participants draw cards describing situations, roles and constraints, play out the consequences of a decision by the rules, and then discuss in small groups. The author has observed that many participants name their habitual patterns of thought (for example, “I always assume the other person will say no”) more quickly in the simulation than in lectures. This is the author’s observation, not a research finding: there was no control group, the observer knew which activity participants attended, and naming a pattern is not changing it.

Sandboxes can also reinforce old patterns

One risk needs stating. Games and simulations do not automatically produce exploration: participants may treat the sandbox as a contest to win and repeat the safest strategy in it; the facilitator’s judgement and peers’ eyes can make the sandbox threatening again. If failure in the sandbox brings humiliation, it is no longer low-stakes. A good sandbox needs clear rules, limited consequences, acceptance of failure, and concrete steps for carrying discoveries back into real life; whether these conditions are met matters more than which props are used.