TRACE: Trajectory of Reliance Across Cumulative Experience

A Python implementation of the TRACE model for analysing human reliance on AI in trial-level decision-making datasets.

Naiseh, M. (2026). Reliance as a Trajectory: The TRACE Model of Dynamic Human Reliance on AI. International Journal of Human-Computer Interaction. (Under revision.)

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What is TRACE?

Most reliance studies report aggregate scores — mean RAIR, mean WOA — that discard all temporal information. TRACE treats those aggregates as time-averaged snapshots of an underlying dynamic trajectory and provides tools to recover the trajectory itself.

TRACE represents each person's reliance disposition as a point in a two-dimensional state space defined by:

• F(t) — following tendency (operationalised as RAIR)
• Res(t) — resistance tendency (operationalised as RSR) The model has four components:

Component	What it does
1. Prior [F₀, Res₀]	Starting position, set by algorithm appreciation and domain expertise
2. Update function	Moves the state after each trial, asymmetrically (γ_D > 1)
3. Decision function	Maps the latent state to an observable follow/resist decision
4. Transfer function	Carries the final state forward to the next context

Components 2 and 3 together make TRACE generative: given only a prior and an AI accuracy sequence, the model produces a complete synthetic sequence of decisions.

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Installation

git clone https://github.com/monaiseh/TRACE-RELIANCE.git
cd TRACE-RELIANCE
pip install -e .

Dependencies: numpy, pandas, matplotlib, scipy

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Quick Start

Your dataset needs three columns per trial:

import pandas as pd
import trace
 
# Your data — one row per trial per participant
df = pd.DataFrame({
    "participant_id":    ["P001", "P001", "P001", ...],
    "trial":             [1, 2, 3, ...],
    "ai_recommendation": [1, 1, 0, ...],   # what the AI advised
    "human_decision":    [1, 0, 0, ...],   # what the participant decided
    "ground_truth":      [1, 1, 0, ...],   # the correct answer
})
 
# Step 1: classify trials and compute trajectories
traj_df = trace.compute_trajectories_by_participant(df)
 
# Step 2: compute trajectory statistics
stats_df = trace.compute_stats_by_participant(traj_df)
print(stats_df[["participant_id", "rair_final", "rsr_final",
                "final_quadrant", "asymmetry_ratio"]])
 
# Step 3: visualise
fig, ax = trace.plot_state_space(traj_df, participant_col="participant_id")
fig.savefig("state_space.png", dpi=150, bbox_inches="tight")

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Trial Types

TRACE classifies each trial into one of four types based on AI correctness and human following behaviour:

Type	AI Correct?	Human Followed?	Label	Update
A	Yes	Yes	Appropriate reliance	F += ε·α_A
B	Yes	No	Under-reliance error	F -= ε·α_B, Res += ε·β_B
C	No	No	Appropriate self-reliance	Res += ε·α_C
D	No	Yes	Over-reliance error	F -= ε·γ_D·α_A, Res -= ε·δ_D·α_C

Type D carries two distinctive features: the asymmetric loss-aversion weight γ_D > 1, and cross-dimensional contamination (δ_D > 0) — following wrong AI advice also degrades the capacity to resist.

ε is the expertise scale: ε = 1 for lay users, ε < 1 for domain experts, who update more slowly.

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Decision and Transfer Functions

Component 3 — Decision function. Maps the latent state to a follow probability, decomposed into two signal-detection parameters:

d'(t) = (F(t) + Res(t)) / 2          # discriminability — calibration quality
c(t)  = -(F(t) - Res(t)) / 2 + ctx   # response bias — directional tendency
p     = Φ(d'(t) - c(t))              # Φ = standard normal CDF

High F and high Res gives high discriminability (well-calibrated); low F and low Res gives low discriminability (disengaged). The criterion c(t) captures which direction a person leans, and is modulated by decision confidence, stakes, and presentation format.

Component 4 — Transfer function. Carries reliance across contexts:

R₀_next = λ · R_final + (1 - λ) · P_domain

where λ ∈ [0,1] is moderated by contextual similarity, temporal proximity, and AI system continuity.

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API Reference

Core model (trace.core)

Function	Description
classify_trials(ai, human, gt)	Classify trials into types A–D
trace_update(F, Res, trial_type, params)	Component 2 — one update step
trace_decision(F, Res, context=None)	Component 3 — returns (p_follow, d_prime, c)
generate_decision(F, Res, context, rng)	Sample a binary follow/resist decision
trace_transfer(R_final, P_domain, lam)	Component 4 — initialise the next context
run_full_trace(...)	Full generative model over a trial sequence

Trajectory analysis

Function	Description
compute_trajectories(trial_types)	Running RAIR(t), RSR(t) for one participant
compute_trajectories_by_participant(df)	Apply to a full dataset
compute_trajectory_stats(traj_df)	Trajectory statistics for one participant
compute_stats_by_participant(df)	Apply to a full dataset
get_quadrant(rair, rsr)	Identify state space quadrant

Parameter estimation

Function	Description
estimate_gamma_D(traj_df)	Asymmetry ratio from a trajectory
estimate_lambda(s1_final, s2_initial)	Transfer weight from two-session data
required_trials(p_D)	Minimum session length for a given Type D rate

Trajectory statistics returned

Statistic	Description
rair_final / rsr_final	Final trajectory position
rair_slope / rsr_slope	Linear trend across trials
stabilisation_trial	When the trajectory stopped changing
final_quadrant	appropriate_reliance / over_reliance / under_reliance / disengagement
asymmetry_ratio	Empirical γ_D estimate (expected > 1 for lay users)
alpha_a_hat / alpha_c_hat	Reinforcement rate estimates

Visualisation (trace.plot)

Function	Description
plot_state_space(traj_df)	Trajectories in F–Res state space
plot_trajectories(traj_df)	RAIR(t) and RSR(t) as time series
plot_trial_type_distribution(stats_df)	Bar chart of A/B/C/D counts
plot_asymmetry_ratio(stats_df)	Distribution of γ_D estimates

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Reproducing the Paper's Simulations

python trace_simulation.py

Generates four figures corresponding to Section 4 of the paper:

Output	Content
sim1_anchoring_primacy	P2 — early vs late errors, mean session F
sim2_asymmetric_updating	P1 — asymmetry across γ_D = 1.0 to 2.5
sim3_cross_context_transfer	P4 — carry-over as a function of λ
sim4_parameter_recovery	Recovery at T = 40 plus minimum session length

Note on P3. The selective intervention prediction is deliberately not simulated. Setting γ_D lower and observing that F degrades less restates the update equation rather than testing it; P3 acquires empirical content only when applied to a real intervention whose mechanism is not known in advance. See Section 4.1 of the paper.

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Model Predictions

TRACE generates five testable predictions. The two most directly testable from existing data are:

• P1 (Asymmetric degradation): asymmetry_ratio > 1 for lay users, approaching 1 for domain experts.
• P2 (Sequence primacy): Early Type D errors produce a larger cumulative RAIR deficit than identical errors occurring later, measured as mean session RAIR (the average of RAIR(t) across all trials). Final RAIR may partially converge as the trajectory recovers; the cumulative measure captures time spent in a disrupted reliance state. See examples/trace_example.ipynb for worked code testing both.

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Data Requirements

Ground truth on every trial is required — without it, Types C and D cannot be distinguished.

Minimum session length is design-dependent. Estimating γ_D requires at least 5 Type D events per participant. These occur at rate

p_D = P(AI incorrect) × P(follow)

so the required session length is approximately T ≈ 8 / p_D for 90% participant coverage:

AI accuracy	Follow rate	p_D	Minimum T
70%	70%	0.21	36 (recommend 40)
80%	70%	0.14	~57 (recommend 60)
90%	70%	0.07	~110

Use required_trials(p_D) to compute this for your own design. Studies using highly accurate AI cannot support individual-level γ_D estimation at realistic session lengths, and must either pool across participants or deliberately introduce errors.

Varying AI accuracy within-session is recommended so all four trial types occur. For λ estimation, at least two sessions or tasks per participant are needed.

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Running Tests

pip install pytest
pytest tests/

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Citation

@article{naiseh2026trace,
  title   = {Reliance as a Trajectory: The {TRACE} Model of Dynamic
             Human Reliance on {AI}},
  author  = {Naiseh, Mohammad},
  journal = {International Journal of Human-Computer Interaction},
  year    = {2026},
  note    = {Under revision}
}

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License

MIT License — see LICENSE for details.