Contrasting Probabilistic and Intentional Accounts of Confidence in Perceptual Decisions

This paper demonstrates that confidence in perceptual decisions does not rely on a single computational mechanism, but rather adapts to task demands, with an intentional architecture better explaining incentivized motion discrimination and a hierarchical probabilistic model better capturing un-incentivized luminance discrimination.

The Gist

The Big Question: How Do We Know What We Know?

Imagine you are taking a multiple-choice test. You circle an answer, and then you have to ask yourself: "How sure am I that this is right?"

Scientists have long debated how your brain answers that second question. There are two main theories:

1. The "Two-Step" Theory (Hierarchical): First, your brain makes a choice (like picking "B"). Then, a separate "manager" in your brain looks at the evidence, checks the clock, and calculates: "Hmm, the evidence was strong, and we decided quickly. I'm 90% sure we got this right."
2. The "One-Step" Theory (Intentional/Flat): Your brain doesn't do two steps. Instead, it has four different "races" happening at the same time. One race is for "Answer A, High Confidence," another is for "Answer A, Low Confidence," and so on. The first one to cross the finish line wins, and that determines your answer and your confidence level instantly.

This paper asks: Which of these two theories is actually how our brains work?

The Experiment: Two Different Games

To find the answer, the researchers made people play two different video games. Both games required making a quick choice and saying how confident they were, but the rules were different.

Game 1: The "High-Stakes" Motion Game

• The Task: Watch a cloud of moving dots and guess if they are moving Left or Right.
• The Twist: You get points for your answers.
  • If you are High Confidence and right, you get +2 points.
  • If you are High Confidence and wrong, you lose -3 points.
  • If you are Low Confidence, the points are smaller (+1 or -1).
• The Result: Because the points were so high for being right, people played very strategically. They only said "High Confidence" when they were absolutely sure.
• The Winner: In this game, the "One-Step" (Flat) theory won. The brain seemed to treat "High Confidence/Left" and "Low Confidence/Left" as four different options competing against each other. It was like a sprint where the fastest runner (the most confident choice) won the race immediately.

Game 2: The "Casual" Brightness Game

• The Task: Look at two patches of light and guess which one is brighter (or darker).
• The Twist: There are no points, no rewards, and no feedback. You just do it.
• The Result: People were less careful. They often said "High Confidence" even when they weren't that sure.
• The Winner: In this game, the "Two-Step" (Hierarchical) theory won. The brain seemed to make the choice first, and then do a quick calculation to decide how confident to feel. It was like making a choice, and then a separate "confidence calculator" turning a dial based on how easy the task felt.

The "Aha!" Moment: Context is King

The most surprising finding is that the brain changes its strategy depending on the situation.

• When there are rewards (Game 1): The brain gets efficient. It runs a single, fast race where "Confidence" is just another part of the decision. It's like a professional athlete who has trained to make the perfect move instantly.
• When there are no rewards (Game 2): The brain gets lazy or cautious. It makes the choice first, then takes a moment to "check its work" before deciding how confident to be. It's like a student taking a practice quiz; they pick an answer, then pause to think, "Yeah, that feels right," before writing it down.

Why Does This Matter?

Think of your brain like a Swiss Army Knife.

• Sometimes, you need the knife (the fast, integrated "One-Step" mode) to cut through a tough problem quickly when the stakes are high.
• Other times, you need the screwdriver (the careful, two-step "Two-Step" mode) to gently adjust something when you aren't in a rush.

The paper proves that confidence isn't just one fixed thing in our brains. It's a flexible tool. Our brains are smart enough to switch between a "fast race" mode and a "slow calculation" mode depending on whether we are being rewarded for being right or just doing a casual task.

Summary

• Old Idea: Confidence is always a second step after a decision.
• New Idea: Confidence can be part of the decision itself, but only when the situation demands it (like when there are rewards).
• Takeaway: The human mind is adaptable. We don't just have one way of thinking; we have different "modes" for different jobs.

Technical Summary

1. Problem Statement

The study addresses a fundamental debate in cognitive neuroscience regarding the computational architecture of metacognitive confidence. Two primary frameworks exist:

• Hierarchical (Probabilistic) Account: Confidence is a second-order process. A primary decision is made first (via evidence accumulation), and a separate metacognitive system subsequently reads out decision variables (e.g., the balance of evidence and response time) to estimate the probability of correctness.
• Intentional (Integrated/Flat) Account: Confidence is a first-order process. Choice and confidence are determined simultaneously through a multidimensional drift-diffusion process where distinct accumulators compete for each possible choice–confidence combination (e.g., "Left-High," "Left-Low," "Right-High," "Right-Low").

The central question is whether the brain utilizes a single, fixed architecture for confidence across all contexts, or if the computational mechanism adapts based on task demands (e.g., incentives, feedback).

2. Methodology

Experimental Tasks

The authors utilized two distinct perceptual decision-making tasks with simultaneous choice and confidence reporting (participants report both in a single motor act):

1. Random-Dots Motion Discrimination Task:

   • Participants: 4 participants.
   • Stimulus: Coherent motion (left/right) with varying strength (0% to 51.2%).
   • Reporting: A robotic handle moved to one of four targets (Left/Right $\times$ High/Low Confidence).
   • Incentives: Confidence was incentivized via an asymmetric payoff structure (e.g., correct high-confidence = +2 pts; incorrect high-confidence = -3 pts). Feedback was provided trial-by-trial.
   • Context: This task encourages strategic optimization of the choice-confidence trade-off.

2. Luminance Discrimination Task:

   • Participants: 4 additional participants.
   • Stimulus: Two patches of vertical bars with varying luminance differences (Choose-Brighter or Choose-Darker variants). Noise was added to individual bars.
   • Reporting: Simultaneous keypress for choice and confidence.
   • Incentives: No incentives or feedback were provided.
   • Context: This represents a standard, unincentivized perceptual judgment.

Computational Models

The authors fitted two competing models to the behavioral data (Choice, Response Time, Confidence):

• Hierarchical Model (BoE - Balance of Evidence):
  • Uses a 2D Correlated Drift-Diffusion Model (DDM) for the primary decision.
  • Confidence is computed post-decision using a 2D confidence map based on the state of the losing accumulator ($x_{loser}$) and decision time ($t$).
  • Assumes a readout mechanism that calculates the posterior probability of being correct.
• Integrated (Flat) Model (RTCON-based):
  • Uses four parallel drift-diffusion processes (races), one for each choice-confidence combination.
  • Evidence is partitioned into four regions by internal criteria.
  • The first accumulator to reach a bound determines the choice, confidence, and response time simultaneously.

Analysis

• Model Fitting: Maximum Likelihood Estimation (using the BADS algorithm) was used to fit both models to single-trial data.
• Model Comparison: Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) were calculated to penalize model complexity and determine the best fit.
• Behavioral Analysis: Mixed-effects regression models analyzed the relationships between stimulus strength, response time, accuracy, and confidence.

3. Key Results

Behavioral Patterns

• General Trends: In both tasks, higher stimulus strength led to higher accuracy and faster response times. High-confidence decisions were generally faster and more accurate than low-confidence ones.
• Critical Divergence:
  • Motion Task (Incentivized): Confidence increased with stimulus strength for both correct and incorrect trials. High-confidence reports were frequent (76%).
  • Luminance Task (Unincentivized): Confidence increased with stimulus strength for correct trials but did not increase for incorrect trials. High-confidence reports were rare (28%).

Model Performance

• Motion Task (Incentivized):
  • The Integrated (Flat) Model provided a superior fit (lower AIC/BIC) for 3 out of 4 participants.
  • It successfully captured the strong positive correlation between confidence and stimulus strength on error trials and the specific relationship between RT and confidence.
  • The Hierarchical model struggled to reproduce the steep increase in confidence on error trials without compromising its fit to response times.
• Luminance Task (Unincentivized):
  • The Hierarchical Model provided a significantly better fit for all participants.
  • The Integrated model failed completely. It could not reproduce the low frequency of high-confidence reports without sacrificing the accuracy of RT predictions. The flat architecture intrinsically links the frequency of a confidence level to its speed/accuracy; it could not explain why participants frequently made slow, low-confidence errors in this task.
• Instruction-Dependent Bias: In the luminance task, a "Positive Evidence Bias" (PEB) was observed where fluctuations in the selected patch influenced confidence more than the unselected patch. This bias depended on the instruction (Choose-Brighter vs. Choose-Darker), suggesting the sensory weighting is flexible, though the core architectural failure of the flat model remained.

4. Key Contributions

1. Context-Dependent Architecture: The study provides empirical evidence that the brain does not rely on a single, universal mechanism for confidence. Instead, the computational strategy shifts:
   • Incentivized/Simultaneous contexts favor an Integrated/Intentional strategy (flat competition).
   • Unincentivized/Standard contexts favor a Hierarchical/Probabilistic strategy (sequential readout).
2. Resolution of the "Flat" vs. "Hierarchical" Debate: The paper demonstrates that neither model is universally superior. The failure of the flat model in the luminance task and the hierarchical model in the motion task highlights that the "correct" architecture depends on task structure (specifically, the presence of incentives and feedback).
3. Neurophysiological Implications: The findings align with recent neurophysiological data (e.g., Vivar-Lazo & Fetsch, 2025) showing that in incentivized tasks, neurons in the Lateral Intraparietal (LIP) cortex encode choice-confidence combinations directly, supporting the integrated model. Conversely, the hierarchical model implies a more complex, sequential neural computation that may be reserved for non-incentivized, passive judgment tasks.
4. Methodological Rigor: By fitting models to the joint likelihood of choice, RT, and confidence (rather than just summary statistics), the authors revealed trade-offs in model parameters that previous studies might have missed.

5. Significance

This work fundamentally challenges the assumption that metacognition is a fixed, second-order process. It suggests that confidence is a flexible cognitive variable that can be implemented as a primary decision variable when the task structure (e.g., reward contingencies) demands it.

• Theoretical Impact: It bridges the gap between "intentional" frameworks (where action and confidence are coupled) and "probabilistic" frameworks (where confidence is an estimate of truth). It suggests the brain optimizes computational cost and accuracy by switching architectures based on external demands.
• Clinical/Practical Relevance: Understanding that confidence mechanisms are adaptable helps explain why confidence deficits (metacognitive impairments) might manifest differently depending on whether a patient is under pressure/incentivized or in a passive state. It also informs the design of AI systems where confidence reporting might need to be decoupled or coupled from decision processes depending on the application's reward structure.

In conclusion, the paper argues that the brain transforms second-order metacognitive evaluations into first-order action competitions when the environment rewards such a strategy, but reverts to hierarchical processing when such incentives are absent.