Computing global confidence: psychophysical evidence for an integration mechanism Vincent de

2,3 Gardelle ,

1. Division of Psychology, Nanyang Tehcnological University, Singapore 2. Centre d’Économie de la Sorbonne, CNRS UMR 8174, Paris, France 4. Laboratoire des Systèmes Perceptifs, CNRS UMR 8248, Paris, France

Pascal

4,5 Mamassian

3. Paris School of Economics, France 5. Département d’Études Cognitives, École Normale Supérieure, Paris, France

Background

Procedure

Using the forced-choice paradigm on perceptual confidence [1-3], we showed that humans are able to make confidence judgments over multiple trials of perceptual tasks [4]. This provides evidence for the existence of a metacognitive system that computes global confidence.

Question

Metacognitive accuracy

Does this metacognitive system integrate information across multiple perceptual decisions when computing global confidence? If NO… If YES…

A:4

Results: Efficiency & Weighting A or B?

B:4 “Blue” “Red” “Red” “Blue”

“Red” “Red” “Blue” “Blue”

a set of perceptual trials: Prompt another set of trials with Prompt difficulties randomly Set label a different target d’ Set label sampled with relative to Set A & & (e.g., d’ = 2) Set size (s) an expected target d’ Set size (s) (e.g., d’ = 1) Set A’s size = Set B’s size (e.g., = 4)

“A”

Second-order 2IFC confidence judgment: “In which set do you think you have given more correct responses?” “Set A”

Procedure parameters • Set sizes = {1, 2, 4, 8}; 112 judgments in total for each set size • 1 block = 32 judgments; 1 session = 7 blocks; 2 sessions in total (1 per day) • Judgments of different set sizes were randomly interleaved within a block • Confidence judgments: target d’=1 vs target d’=2 (order randomized)

Results: Evidence for Integration Number of perceptual decisions

Stimulus First-order Perceptual task: Orientation discrimination “Does the grating point to the red or the blue regions?” “Blue” Psychophysics parameters • Duration = 200 ms • Michelson contrast = 0.4 • Spatial frequency = 2 cpd • Gabor SD= 1 deg

“Red” Performance calibration In separate calibration sessions, we estimated subject’s psychometric function for this task. Then, in the main experiment, we were able to target specific difficulty levels for different stimuli presentations.

Integration Efficiency: human observers were close to ideal for set size = 2, but efficiency dropped significantly as set size increased. Confidence integration efficiency

Alan L.F.

1 Lee ,

We computed the confidence 2IFC d’ for the ideal integrator for set size s = {2, 4, 8} based on human’s confidence 2IFC d’ as follows: ′ 𝑑𝑖𝑑𝑒𝑎𝑙,𝑠 = 𝑠𝑑 ′ ℎ𝑢𝑚𝑎𝑛,𝑠=1

1

0.5

0

We then computed the confidence integration efficiency E for s = {2, 4, 8} as follows: 2 ′ 𝑑ℎ𝑢𝑚𝑎𝑛,𝑠 𝐸= 2 ′ 𝑑 𝑖𝑑𝑒𝑎𝑙,𝑠 1

2

4

Set size

8

Position-specific weighting of response times: Recency effect If different positions were weighted equally, all the lines would be flat.

s=1

s=2

Set Size (s) s=4

s=8

(n=9) Metacognitive accuracy increased with set size, suggesting that the metacognitive system integrates information over multiple perceptual decisions.

Logistic regression: X’s = RTs of the perceptual trials, Y = confidence choice We plot regression weights over positions in set, which are larger for later positions, suggesting that RTs of later trials may have larger influence on confidence choice.

References [1] Barthelmé & Mamassian (2009) PLoS Comput Biol. [2] Barthelmé & Mamassian (2010) PNAS [3] de Gardelle & Mamassian (2014) Psychol Sci. [4] Lee, de Gardelle, Mamassian (2014) VSS

Efficiency & Weighting Stimulus Results: Evidence for Integration

Question. Does this metacognitive system integrate information ... We then computed the confidence integration efficiency E for s = {2, 4, 8} as follows: = ℎ ,. ′. 2.

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