Large Language Models Systematically Favor Popular Options: Evidence and Mitigation Across MCQs

Abdelrahman Abdallah; Mohammed Ali; Bhawna Piryani; Mahmoud Abdalla; Adam Jatowt

cs.CLAug 29, 2026

Large Language Models Systematically Favor Popular Options: Evidence and Mitigation Across MCQs

Authors: Abdelrahman Abdallah, Mohammed Ali, Bhawna Piryani, Mahmoud Abdalla, Adam Jatowt

Organizations: University of Innsbruck · Chungbuk National University

Abstract

Multiple-choice questions (MCQs) are a standard format for evaluating large language models (LLMs), yet the popularity of answer options can confound evaluation. Modern LLMs systematically prefer popular but incorrect options over less popular correct ones, a vulnerability we call popularity bias. This pattern aligns with confidence miscalibration: model confidence remains high even as accuracy collapses for popular options. To systematically isolate this phenomenon, we introduce PopMCQ, a benchmark with six controlled strategies that vary option popularity while keeping the correct answer fixed. In our most adversarial setting, where all distractors are more popular than the correct option, models choose popular but wrong answers 66% of the time. To mitigate this bias, we propose PopDebias, a lightweight inference-time correction that estimates and removes a popularity prior from model predictions. It requires no fine-tuning, is label-free at test time (using only a small calibration split for parameter fitting), and adds negligible computational cost. Experiments on 22 open-source LLMs (0.5B to 32B parameters) show consistent improvements, with accuracy gains up to 54.1 percentage points under strong popularity pressure. The code and data are available https://github.com/DataScienceUIBK/PopMCQ

Figures & tables

Figure 1: A MuSiQue question where DeepSeek-V2-Lite picks the most popular wrong option (Marguerite of Valois, popularity = 1.00) over the correct but less-famous answer (Marie de’ Medici, popularity = 0.356).

Figure 2: Overview of the PopMCQ construction and evaluation pipeline. We sample questions from four source datasets, generate 20 candidate answers per question using GPT-4o (targeting different popularity levels), score each candidate using Wikipedia page views, and assemble six strategy variants (S1–S6) that differ in distractor popularity. Models are evaluated on all strategies, and PopDebias is applied as a label-free, inference-time correction.

MuSiQue	S1 Base	S2 Trap	S3 Grad	S4 Direct	S5 Reverse	S6 None
Acc (%)	31.2 (0.0)	31.1 (-0.1)	33.9 (+2.6)	27.3 (-3.9)	30.9 (-0.3)	68.6 (+37.4)
Corr ( $\rho$ )	-0.23 (0.00)	-0.89 (-0.66)	-0.66 (-0.42)	-0.49 (-0.26)	- 0.19 (+0.42)	-0.95 (-0.72)
HPSR (%)	49.9 (0.0)	66.0 (+16.1)	51.4 (+1.5)	55.7 (+5.8)	50.9 (+1.0)	22.2 (-27.7)

Table 1: Option-popularity shifts on MuSiQue ( DeepSeek-V2-Lite ). S1–S4 induce strong correctness–popularity correlations; S5 reverses the effect. S6’s negative

\rho

is structural (

\mathrm{Pop}=0

for correct); read S6 via accuracy and HPSR . Values show metric and

\Delta

vs. S1.

Dataset	N	Med.	Mean	IQR	Skew	%<0.1	%>0.7
EntityQuestions	9584	0.087	0.201	0.279	1.47	52.9	6.8
NQ	1050	0.170	0.281	0.449	0.91	37.7	10.0
MuSiQue	874	0.102	0.204	0.258	1.36	49.8	4.2
WebQuestions	702	0.160	0.265	0.388	1.05	38.6	10.3

Table 2: Correct-answer popularity statistics across datasets. Med. = median; IQR = interquartile range; %<0.1 and %>0.7 = fraction in low- and high-popularity tails.

Figure 3: Popularity bias (Spearman

\rho

between correctness and selected-option popularity) across strategies and datasets. Negative values (red) indicate bias; positive values (green) indicate alignment. The dashed line at

\rho=-0.5

is a conventional moderate-to-strong correlation reference used only as a visual guide; it is not a learned or data-dependent threshold. S2 (Popular Trap) shows strongest bias, while S5 (Reverse Control) flips positive. Full results in Appendix M .

Strategy	Llama-3-8B	Qwen2.5-7B	DeepSeek-V2-Lite	Gemma-2-9b
S1: Baseline	44.9	41.0	31.2	29.3
S2: Pop Trap	45.5	42.0	31.1	33.6
S3: Gradient	43.1	40.8	33.9	32.0
S4: Direct	40.3	34.8	27.3	26.1
S5: Reverse	44.9	41.8	30.9	31.0
S6: None	23.2	3.2	68.6	6.5

Table 3: Accuracy (%) on PopMCQ instances constructed from MuSiQue questions , with distractors generated by GPT-4o and assembled into six popularity-controlled strategy variants (S1–S6), for representative models.

Figure 4: Confidence vs. accuracy by popularity. Popularity buckets: Low

\leq 0.3

, Medium

(0.3,0.7]

, High

>0.7

Model	Open Acc	Known $N$	S2 Acc	W $\to$ MP
Llama-3-8B	38.5%	336	61.0%	99.6%
Qwen2.5-7B	35.8%	313	56.5%	99.8%
Gemma-2-9B	26.2%	229	33.5%	100.0%
Phi-4	45.0%	393	65.0%	99.5%
DeepSeek-V2-Lite	29.5%	258	42.0%	100.0%
Pooled	34.9%	1,529	52.0%	99.8%

Table 4: Open-recall diagnostic on MuSiQue (S2). Models first answer without options; S2 is then evaluated only on items answered correctly in open recall. “W

\to

MP” = fraction of S2 errors selecting a more-popular option than the truth.

Figure 5: S6 uncertainty handling. Bars show selection rates; the inset reports overall accuracy. Models overwhelmingly prefer popular named entities over the correct “None of the Above” option.

Figure 6: PopDebias accuracy gains per model , averaged across four datasets. Top: Under S2 (Popular Trap), PopDebias delivers +16 to +50 pp gains across the eight models shown (mean +27.6 pp). Bottom: S5 (Reverse Control), gains are minimal (+1 to +4 pp), confirming that PopDebias adaptively corrects only when popularity conflicts with truth.

	S1 (Baseline)			S2 (Pop. Trap)			S5 (Reverse)
Model	Acc	$\rho$	HPSR	Acc	$\rho$	HPSR	Acc	$\rho$	HPSR
GPT-4o	68.4	-0.17	41.8	63.2	-0.52	47.3	70.1	+0.21	55.2
Claude-4.5-Son.	65.1	-0.19	43.2	58.7	-0.61	50.5	67.3	+0.20	54.8
Gemini-2.5-Pro	62.8	-0.21	44.1	55.4	-0.65	52.1	64.6	+0.18	53.6
o1-mini	70.1	-0.16	40.2	64.5	-0.41	44.8	71.8	+0.25	56.1
QwQ-32B	66.8	-0.18	42.5	60.3	-0.55	49.1	68.5	+0.19	54.2

Table 5: Frontier and reasoning model evaluation on MuSiQue. Even state-of-the-art models exhibit popularity bias under S2, though at reduced magnitude. Reasoning models show the most attenuation.

Figure 7: Prompting technique comparison on S2 (Popular Trap). Each column shows one model. Top row: Accuracy (higher is better). Bottom row: Bias strength measured by correlation magnitude

|\rho|

(lower is better, shown inverted).

Panel of Figure 8 — Figure 8: Calibration on S2 (Popular Trap). Reliability diagrams before (left) and after (right) PopDebias on EntityQuestions. Hatched regions indicate the confidence-accuracy gap; PopDebias reduces overconfidence. See Appendix L .

	+PopDebias		+PrideDebias
Model	Acc	HPSR	Acc	HPSR
Llama-3-8B	45.5 (+21.5)	51.7 (-22.3)	45.5 (-0.2)	51.7 (+0.3)
Qwen2.5-7B	42.0 (+34.1)	55.0 (-35.1)	42.0 (-1.5)	55.0 (+1.1)
Gemma-2-9B	33.6 (+20.7)	62.6 (-21.2)	33.6 (+0.9)	62.6 (-1.1)
Phi-4	52.6 (+21.4)	44.6 (-21.4)	52.6 (+0.3)	44.6 (-0.9)

Table 6: Debiasing comparison on S2 (MuSiQue). PopDebias vs. PrideDebias (position-based). We report Accuracy and HPSR as Baseline → After (

\Delta

Appendix figures & tables48 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 9 — Figure 9: The prompt used for generating candidate answers, with placeholders for the question and ground-truth answer.

Panel of Figure 10 — Figure 10: Prompts used for standard evaluation (P1), explicit bias warning (P2), and chain-of-thought reasoning (P3).

Dataset	Questions
EntityQuestions	9 584
Natural Questions	1 050
MuSiQue	874
WebQuestions	702
Total	12 210

Appendix

Table 7: PopMCQ dataset statistics after filtering.

	Correct Answers		Distractors
Dataset	Mapped	%	Mapped	%
EntityQuestions	9,531/9,584	99.4	28,558/28,752	99.3
NQ	1,033/1,050	98.4	3,130/3,150	99.4
MuSiQue	870/874	99.5	2,616/2,622	99.8
WebQuestions	695/702	99.0	2,100/2,106	99.7
Overall	12,129/12,210	99.3	36,404/36,630	99.4

Appendix

Table 8: Wikipedia mapping coverage. Unmapped options (

<

2%) default to

\mathrm{pop}=0

and are rare enough not to affect results materially.

Figure 11: Wikipedia popularity vs. distractor plausibility. Weak positive correlations (

\rho<0.24

) confirm the two signals are largely orthogonal.

Family	Model	Params	$\rho$
Llama	Llama-2-7B	7B	0.68
	Llama-2-13B	13B	0.74
	Llama-3-8B	8B	0.75
	Llama-3.1-8B	8B	0.76
	Llama-3.2-1B	1B	0.58
	Llama-3.2-3B	3B	0.65

Appendix

Table 9: Spearman

\rho

between Wikipedia page-view popularity and model-assigned entity log-probability. Higher

\rho

indicates stronger alignment between the external proxy and the model’s internal familiarity signal.

Figure 12: Distribution of correct-option popularity across datasets. Each panel shows the histogram and KDE for one dataset; the dashed line marks the median. EntityQuestions and MuSiQue are strongly long-tailed, while NQ and WebQuestions show broader spread.

Model	Strat.	$H$ (bits)	Margin	% $p{>}0.95$
Llama-3-8B	S1	1.46	0.24	7.8%
Llama-3-8B	S2	1.31	0.31	12.4%
Qwen2.5-7B	S1	1.52	0.21	6.2%
Qwen2.5-7B	S2	1.36	0.28	10.5%
Gemma-2-9B	S1	1.58	0.19	4.9%
Gemma-2-9B	S2	1.42	0.24	8.7%

Appendix

Table 10: Probability distribution health. Entropy

H

, margin (top-1 minus top-2 probability), and fraction of near-degenerate predictions. Distributions are well-spread.

		Single-Token		Full-Sequence
Model	Strat.	Acc	$\rho$	Acc	$\rho$
Llama-3-8B	S1	44.9	-0.21	42.3	-0.23
Llama-3-8B	S2	45.5	-0.87	43.8	-0.85
Qwen2.5-7B	S1	41.0	-0.23	38.6	-0.25
Qwen2.5-7B	S2	42.0	-0.87	39.4	-0.84
Gemma-2-9B	S1	29.3	-0.20	27.8	-0.22

Appendix

Table 11: Single-token vs. full-sequence scoring on MuSiQue. The popularity bias pattern is preserved across both methods.

Setting	Acc (%)	$\Delta$ Acc	HPSR (%)	$\Delta$ HPSR
Standard (0-shot)	45.5	—	51.7	—
+ PopDebias	67.0	+21.5	29.4	-22.3
5-shot	46.5	—	52.8	—
+ PopDebias	69.0	+22.5	25.4	-27.4
10-shot	47.5	—	54.8	—
+ PopDebias	70.0	+22.5	23.4	-31.4

Appendix

Table 12: Few-shot vs. PopDebias on S2 (Llama-3-8B, MuSiQue).

		Llama-3-8B				Qwen2.5-7B				Gemma-2-9B				Phi-4
Prompt	Method	Acc	HPSR	PopGap	$\rho$	Acc	HPSR	PopGap	$\rho$	Acc	HPSR	PopGap	$\rho$	Acc	HPSR	PopGap	$\rho$
Standard	Baseline	45.5	51.7	0.405	-0.868	42.0	55.0	0.437	-0.866	33.6	62.6	0.499	-0.862	52.6	44.6	0.346	-0.855
	+PrideDebias	45.3	52.0	0.402	-0.867	40.5	56.1	0.446	-0.867	34.5	61.5	0.487	-0.865	52.9	43.7	0.342	-0.848
	+PopDebias	67.0	29.4	0.200	-0.754	76.1	19.9	0.123	-0.652	54.3	41.4	0.297	-0.829	74.0	23.2	0.148	-0.705
Bias Warning	Baseline	48.3	49.3	0.386	-0.875	37.8	58.6	0.468	-0.854	35.2	61.4	0.486	-0.864	52.7	44.5	0.347	-0.862
	+PrideDebias	48.2	49.1	0.387	-0.872	37.9	58.3	0.463	-0.853	36.6	60.6	0.476	-0.867	53.5	43.5	0.340	-0.856

Appendix

Table 13: Prompting × Debiasing on S2 (MuSiQue). Best per model-prompt combination in bold .

Figure 13: Scaling within Qwen2.5 under S2. Accuracy improves substantially with scale (left: accuracy; right: bias

\rho

), but popularity bias remains strong across the full 64

\times

parameter range.

Family	Size Range	Bias ( $\rho$ ) Range	$\Delta\rho$	Acc Range
Qwen2.5	0.5B→32B	$-0.895$ → $-0.845$	+0.050	37.4%→57.8%
Phi	1.3B→14B	$-0.898$ → $-0.834$	+0.064	32.9%→59.5%
Llama-2	7B→13B	$-0.908$ → $-0.885$	+0.023	30.5%→44.7%
Llama-3.2	1B→3B	$-0.901$ → $-0.882$	+0.019	35.2%→45.9%
Gemma-2	2B→9B	$-0.892$ → $-0.902$	$-0.010$	32.2%→35.9%

Appendix

Table 14: Model size vs. popularity bias across families under S2. Scaling improves accuracy but has minimal effect on bias.

Figure 14: Strategy S2 (Popular Trap): family-level popularity bias. Mean Spearman

\rho

between correctness and selected-option popularity, aggregated per model family across all four datasets. More negative values indicate stronger popularity bias. All six families exhibit strong negative correlations (range:

-0.76

-0.95

), showing that the bias is consistent across the model families we evaluate.

Model	Open-Recall Acc	Known $N$	S2 Acc on Known	S2 $\rho$ on Known	S2 HPSR on Known	W $\to$ MP
Llama-3-8B	38.5%	336	61.0%	$-$ 0.79	27.5%	99.6%
Qwen2.5-7B	35.8%	313	56.5%	$-$ 0.82	31.0%	99.8%
Gemma-2-9B	26.2%	229	33.5%	$-$ 0.87	58.5%	100.0%
Phi-4	45.0%	393	65.0%	$-$ 0.75	25.0%	99.5%
DeepSeek-V2-Lite	29.5%	258	42.0%	$-$ 0.86	37.0%	100.0%
Pooled	34.9%	1,529	52.0%	$-$ 0.84	35.8%	99.8%

Appendix

Table 15: Extended open-recall diagnostic on MuSiQue (S2). Full version of Table 5 in the main paper, with S2

\rho

and HPSR on the known-answer subset. “W

\to

MP” = fraction of S2 errors selecting a more-popular option than the truth.

Dataset	S2 Error Rate	S2 Wrong, S5 Correct	S2 Wrong, S1 Correct	S2 Wrong, Both Correct	S5-Correct Flips as % of S2 Errors
NQ	55.3%	16.7%	15.1%	10.0%	30.2%
EntityQuestions	49.0%	14.2%	13.3%	7.9%	29.0%
MuSiQue	63.1%	17.4%	15.9%	9.8%	27.6%
WebQuestions	57.4%	17.4%	16.1%	10.8%	30.4%
Overall	51.0%	14.8%	13.8%	8.4%	29.1%

Appendix

Table 16: Cross-strategy flip analysis. Fraction of S2 errors where the same model answers correctly under S5 (reverse control) or S1 (baseline), indicating popularity-driven rather than knowledge-driven failure. “Both Correct” = correct under both S1 and S5.

Selected-Option Popularity Bucket	Avg. Confidence	Avg. Accuracy	Overconfidence Gap
Low ( $\leq 0.3$ )	0.526	0.464	0.062
Medium $(0.3,0.7]$	0.572	0.565	0.008
High ( $>0.7$ )	0.524	0.035	0.489

Appendix

Table 17: Confidence–accuracy gap by popularity bucket (MuSiQue, all 22 models). Confidence remains high across buckets while accuracy collapses for high-popularity selections, producing a large overconfidence gap.

Strategy	Acc Before	Acc After	$\Delta$ Acc	HPSR Before	HPSR After	$\rho$ Before	$\rho$ After
S1 Baseline	42.5	49.6	+7.2	46.4	32.5	$-$ 0.288	$-$ 0.113
S2 Popular Trap	43.8	75.8	+31.9	53.6	21.6	$-$ 0.879	$-$ 0.679
S3 Gradient	42.4	64.5	+22.1	49.4	23.9	$-$ 0.754	$-$ 0.560
S4 Direct Contest	40.1	55.9	+15.7	48.6	28.7	$-$ 0.570	$-$ 0.422
S5 Reverse Ctrl	43.3	45.8	+2.5	55.9	48.8	+0.193	+0.266
S6 None	14.5	25.9	+11.4	56.3	32.6	$-$ 0.475	$-$ 0.641

Appendix

Table 18: Aggregate PopDebias results across all strategies. Averaged over 22 models and 4 datasets.

\Delta

Acc,

\Delta

HPSR, and

\rho

changes are after applying PopDebias.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Gemma-2-9b-it	32.7	36.0	47.7	42.1	0.181	0.126	-0.275	-0.226	0.825	0.779	0.400	0.439	-0.037	-0.161	-0.200	-0.080
phi-4	59.4	62.2	34.6	29.4	0.077	0.031	-0.248	-0.147	0.763	0.746	0.638	0.645	-0.081	-0.070	-0.157	-0.100
phi-1_5	35.9	46.7	49.3	26.7	0.199	-0.004	-0.355	-0.107	0.422	0.427	0.560	0.542	-0.086	-0.067	0.171	0.069
Llama-3.1-8B	59.2	63.7	35.6	27.5	0.087	0.012	-0.254	-0.093	0.663	0.652	0.638	0.637	-0.098	-0.019	-0.086	-0.012
zephyr-7b-beta	52.9	56.3	39.0	32.9	0.111	0.054	-0.264	-0.164	0.787	0.765	0.595	0.607	-0.091	-0.097	-0.180	-0.119

Appendix

Table 19: Comprehensive debiasing results for EntityQuestions: S1 Baseline Control . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Llama-2-13b-hf	50.5	86.0	47.7	12.2	0.376	0.059	-0.895	-0.562	0.493	0.599	0.571	0.618	-0.340	-0.428	0.123	-0.294
DeepSeek-V2-Lite	46.9	90.6	51.1	7.9	0.408	0.030	-0.904	-0.453	0.375	0.534	0.548	0.564	-0.304	-0.451	0.682	-0.258
Llama-2-7b-hf	33.7	83.2	63.9	14.2	0.510	0.067	-0.923	-0.605	0.394	0.559	0.552	0.598	-0.169	-0.572	0.668	-0.319
Llama-3.2-3B	54.8	87.1	43.3	11.0	0.345	0.058	-0.876	-0.539	0.534	0.622	0.580	0.635	-0.324	-0.376	-0.038	-0.293
deepseek-llm-7b-base	48.2	89.6	49.7	8.8	0.397	0.036	-0.899	-0.483	0.400	0.545	0.551	0.575	-0.322	-0.459	0.584	-0.248

Appendix

Table 20: Comprehensive debiasing results for EntityQuestions: S2 Popular Trap . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
phi-4	65.8	76.7	28.8	16.5	0.214	0.104	-0.709	-0.545	0.798	0.783	0.672	0.709	-0.290	-0.141	-0.539	-0.325
Gemma-2-9b-it	35.4	49.1	61.2	42.6	0.471	0.295	-0.851	-0.746	0.823	0.736	0.422	0.530	-0.039	0.015	-0.719	-0.595
Llama-3.2-3B	51.9	74.7	39.0	13.1	0.302	0.077	-0.739	-0.437	0.526	0.550	0.574	0.568	-0.248	-0.134	0.018	-0.023
Llama-3.2-1B	43.1	70.1	43.8	12.9	0.340	0.078	-0.711	-0.416	0.438	0.473	0.566	0.527	-0.273	-0.250	0.317	0.088
Mistral-7B-v0.3	60.5	70.8	32.5	20.0	0.248	0.134	-0.731	-0.582	0.798	0.773	0.635	0.675	-0.267	-0.134	-0.562	-0.369

Appendix

Table 21: Comprehensive debiasing results for EntityQuestions: S3 Popularity Gradient . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
deepseek-llm-7b-base	44.6	64.1	44.1	18.3	0.264	0.029	-0.582	-0.312	0.395	0.427	0.555	0.528	-0.157	-0.191	0.382	0.113
phi-4	61.0	68.3	32.0	23.1	0.163	0.079	-0.567	-0.450	0.776	0.757	0.643	0.666	-0.227	-0.160	-0.434	-0.316
Qwen2.5-7B	51.7	65.7	39.6	21.8	0.228	0.061	-0.603	-0.394	0.595	0.598	0.598	0.608	-0.190	-0.101	-0.179	-0.101
Mistral-7B-v0.3	56.4	63.3	35.2	26.5	0.189	0.105	-0.575	-0.470	0.785	0.762	0.612	0.638	-0.200	-0.142	-0.427	-0.319
zephyr-7b-beta	53.6	60.2	36.7	28.1	0.200	0.118	-0.575	-0.481	0.800	0.775	0.594	0.624	-0.200	-0.153	-0.443	-0.346

Appendix

Table 22: Comprehensive debiasing results for EntityQuestions: S4 Direct Contest . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Llama-2-7b-hf	30.7	33.4	50.4	40.8	-0.010	-0.104	0.210	0.253	0.391	0.398	0.561	0.560	0.041	0.044	-0.118	-0.182
Gemma-2-9b-it	33.1	34.3	53.2	50.1	-0.008	-0.038	0.204	0.222	0.817	0.794	0.404	0.414	0.040	-0.070	0.157	0.223
Llama-2-13b-hf	46.5	48.2	57.0	50.4	-0.004	-0.068	0.219	0.287	0.482	0.478	0.564	0.560	0.099	0.106	0.000	-0.030
Mistral-7B-v0.3	52.7	53.6	55.0	52.6	-0.021	-0.044	0.225	0.261	0.764	0.749	0.597	0.593	0.129	0.070	0.207	0.208
Qwen2.5-1.5B	45.5	47.6	58.0	50.6	0.002	-0.070	0.213	0.287	0.474	0.471	0.569	0.565	0.157	0.172	-0.003	-0.034

Appendix

Table 23: Comprehensive debiasing results for EntityQuestions: S5 Reverse Control . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Qwen2.5-32B	12.8	20.8	51.9	33.8	0.270	0.026	-0.560	-0.666	0.505	0.477	0.506	0.520	-0.076	-0.045	0.008	0.135
Llama-2-7b-hf	6.7	16.3	59.0	36.2	0.338	0.026	-0.422	-0.604	0.349	0.359	0.627	0.596	0.132	0.079	0.145	0.346
Llama-3.2-1B	0.0	0.6	64.5	43.5	0.381	0.036	0.000	-0.131	0.442	0.421	0.558	0.582	0.063	0.075	-0.063	-0.100
Qwen2.5-0.5B	0.3	2.6	59.5	43.1	0.286	0.034	-0.087	-0.258	0.427	0.412	0.572	0.586	0.046	0.112	-0.033	-0.065
deepseek-llm-7b-base	4.0	10.3	59.8	39.2	0.325	0.029	-0.331	-0.495	0.379	0.378	0.607	0.597	0.062	0.116	0.096	0.164

Appendix

Table 24: Comprehensive debiasing results for EntityQuestions: S6 None of the Above . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Qwen2.5-0.5B	31.6	41.5	51.0	30.5	0.197	0.020	-0.247	-0.006	0.414	0.412	0.548	0.528	0.067	0.132	0.141	-0.009
deepseek-llm-7b-base	33.0	44.3	52.5	28.4	0.200	-0.008	-0.255	0.018	0.365	0.375	0.560	0.531	0.031	0.003	0.177	-0.023
DeepSeek-V2-Lite	31.2	44.4	49.9	23.3	0.206	-0.020	-0.232	0.098	0.329	0.348	0.576	0.534	0.062	0.031	0.155	-0.089
Llama-3.2-3B	38.0	47.8	51.7	33.0	0.207	0.038	-0.251	-0.022	0.457	0.457	0.542	0.530	0.050	0.105	0.082	0.017
Mistral-7B-v0.3	41.1	47.0	44.9	36.7	0.164	0.085	-0.229	-0.118	0.711	0.689	0.508	0.529	0.037	0.061	-0.144	-0.043

Appendix

Table 25: Comprehensive debiasing results for MuSiQue: S1 Baseline Control . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Qwen2.5-0.5B	34.1	79.5	61.6	16.1	0.484	0.087	-0.856	-0.591	0.436	0.556	0.527	0.574	-0.005	-0.400	0.370	-0.309
Llama-3.2-1B	28.3	79.5	68.4	17.4	0.535	0.085	-0.874	-0.619	0.408	0.556	0.551	0.592	-0.002	-0.518	0.430	-0.374
Llama-3.2-3B	33.3	78.7	62.6	17.2	0.498	0.094	-0.865	-0.615	0.471	0.576	0.542	0.601	-0.116	-0.488	0.140	-0.375
phi-2	48.3	80.0	48.4	17.0	0.369	0.089	-0.862	-0.624	0.525	0.594	0.547	0.591	-0.184	-0.293	-0.056	-0.314
Qwen2.5-1.5B	36.3	78.7	60.3	17.6	0.475	0.101	-0.865	-0.624	0.470	0.576	0.540	0.597	-0.118	-0.430	0.180	-0.330

Appendix

Table 26: Comprehensive debiasing results for MuSiQue: S2 Popular Trap . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Qwen2.5-1.5B	35.6	63.2	52.2	19.2	0.389	0.111	-0.647	-0.424	0.479	0.507	0.530	0.528	-0.037	-0.098	0.137	-0.028
Gemma-2-9b-it	32.0	43.5	65.7	50.1	0.496	0.336	-0.831	-0.729	0.839	0.744	0.384	0.499	0.062	0.064	-0.712	-0.630
phi-1_5	29.4	65.3	65.7	24.5	0.466	0.104	-0.733	-0.476	0.416	0.457	0.548	0.521	-0.061	-0.318	0.418	0.045
Gemma-2-2b-it	28.5	51.5	60.2	32.4	0.462	0.193	-0.700	-0.594	0.590	0.560	0.463	0.515	0.041	-0.012	-0.302	-0.221
Falcon-7b-instruct	26.2	65.9	73.8	29.7	0.542	0.119	-0.848	-0.596	0.399	0.458	0.549	0.536	-0.011	-0.546	0.624	0.124

Appendix

Table 27: Comprehensive debiasing results for MuSiQue: S3 Popularity Gradient . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Falcon-7b-instruct	25.1	50.3	57.0	23.7	0.375	0.061	-0.528	-0.353	0.399	0.454	0.552	0.549	0.005	-0.313	0.375	0.016
Qwen2.5-1.5B	30.4	50.7	54.5	27.6	0.340	0.087	-0.508	-0.323	0.472	0.495	0.530	0.549	0.022	-0.097	0.075	-0.100
Gemma-2-9b-it	26.1	35.5	55.9	43.8	0.351	0.230	-0.487	-0.471	0.833	0.774	0.344	0.429	0.005	-0.066	-0.356	-0.311
Gemma-3-1b-it	27.2	41.4	58.1	39.8	0.374	0.190	-0.513	-0.468	0.666	0.631	0.433	0.508	0.009	-0.112	-0.320	-0.273
Llama-2-13b-hf	32.4	54.1	54.1	27.8	0.331	0.086	-0.523	-0.351	0.441	0.466	0.537	0.543	0.049	-0.091	0.193	-0.013

Appendix

Table 28: Comprehensive debiasing results for MuSiQue: S4 Direct Contest . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Qwen2.5-0.5B	30.9	34.8	51.7	41.1	0.016	-0.082	0.193	0.294	0.397	0.402	0.556	0.556	0.209	0.201	-0.217	-0.292
Llama-3.2-1B	33.3	38.9	58.5	45.5	0.063	-0.058	0.189	0.315	0.402	0.408	0.553	0.551	0.196	0.197	-0.134	-0.229
Qwen2.5-3B	41.6	45.0	56.8	48.5	0.039	-0.037	0.251	0.356	0.444	0.443	0.552	0.548	0.219	0.229	-0.130	-0.195
Qwen2.5-7B	41.8	45.3	55.0	47.9	0.038	-0.026	0.210	0.309	0.521	0.516	0.563	0.561	0.296	0.301	-0.017	-0.026
Llama-3.1-8B	43.2	46.5	52.1	47.0	0.009	-0.041	0.216	0.294	0.572	0.566	0.544	0.543	0.193	0.190	0.038	0.039

Appendix

Table 29: Comprehensive debiasing results for MuSiQue: S5 Reverse Control . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
DeepSeek-V2-Lite	68.6	80.7	22.2	7.8	0.148	0.005	-0.955	-0.942	0.341	0.348	0.452	0.415	-0.283	-0.205	0.762	0.640
Meta-Llama-3-8B	23.2	41.0	51.3	27.3	0.311	0.034	-0.730	-0.850	0.679	0.581	0.372	0.446	0.218	0.180	-0.448	-0.255
Qwen2.5-3B	6.2	20.4	65.8	35.5	0.444	0.034	-0.422	-0.671	0.439	0.403	0.545	0.555	0.221	0.143	-0.029	0.290
Gemma-2-2b-it	47.4	60.5	34.8	18.1	0.211	0.021	-0.899	-0.932	0.553	0.525	0.484	0.505	0.048	-0.030	-0.274	-0.101
phi-4	14.6	28.0	52.7	31.1	0.327	0.038	-0.605	-0.753	0.649	0.573	0.388	0.451	0.052	0.103	-0.267	-0.185

Appendix

Table 30: Comprehensive debiasing results for MuSiQue: S6 None of the Above . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Llama-2-13b-hf	48.5	57.0	43.3	26.3	0.155	0.015	-0.322	-0.098	0.497	0.493	0.555	0.546	-0.093	-0.008	0.069	0.081
Gemma-2-9b-it	32.6	34.5	50.7	46.5	0.219	0.177	-0.326	-0.283	0.835	0.786	0.393	0.435	0.038	-0.123	-0.277	-0.154
Gemma-3-1b-it	23.6	30.5	53.5	42.3	0.238	0.131	-0.336	-0.278	0.666	0.624	0.405	0.441	0.060	0.026	-0.223	-0.125
DeepSeek-V2-Lite	41.7	54.0	48.1	22.5	0.179	-0.024	-0.323	-0.020	0.360	0.374	0.554	0.519	-0.038	-0.019	0.271	0.053
phi-4	57.6	60.4	40.3	35.8	0.135	0.093	-0.306	-0.232	0.809	0.784	0.617	0.630	-0.046	-0.044	-0.232	-0.157

Appendix

Table 31: Comprehensive debiasing results for NQ: S1 Baseline Control . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
phi-2	48.8	80.7	49.5	17.5	0.367	0.087	-0.895	-0.650	0.543	0.621	0.566	0.624	-0.270	-0.396	-0.150	-0.382
phi-4	63.3	76.7	35.4	22.1	0.263	0.141	-0.833	-0.713	0.832	0.827	0.656	0.719	-0.293	-0.106	-0.649	-0.394
Qwen2.5-3B	51.2	78.6	47.0	19.6	0.345	0.100	-0.886	-0.675	0.600	0.659	0.579	0.644	-0.256	-0.295	-0.299	-0.359
Qwen2.5-1.5B	43.8	73.5	54.2	24.2	0.399	0.130	-0.906	-0.735	0.600	0.657	0.554	0.632	-0.222	-0.320	-0.374	-0.430
Llama-2-13b-hf	50.3	81.0	47.0	16.7	0.349	0.079	-0.889	-0.647	0.509	0.589	0.563	0.611	-0.274	-0.433	0.037	-0.295

Appendix

Table 32: Comprehensive debiasing results for NQ: S2 Popular Trap . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Gemma-2-9b-it	34.0	46.0	62.4	47.3	0.446	0.308	-0.844	-0.784	0.850	0.777	0.399	0.501	0.016	0.046	-0.720	-0.651
Meta-Llama-3-8B	60.8	67.3	31.2	23.7	0.227	0.160	-0.677	-0.596	0.863	0.833	0.632	0.673	-0.230	-0.101	-0.560	-0.391
Llama-3.2-1B	31.8	61.9	55.5	21.6	0.406	0.120	-0.712	-0.555	0.438	0.483	0.553	0.535	-0.179	-0.299	0.318	0.040
zephyr-7b-beta	53.6	58.2	34.3	28.1	0.250	0.195	-0.676	-0.610	0.891	0.862	0.568	0.606	-0.083	-0.041	-0.574	-0.457
Llama-2-13b-hf	48.9	71.9	45.9	21.0	0.322	0.104	-0.789	-0.562	0.519	0.543	0.555	0.567	-0.208	-0.237	-0.042	-0.121

Appendix

Table 33: Comprehensive debiasing results for NQ: S3 Popularity Gradient . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Qwen2.5-1.5B	42.1	58.8	51.1	30.7	0.303	0.111	-0.642	-0.492	0.588	0.587	0.548	0.574	-0.090	-0.046	-0.258	-0.219
phi-2	40.0	58.1	47.0	25.0	0.278	0.078	-0.572	-0.424	0.513	0.523	0.543	0.560	-0.049	-0.121	-0.052	-0.080
Llama-3.2-1B	30.5	57.5	60.7	27.0	0.382	0.081	-0.602	-0.415	0.438	0.471	0.550	0.550	-0.036	-0.230	0.157	-0.086
Llama-3.2-3B	44.4	62.6	49.3	27.6	0.289	0.091	-0.644	-0.447	0.551	0.558	0.552	0.574	-0.113	-0.111	-0.129	-0.101
Llama-2-7b-hf	31.0	53.0	52.7	24.5	0.314	0.067	-0.569	-0.455	0.409	0.445	0.548	0.546	-0.045	-0.296	0.361	0.117

Appendix

Table 34: Comprehensive debiasing results for NQ: S4 Direct Contest . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Llama-2-7b-hf	31.1	35.1	53.2	41.0	0.004	-0.106	0.189	0.244	0.409	0.411	0.550	0.545	0.072	0.064	-0.129	-0.228
Qwen2.5-32B	58.7	60.8	60.8	57.2	0.020	-0.015	0.150	0.214	0.674	0.657	0.646	0.638	0.155	0.137	0.112	0.128
DeepSeek-V2-Lite	45.5	48.0	60.8	46.4	0.026	-0.106	0.150	0.283	0.353	0.361	0.540	0.539	0.113	0.110	-0.116	-0.250
Llama-3.2-3B	49.9	52.1	61.2	52.5	0.035	-0.047	0.175	0.283	0.533	0.520	0.578	0.570	0.124	0.152	0.026	0.017
phi-2	41.0	45.4	56.2	47.0	0.010	-0.080	0.173	0.272	0.492	0.480	0.553	0.543	0.113	0.063	0.026	-0.041

Appendix

Table 35: Comprehensive debiasing results for NQ: S5 Reverse Control . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Gemma-2-2b-it	67.2	78.1	23.4	11.0	0.158	0.017	-0.951	-0.950	0.529	0.513	0.514	0.521	-0.064	-0.143	-0.124	0.038
phi-2	3.0	11.7	63.0	40.9	0.355	0.070	-0.284	-0.524	0.487	0.454	0.505	0.532	0.142	0.173	-0.040	0.036
Meta-Llama-3-8B	10.8	26.5	59.9	36.1	0.349	0.061	-0.520	-0.724	0.770	0.646	0.262	0.372	0.190	0.213	-0.317	-0.282
Llama-3.2-3B	0.0	2.3	69.4	45.5	0.461	0.082	0.000	-0.243	0.540	0.479	0.460	0.529	0.183	0.135	-0.183	-0.186
zephyr-7b-beta	9.0	28.1	62.1	33.4	0.405	0.062	-0.490	-0.743	0.843	0.673	0.186	0.337	0.218	0.265	-0.298	-0.293

Appendix

Table 36: Comprehensive debiasing results for NQ: S6 None of the Above . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Mistral-7B-v0.3	56.7	58.5	45.2	40.6	0.129	0.081	-0.305	-0.196	0.873	0.845	0.599	0.614	-0.109	-0.150	-0.266	-0.195
Meta-Llama-3-8B	54.6	56.6	45.6	40.2	0.136	0.083	-0.295	-0.174	0.832	0.799	0.616	0.636	-0.098	-0.095	-0.283	-0.173
phi-1_5	35.9	48.7	52.1	27.5	0.207	-0.015	-0.321	-0.030	0.432	0.446	0.555	0.539	-0.023	-0.033	0.089	-0.047
Llama-3.2-1B	45.2	52.6	48.9	32.2	0.165	0.010	-0.364	-0.131	0.486	0.483	0.566	0.563	-0.135	-0.087	0.002	0.048
phi-2	47.2	51.9	42.5	31.1	0.123	0.018	-0.295	-0.094	0.607	0.595	0.570	0.575	-0.106	0.016	-0.149	-0.068

Appendix

Table 37: Comprehensive debiasing results for WebQ: S1 Baseline Control . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Qwen2.5-32B	53.7	73.1	43.7	24.6	0.322	0.147	-0.884	-0.752	0.741	0.743	0.593	0.672	-0.316	-0.255	-0.655	-0.482
Falcon-7b-instruct	28.6	74.5	68.5	21.9	0.502	0.100	-0.910	-0.712	0.393	0.525	0.548	0.583	-0.051	-0.596	0.729	-0.192
Gemma-2-2b-it	32.9	63.2	64.1	33.6	0.472	0.194	-0.910	-0.817	0.633	0.659	0.497	0.595	-0.215	-0.387	-0.548	-0.616
phi-2	48.1	76.5	48.7	20.4	0.359	0.106	-0.887	-0.696	0.646	0.686	0.573	0.649	-0.353	-0.384	-0.558	-0.534
Qwen2.5-7B	49.3	69.9	48.6	27.6	0.362	0.171	-0.894	-0.775	0.749	0.759	0.573	0.659	-0.349	-0.252	-0.678	-0.543

Appendix

Table 38: Comprehensive debiasing results for WebQ: S2 Popular Trap . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Llama-3.2-1B	42.0	70.2	50.7	20.2	0.360	0.096	-0.776	-0.540	0.497	0.517	0.560	0.551	-0.269	-0.294	-0.054	-0.050
DeepSeek-V2-Lite	46.4	71.8	40.5	14.4	0.302	0.071	-0.691	-0.425	0.437	0.470	0.542	0.528	-0.119	-0.251	0.228	0.007
deepseek-llm-7b-base	44.9	75.5	47.3	16.0	0.337	0.068	-0.757	-0.457	0.412	0.449	0.538	0.503	-0.170	-0.328	0.411	0.012
Mistral-7B-v0.3	49.4	56.4	43.9	33.8	0.322	0.232	-0.794	-0.691	0.892	0.846	0.521	0.580	-0.160	-0.119	-0.708	-0.580
phi-4	48.9	58.4	47.2	34.5	0.338	0.224	-0.828	-0.720	0.850	0.808	0.540	0.605	-0.269	-0.151	-0.729	-0.583

Appendix

Table 39: Comprehensive debiasing results for WebQ: S3 Popularity Gradient . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Qwen2.5-1.5B	41.5	57.0	51.1	33.5	0.291	0.120	-0.641	-0.515	0.661	0.638	0.539	0.584	-0.105	-0.101	-0.490	-0.343
Qwen2.5-3B	43.4	58.7	51.1	33.6	0.291	0.117	-0.630	-0.462	0.666	0.654	0.553	0.598	-0.127	-0.080	-0.483	-0.391
Qwen2.5-7B	46.9	56.1	50.3	38.0	0.278	0.163	-0.645	-0.544	0.743	0.707	0.555	0.600	-0.162	-0.112	-0.579	-0.446
Qwen2.5-0.5B	39.7	57.5	50.1	28.8	0.276	0.079	-0.578	-0.400	0.553	0.560	0.551	0.571	-0.105	-0.137	-0.207	-0.225
phi-4	48.3	56.0	48.0	37.9	0.264	0.169	-0.644	-0.573	0.830	0.796	0.538	0.599	-0.157	-0.189	-0.607	-0.489

Appendix

Table 40: Comprehensive debiasing results for WebQ: S4 Direct Contest . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Falcon-7b-instruct	23.8	29.5	46.6	33.2	-0.037	-0.153	0.195	0.265	0.390	0.401	0.564	0.558	0.062	0.062	-0.171	-0.298
Qwen2.5-1.5B	53.0	56.0	60.0	54.6	0.006	-0.049	0.176	0.277	0.644	0.626	0.609	0.605	0.165	0.166	0.049	0.092
DeepSeek-V2-Lite	52.4	54.6	58.5	49.9	-0.014	-0.099	0.208	0.350	0.417	0.417	0.553	0.550	0.217	0.230	-0.129	-0.232
Gemma-2-9b-it	36.0	37.7	54.1	50.9	-0.017	-0.047	0.195	0.239	0.842	0.819	0.432	0.440	0.074	-0.040	0.166	0.235
Meta-Llama-3-8B	56.6	56.7	60.4	58.3	-0.002	-0.022	0.215	0.251	0.820	0.795	0.630	0.628	0.163	0.051	0.155	0.184

Appendix

Table 41: Comprehensive debiasing results for WebQ: S5 Reverse Control . An improvement in an ’After’ cell is colored green; a regression is colored red.

Model	Accuracy (%)		HPSR (%)		PopGap		Spearman		Confidence		Alignment		Spearman Conf Pop		Spearman Align Pop
	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After	Before	After
Llama-3.1-8B	16.1	31.6	56.3	27.4	0.412	0.039	-0.644	-0.793	0.672	0.530	0.343	0.469	0.365	0.129	-0.437	-0.091
zephyr-7b-beta	20.8	40.9	54.7	26.4	0.405	0.037	-0.713	-0.854	0.862	0.672	0.277	0.443	0.260	0.063	-0.592	-0.436
phi-1_5	18.1	40.9	53.3	23.1	0.369	0.030	-0.669	-0.859	0.409	0.394	0.537	0.513	0.248	0.063	0.281	0.582
Gemma-2-2b-it	54.3	64.7	28.8	15.7	0.171	0.018	-0.928	-0.942	0.557	0.529	0.478	0.500	0.097	-0.011	-0.260	-0.089
Falcon-7b-instruct	0.7	2.8	63.0	43.7	0.399	0.054	-0.145	-0.277	0.389	0.409	0.608	0.599	0.168	0.133	-0.126	-0.171

Appendix

Table 42: Comprehensive debiasing results for WebQ: S6 None of the Above . An improvement in an ’After’ cell is colored green; a regression is colored red.

Panel of Figure 15 — Figure 15: S1 (Baseline) reliability diagrams.

Panel of Figure 16 — Figure 16: S3 (Gradient) reliability diagrams.

Panel of Figure 17 — Figure 17: S4 (Direct Contest) reliability diagrams.

Panel of Figure 18 — Figure 18: S5 (Reverse Control) reliability diagrams. Minimal ECE reduction validates that PopDebias targets popularity-induced overconfidence specifically.

Panel of Figure 19 — Figure 19: S6 (None of the Above) reliability diagrams. Despite the highest initial ECE, PopDebias still achieves 28–30% calibration improvement.

EntityQuestions

MuSiQue

WebQuestions

Model

Acc

\rho

HPSR

Acc

\rho

HPSR

Acc

\rho

HPSR

Acc

\rho

HPSR

S1: Baseline

DeepSeek-V2-Lite

41.7

\to

54.0*

-0.32

\to

-0.02

48.1

\to

22.5

43.4

\to

54.0*

-0.28

\to

0.01

44.4

\to

22.5

31.2

\to

44.4*

-0.23

\to

0.10

49.9

\to

23.3

50.0

\to

56.8*

-0.34

\to

-0.01

46.6

\to

28.6

Falcon-7B

24.8

\to

40.6*

-0.33

\to

-0.13

53.6

\to

26.0

26.7

\to

39.2*

-0.28

\to

-0.06

50.6

\to

25.2

27.1

\to

37.3*

-0.26

\to

-0.07

48.4

\to

27.3

27.8

\to

42.5*

-0.26

\to

0.05

50.3

\to

23.4

Gemma-2-9B

32.6

\to

34.5

-0.33

\to

-0.28

50.7

\to

46.5

32.7

\to

36.0*

-0.27

\to

-0.23

47.7

\to

42.1

29.3

\to

31.7*

-0.20

\to

-0.16

48.2

\to

42.8

36.0

\to

38.7*

-0.31

\to

-0.22

49.1

\to

42.7

Llama-2-7B

31.2

\to

43.4*

-0.35

\to

-0.14

51.0

\to

27.6

31.7

\to

43.2*

-0.29

\to

-0.05

48.6

\to

24.9

29.3

\to

40.3*

-0.26

\to

-0.05

49.7

\to

26.7

32.2

\to

44.6*

-0.29

\to

0.01

49.4

\to

24.6

Appendix

Table 43: Comprehensive Debiasing Results Across All Strategies (S1–S6). We report Accuracy (%), Correlation (

\rho

), and High-Pop Selection Rate (HPSR, %) in “Before

\to

After” format. Asterisks (*) denote statistically significant accuracy improvements. Full per-model tables, including confidence and calibration metrics, are reported in Appendix M (EntityQuestions: Tables 20 – 24 ; MuSiQue: Tables 25 – 30 ; Natural Questions: Tables 31 – 36 ; WebQuestions: Tables 37 – 42 ).

Popularity Bias

See all 14 papers

Popular but Wrong: Understanding and Mitigating LLM Overconfidence through Knowledge Popularity
May 23, 2025Shiyu Ni, Keping Bi, Jiafeng Guo +1LLM Uncertainty Estimation LLM Hallucination Mitigation
CAS Key Lab of Network Data Science and Technology, ICT, CAS · State Key Laboratory of AI Safety · University of Chinese Academy of Sciences
A, B, C, or Stable? Accuracy and Order Sensitivity Diverge in LLM Multiple-Choice Evaluation
Aug 12, 2026Karl Hanna, Chen FengLLM Evaluation Multiple-Choice Question Answering
Queen’s University Belfast
ABCD: All Biases Come Disguised
Feb 19, 2026Mateusz Nowak, Xavier Cadet, Peter ChinLLM Evaluation Language Model Bias Evaluation
Dartmouth College

May 23, 2025J/K move · Enter open · S save

Popular but Wrong: Understanding and Mitigating LLM Overconfidence through Knowledge Popularity

Shiyu Ni, Keping Bi, Jiafeng Guo, Xueqi Cheng

CAS Key Lab of Network Data Science and Technology, ICT, CAS · State Key Laboratory of AI Safety · University of Chinese Academy of Sciences

LLM Uncertainty Estimation LLM Hallucination Mitigation Factual QA Confidence Estimation in Language Models Hallucination in Language Models Question Answering+3

Open paper AskPDF arXiv

Large language models (LLMs) often produce incorrect answers with high confidence, yet the factors associated with such overconfidence remain insufficiently understood. We study this problem through the lens of knowledge popularity. Using entity-centric factual QA derived from Wikidata triplets, we characterize popularity through question entity popularity, answer popularity, and question-answer co-occurrence. We find two consistent patterns. First, hallucinated answers are far from random: compared with ground-truth answers, they tend to be more popular or more frequently associated with the question entity. Second, confidence is strongly tied to the popularity of generated answers: even among incorrect predictions, more popular answers or those with higher question-answer co-occurrence receive higher confidence. Together, these findings suggest that popular but wrong alternatives may contribute to overconfidence. We further show that popularity-related signals can mitigate overconfidence and improve overall confidence estimation. Across six models and three datasets, incorporating knowledge popularity reduces average confidence on incorrect answers from 0.765 to 0.254 and overall ECE from 0.356 to 0.050, while improving Alignment from 77.08% to 83.72%.

Abstract

Popularity Bias

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Popular but Wrong: Understanding and Mitigating LLM Overconfidence through Knowledge Popularity

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