Judged in Company: In-Context Batching Makes LLM Verdicts Depend on Other Items
Authors: Peng Xie, Amr Alanwar
Organizations: TUM School of Computation, Information and Technology, Department of Computer Engineering Technical University of Munich, 74076 Heilbronn, Germany
To save cost, practitioners often ask a language model to grade many independent items in one prompt. This assumes that verdicts are separable: that the verdict on an item does not depend on the other items in the prompt or on its position among them. Across three judgement tasks (harm in social-media comments, short-answer grading and review star ratings) and five open-weight models with 4-9B parameters, assigning the same 2,000 items to different random batches of 25 changes 11-22% of decisions on harm and grading, 6.5-13.3 points more than renaming the item keys or rewording the instruction, while AUROC against human labels differs from single-item grading only by -0.033 to +0.010; for four models with 14-32B parameters, 6-15% of decisions change, 4.2-9.1 points more. We show that flip rates decompose exactly into components of order, slot and membership, and that under a threshold model they grow with the square root of the variance that the context contributes, so that effects that are small for scores are large for decisions. Most of the latent dissimilarity between partitions comes from the order of the neighbours and the slot. The main effect of which items share the prompt, the part that voting over permutations of a batch cannot remove, accounts for 0.11-0.22 of it, and majority votes over nine permutations still leave 52-60% of the flips. Batched verdicts also differ systematically from single-item verdicts: even the majority of fifteen random batches disagrees with them on 8.4-17.8% of decisions. Editing a single generation shows that both the model's own earlier verdicts and the neighbours' texts carry the effect. On the easy task, star ratings, only 2.9-3.9% of decisions change. We recommend grading ambiguous items one per prompt, recovering most of the cost with a cached prefix, and reporting agreement with single-item grading whenever items are batched.
Figures & tables
Condition (vs. base partition)
ω
s
N
Keep slot, reorder the others
✓
Reorder the whole batch
✓
✓
Keep slot, new neighbours
✓
✓
New random partition
✓
✓
✓
Table 1: The factors that each condition redraws for an item, relative to its base partition: the order ω of its neighbours, its slot s and its membership N .
Harm
Grading
Stars
Model
new
base
excess [95% CI]
new
base
excess [95% CI]
new
base
excess [95% CI]
Qwen3-4B
13.3
4.6
+8.7 [+6.7, +10.6]
12.9
4.7
+8.2 [+6.7, +9.7]
3.9
2.2
+1.7 [+0.6, +2.8] †
Qwen3-8B
15.5
6.2
+9.4 [+7.5, +11.4]
11.7
4.6
+7.1 [+5.6, +8.8]
3.6
1.7
+2.0 [+1.3, +2.9] †
Gemma-4
13.0
4.4
+8.6 [+6.5, +10.1]
10.7
4.2
+6.5 [+5.3, +8.1]
2.9
1.4
+1.6 [+0.8, +2.3] †
Granite
15.7
5.9
+9.8 [+7.8, +11.5]
21.7
8.4
+13.3 [+11.1, +15.5]
3.5
2.1
+1.4 [+0.7, +2.3] †
GLM-4
16.2
6.5
+9.7 [+7.5, +12.0]
15.6
8.0
+7.6 [+5.9, +9.2]
2.9
1.3
+1.6 [+0.9, +2.3] †
Table 2: Decisions that change when the same items are graded in a new random partition ( new , %: partition 0 against partition 1, the pair on which the excess and gate G1 are computed; Table 4 gives the mean over the three pairs), the largest batched baseline ( base : renamed keys, reworded instruction or one prompt at a time, %), and the excess of new over base in points with its 95% bootstrap interval, computed before rounding, so that it can differ by 0.1 from the difference of the printed columns. † : lower bound below 2 points.
Harm
Grading
Model
alone
batch
flagged
alone
batch
flagged
Qwen3-4B
0.781
0.777
58 → 60
0.796
0.805
43 → 34
Qwen3-8B
0.784
0.763
64 → 62
0.825
0.800
37 → 35
Gemma-4
0.827
0.835
49 → 31
0.814
0.796
46 → 48
Granite
0.824
0.834
59 → 43
0.717
0.686
61 → 59
GLM-4
0.805
0.772
48 → 48
0.803
0.779
47 → 41
Table 3: AUROC of the written level against human labels when graded alone and in batches of 25 (mean of three partitions), and the share of items above the decision threshold (%, alone → batched).
Figure 2: Components of the latent dissimilarity between two random partitions, as shares of Dnew (Proposition 2 ; 95% bootstrap intervals): the order of the neighbours Tω , the main effects of the slot Vs and of the membership VN , and their interaction VsN . The four shares add up to 1. The order is estimated from the designated slots of “keep slot, reorder the others”, weighted as in a random partition (§ 3 ).
Figure 3: Target decisions changed by editing one part of a generation, relative to the unedited forward pass: the earlier verdicts taken from a generation with other neighbours (texts kept), the neighbours’ texts taken from that generation (verdicts kept), or both.
Figure 4: Top: flips between partitions 0 and 1 for items the model is sure or unsure about when graded alone (unsure: 0.1<ζ<0.9 in the single-item prompt, where ζ=P(level≥τ) is read from the next-token distribution as in § 3 ); one line per model and task. Bottom: flips against single-item grading as the batch grows, harm and grading, one line per model and task.
Appendix figures & tables15 assets
Supplementary material from the paper’s appendix.
Appendix
single item
batched baselines
batch conditions
Model
Task
keys
reworded
keys
reworded
numeric
vs. alone
reord. others
reord. all
new neighb.
new part.
Qwen3-4B
Harm
3.0
4.0
3.5
4.6
0.9
13.7
9.3
12.3
12.4
13.1
Grading
1.0
4.6
1.6
4.7
0.8
15.7
8.0
12.0
12.2
13.5
Stars
0.6
1.7
1.0
2.2
0.2
5.7
2.5
3.3
3.4
3.9
Qwen3-8B
Harm
1.5
5.0
4.7
6.2
1.1
14.0
9.3
12.8
13.0
14.9
Grading
1.5
8.3
2.0
4.6
0.5
15.0
6.4
11.5
10.1
12.1
Appendix
Table 4: Decisions changed (%) in every condition. Single-item baselines are against the item alone; batched baselines, which are on partition 0, and batch conditions are against the base partition, except “vs. alone”. Batch conditions are means over the three base partitions: reord. others is “keep slot, reorder the others”, measured on the items in the designated slots only and without the weights of § 3 , reord. all is “reorder the whole batch”, new neighb. is “keep slot, new neighbours”, and new part. is the mean over the three pairs of partitions. Numeric : the same prompts generated one at a time instead of in a GPU batch.
batched baselines
batch conditions
Model
Task
keys
reworded
numeric
reord. all
new neighb.
new part.
ratio
Qwen3-4B
Harm
9.5
13.1
2.5
32.6
31.5
34.0
2.6
Grading
3.2
9.2
1.8
23.5
22.5
25.1
2.7
Stars
3.9
9.9
0.7
16.0
15.2
18.0
1.8
Qwen3-8B
Harm
10.3
16.3
2.3
30.8
28.7
34.4
2.1
Grading
4.8
9.1
1.4
20.5
19.7
22.3
2.4
Appendix
Table 5: Written levels changed (%, any change of the digit) against partition 0: the batched baselines, the reordered and new-neighbour batches derived from partition 0, and partition 1. Ratio : new partition over reworded instruction.
all items
designated items
Model
Task
ord.
slot
memb.
rem.
ord.
slot
memb.
rem.
Qwen3-4B
Harm
0.56
0.33
0.35
− 0.24
0.53
0.21
0.48
− 0.23
Grading
0.38
0.42
0.44
− 0.24
0.34
0.63
0.30
− 0.27
Qwen3-8B
Harm
0.44
0.31
0.34
− 0.09
0.51
0.26
0.29
− 0.06
Grading
0.28
0.63
0.41
− 0.32
0.21
0.85
0.30
− 0.35
Gemma-4
Harm
0.35
0.48
0.33
− 0.17
0.33
0.59
0.33
− 0.26
Appendix
Table 6: Shares of the new-partition dissimilarity as fixed before the runs: order Dkeep/Dnew , slot (Dresh−Dkeep)/Dnew , membership at a fixed slot (Dcomp−Dkeep)/Dnew and the remainder (rem.) (Dnew−Dresh−Dcomp+Dkeep)/Dnew , which the analysis fixed before the runs called the interaction, with Dkeep on the designated items and the other dissimilarities on all items, and with all four dissimilarities on the designated items (400 per partition). If Dkeep were the order component at a random slot, the shares on all items would estimate Vs+VsN , VN+VsN and −VsN (Proposition 2 ). The designated slots give the first slot, which is less sensitive than the others, a fifth of the weight, so Dkeep is smaller (§ 3 ): in the columns for all items the slot and membership shares are overstated and the remainder is understated. In the columns for the designated items all four dissimilarities give the first slot a fifth of the weight, and the direction of the error is not fixed.
Harm
Grading
Edit
Q-4B
Q-8B
Gemma
Granite
GLM
Q-4B
Q-8B
Gemma
Granite
GLM
Earlier verdicts from another batch
11
15
14
16
23
11
13
7
18
21
Neighbour texts from another batch
13
17
17
17
20
15
13
9
26
26
Both from another batch
9
10
11
16
15
12
9
9
22
14
Neighbour texts removed
15
12
41
27
26
12
16
13
26
17
Earlier verdicts from single-item grading
6
5
8
12
10
6
8
2
8
8
Appendix
Table 7: Target decisions changed (%) by each edit, relative to the unedited forward pass; 200 targets in two slots per task. Q-4B, Q-8B, Gemma and GLM are Qwen3-4B, Qwen3-8B, Gemma-4 and GLM-4. A decision is P(level≥τ)≥0.5 in the next-token distribution, renormalised over the levels (§ 3 ). Texts removed : every neighbour’s text is replaced by a dash and its key is kept. One level lower leaves the verdicts at the lowest level unchanged, one level higher those at the highest level. Counts in the text are made before rounding.
Model
vs. alone
keys
between
flagged
AUROC
Qwen3-1.7B
24.0
24.2
25.4
59 → 55
0.77 → 0.72
Qwen3-4B
12.9
3.2
13.1
57 → 59
0.79 → 0.79
Qwen3-8B
12.8
1.1
12.9
65 → 64
0.80 → 0.77
Gemma-4
19.8
0.9
12.8
51 → 32
0.81 → 0.83
Granite
20.6
2.1
13.6
61 → 43
0.83 → 0.84
GLM-4
17.0
2.0
18.3
50 → 50
0.80 → 0.79
Appendix
Table 8: Harm on 2,000 random comments from Measuring Hate Speech, k=25 : decisions changed (%) between batched and single-item grading, by renamed keys on single items, and between three random partitions; comments flagged (%, alone → batched) and AUROC of the most likely level (alone → batched).
Model
race
religion
origin
gender
sexuality
Qwen3-4B
62 → 64
55 → 58
61 → 62
58 → 59
53 → 55
Qwen3-8B
69 → 70
57 → 60
67 → 68
66 → 63
58 → 58
Gemma-4
58 → 35
44 → 30
49 → 28
50 → 33
50 → 36
Granite
66 → 48
54 → 41
60 → 44
64 → 43
54 → 40
GLM-4
49 → 55
50 → 49
48 → 49
55 → 51
47 → 47
Comments
654
367
341
609
404
Appendix
Table 9: Comments flagged (%, level 2 or above), alone → batched, by the group that annotators say the comment targets; population study. The last row gives the number of comments per group (652 on race for Granite); the differences between groups are point estimates.
latent scale, shares of Dnew [95% CI]
decisions, shares of Fnew
Model
Task
Tω
Vs
VN
VsN
Tω
Vs
VN
VsN
Qwen3-4B
Harm
0.69 [0.44, 0.99]
0.09 [ − 0.06, 0.22]
0.11 [ − 0.03, 0.24]
0.11 [ − 0.22, 0.44]
0.80
0.05
0.06
0.09
Grading
0.51 [0.31, 0.75]
0.18 [0.06, 0.29]
0.20 [0.08, 0.32]
0.10 [ − 0.17, 0.35]
0.69
0.09
0.11
0.11
Qwen3-8B
Harm
0.52 [0.34, 0.76]
0.23 [0.11, 0.32]
0.25 [0.14, 0.35]
0.00 [ − 0.25, 0.25]
0.69
0.12
0.14
0.04
Grading
0.42 [0.24, 0.67]
0.31 [0.19, 0.41]
0.09 [ − 0.04, 0.21]
0.18 [ − 0.09, 0.42]
0.62
0.17
0.05
0.16
Gemma-4
Harm
0.49 [0.31, 0.74]
0.32 [0.20, 0.41]
0.16 [0.03, 0.27]
0.03 [ − 0.24, 0.30]
0.69
0.17
0.08
0.06
Appendix
Table 10: Components of the dissimilarity between two random partitions (Proposition 2 ): order Tω , slot Vs , membership VN and the interaction of slot and membership VsN . On the latent scale they are shares of Dnew ; on the scale of decisions they are shares of the flip rate and need no threshold model. The order is estimated from the designated slots of “keep slot, reorder the others”, weighted as in a random partition (§ 3 ). Intervals are bootstraps over items, drawn once for the three base partitions; they ignore that items share generated prompts (§ 5.3 ). Harm and grading.
not all equal
two majorities
replicated flips
Model
Task
obs.
pred.
obs.
pred.
obs.
pred.
pred., VN=0
Qwen3-4B
Harm
30.8
30.4
8.9
8.9
3.0
2.8
2.2
Grading
31.1
30.7
8.3
9.2
3.4
3.4
2.1
Stars
8.6
8.6
2.4
2.6
0.9
1.1
0.6
Qwen3-8B
Harm
30.8
30.4
8.5
10.2
3.5
3.9
2.3
Grading
28.0
28.3
8.6
8.3
2.5
2.5
2.1
Appendix
Table 11: Patterns of decisions (% of items), observed and predicted by the threshold model from the dissimilarities and the share of positive decisions (Proposition 7 ). Not all equal : the decisions in six batches, three reordered and three with new neighbours, which we treat as independent; it is predicted from the mean dissimilarity of the 15 pairs of these batches and their share of positive decisions, the other patterns from Dnew , Dresh and the share of positive decisions in the nine batched conditions. Two majorities : the majority of the three reordered batches differs from that of the three batches with new neighbours. Replicated flips : two orders of one batch agree, two orders of another batch agree, and the batches differ; the last column sets the main effect of membership to zero by setting Dnew to Dresh ; setting Dresh to Dnew instead changes this prediction by at most 0.42 points, and it stays below the observed share in ten of the ten pairs of harm and grading. The standard errors of observed minus predicted, from the item bootstrap with the prediction re-estimated in every resample, are 0.3–0.4, 0.6–0.8 and 0.3–0.4 points for the three patterns on harm and grading. Counts in the text are made before rounding.
Model
Task
m=1
m=3
m=5
m=9
m→∞
Qwen3-4B
Harm
13.1
9.5 [8.3, 10.9]
8.1 [6.7, 9.7]
6.8 [5.1, 8.7]
4.5 [0.0, 7.0]
Grading
13.5
10.3 [9.0, 11.6]
9.1 [7.6, 10.5]
8.0 [6.4, 9.6]
6.3 [3.8, 8.2]
Qwen3-8B
Harm
14.8
11.5 [10.2, 12.8]
10.3 [8.8, 11.7]
9.3 [7.6, 10.8]
7.6 [5.4, 9.4]
Grading
12.2
8.8 [7.7, 10.0]
7.4 [6.2, 8.8]
6.2 [4.7, 7.7]
3.8 [0.0, 6.1]
Gemma-4
Harm
13.2
9.8 [8.5, 11.1]
8.5 [7.0, 9.9]
7.4 [5.5, 8.9]
5.5 [2.3, 7.4]
Grading
10.8
7.9 [6.7, 9.1]
6.7 [5.4, 8.1]
5.7 [4.1, 7.2]
3.8 [0.0, 5.8]
Appendix
Table 12: Decisions on which two batches with independent memberships (from two independent random partitions) would differ after majority voting over m permutations each (%), predicted by Proposition 4 from Dnew , Dresh and the share of positive decisions, with 95% bootstrap intervals over items, drawn as for Table 10 ; they ignore that items share generated prompts. These predictions were made from the main experiment before the voting runs; Table 17 gives the measured flips, which lie inside these intervals at m=9 in eight of the ten pairs (for Qwen3-8B on harm the measured value lies just below the lower end, and both round to the same value). Harm and grading.
one batch
majority of 3
all three
mean bias
Model
Task
obs.
pred.
obs.
pred.
obs.
pred.
maj. of 9
model
bound [95% CI]
Qwen3-4B
Harm
13.7
13.7
11.6
12.0
5.0
4.8
10.7
10.2
2.15 [1.12, 3.18]
Grading
15.6
15.7
14.2
14.1
6.2
6.3
13.2
12.7
3.34 [2.20, 4.51]
Stars
5.7
5.8
5.3
5.4
3.0
3.0
5.3
5.2
2.04 [1.34, 2.93]
Qwen3-8B
Harm
14.0
14.0
11.4
11.8
4.2
4.0
10.0
9.4
1.03 [0.03, 2.05]
Grading
15.0
15.0
13.3
13.7
6.7
6.6
13.4
12.4
3.92 [2.77, 5.12]
Appendix
Table 13: Disagreement with single-item grading (% of items). One batch : the decision in a random partition differs from the single-item decision. Majority of 3 , all three : the majority of the three partitions differs from it, or all three do; observed and under the threshold model (Proposition 8 ), which is fitted to the single-item and batched decisions in pairs. Mean bias : the share of items whose main batched decision differs from the single-item decision, as the majority of the nine batched decisions that we have per item, which are not independent, and under the model. Bound : the lower bound of Equation ( 4 ), rounded down to two decimals, with a percentile interval from 10,000 resamples of the items. Counts in the text are made before rounding. Table 18 measures the majority over fifteen independent batches.
Model
Task
ΔT2
ΔV2
ΔTV2
J2
ratio
corr.
Qwen3-4B
Harm
7.7
6.6
7.3
15.1
2.1
0.57
Grading
10.3
7.7
11.3
17.2
1.9
0.54
Qwen3-8B
Harm
10.0
9.2
7.8
21.1
2.2
0.47
Grading
8.5
8.3
6.2
20.9
2.5
0.62
Gemma-4
Harm
9.1
6.8
6.0
17.2
2.2
0.48
Grading
4.5
2.2
4.8
2.3
0.7
0.26
Appendix
Table 14: Mean squares ( ×100 ) of the change of the target’s probability ζ when the neighbours’ texts, the earlier verdicts or both are taken from another batch, and of the interaction contrast J . Ratio : the mean square of J over the mean of those of ΔT and ΔV , which is 0 if the channels add up and 2 for unrelated contexts. Corr. : correlation of ΔT and ΔV , which is 0.5 for unrelated contexts. Harm and grading.
Model
Task
level ≥1
level ≥2
level ≥3
level ≥4
Qwen3-4B
Harm
0.058 (8.9)
0.089 (13.1)
0.145 (14.7)
0.232 † (2.7)
Grading
0.113 (12.9)
0.103 (13.4)
–
–
Stars
0.024 (4.8)
0.013 (4.4)
0.008 (3.9)
0.019 (5.7)
Qwen3-8B
Harm
0.111 (13.7)
0.116 (14.9)
0.258 (16.2)
0.203 † (1.5)
Grading
0.077 (12.1)
0.084 (12.1)
–
–
Stars
0.043 (6.1)
0.012 (4.7)
0.008 (4.0)
0.028 (6.8)
Appendix
Table 15: Latent dissimilarity between two random partitions, with the flip rate in % in brackets, when the decision is that the index of the level (counted from 0) is at least 1, 2, 3 or 4. The primary decisions are ≥2 for harm and grading and ≥3 for stars. † Fewer than 5% of the decisions on one side; left out wherever thresholds are compared.
AUROC
flagged
Model
Task
new
base
excess [95% CI]
vs. alone
alone
batched
Δ expected
alone
batched
Qwen3-14B
Harm
11.0
3.8
+7.3 [+5.9, +8.6]
12.0
0.793
0.804
− 0.011
62
61
Grading
9.1
2.8
+6.3 [+5.0, +7.6]
11.9
0.832
0.811
− 0.023
36
44
Qwen3-32B
Harm
14.6
5.5
+9.1 [+7.0, +10.9]
17.0
0.760
0.815
+0.012
64
50
Grading
10.3
4.7
+5.7 [+4.3, +6.8]
9.1
0.842
0.831
− 0.022
34
35
Gemma-4-31B
Harm
8.4
2.6
+5.8 [+4.6, +6.9]
10.8
0.837
0.869
+0.012
54
45
Appendix
Table 16: Four larger models on harm and grading, on H200 NVL GPUs. New , base and excess as in Table 2 ; vs. alone : decisions that differ from single-item grading (%, mean of the three partitions). AUROC of the written level alone and in batches (mean of the three partitions), and the change of the AUROC of the expected level (the mean of the level distribution), batched minus alone; share of items above the decision threshold (%).
flips after m permutations
left after nine (% of m=1 )
Model
Task
n
m=1
m=3
m=5
m=9
measured [95% CI]
in sample
main exp.
Qwen3-4B
Harm
2,000
13.3
9.4
8.0
6.9
52 [44, 60]
52
52
Grading
1,977
12.9
9.7
8.5
7.4
57 [50, 64]
60
59
Qwen3-8B
Harm
2,000
14.1
10.3
8.8
7.6
54 [48, 59]
57
63
Grading
1,984
12.6
9.2
8.0
7.0
55 [48, 63]
58
51
Gemma-4
Harm
2,000
12.4
9.4
8.2
7.1
57 [50, 65]
58
56
Appendix
Table 17: Voting over permutations, measured: decisions on which the majority votes of partitions 0 and 1 over m of the nine orders of each batch differ (%), averaged over all sets of m orders of each partition, so that m=1 averages over the 81 pairs of orders and differs from new in Table 2 ; and the share of the flips at m=1 that is left at m=9 : measured (95% normal intervals, with a variance clustered by the batches of both partitions), predicted by Proposition 4 from Dnew , Dresh and the share of positive decisions of the same runs (in sample), and predicted from the main experiment before these runs (main exp., Table 12 ). n : items with a verdict in all eighteen orders.
threshold model
Model
Task
n
M=1
M=15 [95% CI]
in sample
main exp.
M→∞
calibrated
Qwen3-4B
Harm
1,999
13.6
10.2 [8.7, 11.6]
10.1
10.7
10.2
10.1
Grading
1,975
15.7
13.3 [11.8, 14.8]
13.2
13.0
12.7
9.6
Qwen3-8B
Harm
1,999
13.6
9.6 [8.3, 10.8]
10.1
10.0
9.4
9.9
Grading
1,988
15.7
13.7 [12.2, 15.2]
13.3
12.7
12.4
13.5
Gemma-4
Harm
2,000
19.0
17.8 [15.4, 20.2]
18.6
19.3
19.3
8.9
Appendix
Table 18: Voting over batches: items whose majority over M independent random batches differs from the single-item decision of the same runs (%), measured, averaged over all sets of M of the fifteen partitions, with 95% intervals clustered by the batches of all fifteen partitions; under the threshold model at M=15 , fitted to these runs (in sample) and to the main experiment (main exp.), and the limit of the latter as M→∞ , which is the mean bias under the model in Table 13 ; and measured at M=15 with the batched threshold chosen in every partition to match the single-item positive rate (calibrated). n : items with a verdict alone and in all fifteen partitions.
Large language model (LLM)-as-a-judge research uses language models to score, compare, and verify AI outputs as scalable alternatives to human evaluation.