Large language models are widely used to simulate survey respondents, yet their outputs are homogeneous and unfaithful to real inter-group differences, and whether this reflects what a model knows or uses has remained untested. Using representational similarity analysis against Pew American Trends Panel ground truth, we score demographic read-out locations in Mistral-7B and intervene causally across six attribute types. The internal geometry is faithful: attention-head read-outs dominate the standard residual read-out, reaching selection-corrected ρ up to 0.63 -- about 70% of the measurement-reliability ceiling -- and one head, L11 H16, is significantly faithful across all six types, though race-based types stay weak and prompt-fragile, replicating in a second model family. Yet causal use does not track fidelity: the clearest causal pathway (p=0.002) sits in one of the least faithful types, the most faithful type shows no correction-surviving effect, and full identity swaps in the prompt move predictions by under 2% of their error. A 128-dimensional probe on that head lands 21-31% closer to survey truth than the model's answers, yet recovers almost none of the per-question group ordering. Readable, faithfully arranged, and causally used are three dissociable properties of the same model; treating them as one claim is what keeps the "can LLMs simulate populations" debate unresolved.
Figures & tables
Figure 1: Fidelity by depth and component (multi-cue Tmean read-out): orange = best of 32 heads per layer, blue = residual stream, dashed green = FFN output. Dotted line marks layer 11. Maxima here are selected/uncorrected; Table 1 gives held-out values.
Type
Residual best
Head best (selected)
Head (held-out)
Best loc.
AGE × POLPARTY
+0.51
+0.74
+0.59 – 0.63
L11 H19
EDUCATION × INCOME
+0.61
+0.68
+0.58 – 0.63
L14 H1
RELIG × POLPARTY
+0.26
+0.60
+0.50 – 0.52
L11 H16
RACE × POLPARTY
+0.34
+0.61
+0.41 – 0.52
L23 H13
RACE × POLIDEOLOGY
+0.40
+0.50
+0.30 – 0.41
L8 H21
RACE × RELIG
+0.27
+0.45
+0.21 – 0.32
L28 H0
Table 1: Fidelity ( ρ vs. survey ground truth) by read-out. Selected = maximum over locations; held-out = selection-corrected range from two independent corrections (held-out template, Appendix B.3 ; split-half median), on the NaN-cleaned cell set.
selection
symmetric + geometry (held-out)
ceiling
lexical
Type
psel
head
resid
proj
% ceil
partial ρ
p
AGE × POLPARTY
< .0005
0.52
0.39
0.42
74%
0.59
< .0005
EDUCATION × INCOME
< .0005
0.54
0.51
0.49
70%
0.35
< .0005
RELIG × POLPARTY
< .0005
0.44
0.17
0.18
68%
0.59
< .0005
RACE × POLPARTY
< .0005
0.47
0.28
0.30
69%
0.58
< .0005
RACE × POLIDEOLOGY
.0025
0.38
0.26
0.29
53%
0.37
< .0005
Table 2: Every control in Sec. 4 , per attribute type. psel : selection-corrected max-statistic p . head/resid/proj: held-out fidelity of the three families (proj = random 128-d projections). % ceil: L11 H16 fidelity as a fraction of the attenuation ceiling. partial ρ : L11 H16 fidelity partialling out the lexical-baseline RDM.
Figure 2: Fidelity of the fixed location L11 H16 (bars, never re-selected per type) against the best residual-stream read-out for that type (circles); margins +0.05 to +0.34 . Significance ( p<0.001 each, ×1024 Bonferroni) is on the NaN-cleaned cell subset, where race-containing values shift slightly (RACE × RELIG 0.31→0.33 ; RACE × POLPARTY 0.56→0.59 ; exclusions in Appendix A.1 ).
Mistral
Qwen3-8B-Base
OSim-8B-Mid
OSim-8B (post-RL)
Type
ρho
head/resid
ρho ( p )
head/resid
ρho ( p )
head/resid
ρho ( p )
AGE × POLPARTY
0.52
0.78/0.50
0.49 ( < .0005)
0.74/0.50
0.61 ( < .0005)
0.73/0.51
0.57 ( < .0005)
EDUCATION × INCOME
0.54
0.70/0.51
0.58 ( < .0005)
0.68/0.50
0.54 ( < .0005)
0.68/0.53
0.60 ( < .0005)
RELIG × POLPARTY
0.44
0.57/0.37
0.56 ( < .0005)
0.58/0.39
0.56 ( < .0005)
0.56/0.38
0.55 ( < .0005)
RACE × POLPARTY
0.47
0.60/0.37
0.37 (.001)
0.57/0.38
0.38 (.002)
0.63/0.37
0.46 ( < .0005)
RACE × POLIDEOLOGY
0.38
0.59/0.35
0.38 ( < .0005)
0.62/0.36
0.38 ( < .0005)
0.60/0.35
0.40 ( < .0005)
Table 3: Cross-model replication of the fidelity map. head/resid = selected best head vs. best residual read-out. ρho = held-out-template fidelity (max-statistic p in parentheses, 2,000 permutations). Mistral column: that model’s held-out head value, for reference.
Type (split-half fidelity)
Ceiling
32 heads @ L11
Single L11 H16
pitem (32h)
ppair (32h)
AGE × POLPARTY ( 0.63 )
+0.0165
+0.0067 (41%)
−0.0001 (n.s.)
0.0027
0.019
RELIG × POLPARTY ( 0.52 )
+0.0020
+0.0034 (170%, n.s.)
−0.0004 (n.s.)
0.16
0.15
RACE × RELIG ( 0.21 )
+0.0026
+0.0017 (n.s.)
−0.0005 (wrong dir., ppair=1/4096 )
0.31
0.29
Table 4: Causal patching results with the strong instrument. Ceiling = mean full-prompt-swap shift (Sec. 5.1 , this instrument’s question set). Shift = mean directional shift toward the target group’s true distribution; % of ceiling in parentheses where meaningful. pitem = Wilcoxon vs. random-head control over 240 items (descriptive; items are clustered); ppair = exact sign-flip over the 12 pairs (primary).
Figure 3: Causal effect of patching all 32 heads of each layer in turn, at the identity token ( n=240 pair–question items per type). Descriptive view: bars are the item-level paired t of the directional shift toward the target group’s true distribution against a random-layer control; the dashed line is the item-level max-statistic noise ceiling. Inference in the text and Table 5 is cluster-robust (sign flips at the level of the 12 pairs).
item-level (descriptive)
pair-level (primary)
Type
Fidelity
Win layer
t
pmax
twin
pmax
t @L11 →p
Out. ceiling
RACE × POLIDEOLOGY
0.30
L11
4.55
0.0005
3.22
0.066
3.22→0.0020
0.0176
RACE × RELIG
0.21
L1
4.10
0.0005
2.94 (L8)
0.122
0.68→0.27
0.0026
AGE × POLPARTY
0.63
L15
3.31
0.0150
2.37 (L14)
0.266
1.93→0.022
0.0165
RELIG × POLPARTY
0.52
L8
2.94
0.0355
2.58 (L8)
0.210
1.11→0.15
0.0020
EDUCATION × INCOME
0.58
L9
2.47
0.1425
1.57 (L15)
0.822
0.75→0.23
0.0194
Table 5: Per-layer patching sweep, all six types. Fidelity = split-half median (one estimator used consistently; see text for sensitivity). Item-level columns are descriptive ( t over 240 items; max-statistic p over 32 layers); the primary inference is the pair-level max-statistic p (sign flips over 12 pairs, exact) and the pair-level p at the a-priori locus L11 (no layer selection). The item-level and pair-level winning layers can differ, since averaging within pairs reweights the evidence. Output ceiling = mean shift from replacing the entire identity.
Type
t @ L11
ppair
t @ L1
ppair
types not in the sweep that suggested L1:
RACE × POLIDEOLOGY
3.22
0.0020
−0.74
0.77
RACE × POLPARTY
1.28
0.114
1.97
0.033
EDUCATION × INCOME
0.75
0.234
1.24
0.123
types that were in that sweep (L1 column not selection-free):
AGE × POLPARTY
1.93
0.022
0.34
0.386
Table 6: Fixed-location causal test, pair-level (exact sign-flip over 12 pairs, one-sided). L11 was fixed by Sec. 4 before any sweep; L1 is pre-registered only for the upper block (see text). Bonferroni for the 12 tests is 0.0042 ; the single bold entry survives it.
Figure 4: Representational fidelity (split-half median) against cluster-robust causal strength (pair-level t ), one point per attribute type. Left: at the a-priori locus L11 (filled = exact pair-level p<0.05 ). Right: at each type’s own best layer (filled = survives the pair-level max-statistic correction; none does).
Figure 5: Left: distance to survey truth (Wasserstein, lower is better) for the model’s own answer, probes read from the faithful location, and a group-blind baseline built from other cells’ real answers. Right: how much of the true per-question group ordering each read-out recovers (mean per-question Spearman across cells, half-split evaluation; error bars are standard errors), against the reliability ceiling of the metric given survey sampling noise.
Appendix figures & tables6 assets
Supplementary material from the paper’s appendix.
Appendix
Attribute type
Cells
Pairs
AGE × POLPARTY
18
153
EDUCATION × INCOME
33
528
RACE × POLIDEOLOGY
30
435
RACE × RELIG
30
435
RELIG × POLPARTY
30
435
RACE × POLPARTY
28
378
Appendix
Table 7: Cell and same-type pair counts per attribute type. Pairs = (2cells) , the number of RSA observations available for that type.
Attribute type (used)
Cells
Rank of 66 (tied block)
EDUCATION × INCOME
33
7th (7–8)
RACE × POLIDEOLOGY
30
18th (18–22)
RELIG × POLPARTY
30
18th (18–22)
RACE × RELIG
30
18th (18–22)
RACE × POLPARTY
28
23rd (23–24)
AGE × POLPARTY
18
44th (44–46)
Appendix
Table 8: Rank of each used pair among the 66 possible attribute pairs by number of cells clearing n≥30 . Ranks are the best rank within each tied block (competition ranking); the parenthesised range gives the positions that block occupies.
Pooled
AGE × POLPARTY
EDUCATION × INCOME
RACE × RELIG
Read-out
(mixes types)
within-type (the regime used throughout)
raw
+0.185
+0.455
+0.490
+0.072
mean-centred
+0.301
+0.375
+0.454
+0.033
change
+0.116
−0.080
−0.036
−0.039
Appendix
Table 9: Fidelity ( ρ vs. survey truth) at layer 17 before and after removing the shared direction ( vi←vi−vˉ ). Centering was run on three of the six types; full detail above.
Type
L0–7
L8–15
L16–23
L24–31
AGE × POLPARTY
0.36
0.47
0.42
0.42
EDUCATION × INCOME
0.43
0.53
0.46
0.48
RELIG × POLPARTY
0.13
0.21
0.23
0.22
RACE × POLPARTY
0.17
0.24
0.24
0.22
RACE × POLIDEOLOGY
0.18
0.27
0.22
0.21
RACE × RELIG
0.09
0.12
0.15
0.17
Appendix
Table 10: Fidelity averaged over all 32 heads within each quarter of the stack (multi-cue Tmean read-out). Unlike Figure 1 , which takes the best head per layer, a block mean involves no selection, so these values are comparable across depths. Bold marks each type’s peak block.
Figure 6: The full fidelity map: every attention head (32 layers × 32 heads) scored against survey ground truth, per attribute type, multi-cue read-out. Square marks the fixed location L11 H16; circle marks that type’s own maximum; the underlying table is described above. In the two strongest types 84 – 92% of the 1,024 heads exceed ρ=0.3 , against 5% in RACE × RELIG; the level varies with depth rather than at random (Table 10 above) and falls for race-containing types (bottom row). Maxima printed here are uncorrected and match the selected column of Table 1 ; see that table for held-out values.
Swap (% of error)
Mean WD
Dir. ( p )
Type
base
instr.
base
instr.
base
instr.
AGE × POLPARTY
2.6
3.4
0.36
0.65
0.56 (.045)
0.75 ( < .001)
EDUCATION × INCOME
1.0
2.4
0.33
0.59
0.55 (.002)
0.62 ( < .001)
RELIG × POLPARTY
1.6
3.4
0.37
0.64
0.52 (.293)
0.65 ( < .001)
RACE × POLPARTY
3.6
1.5
0.35
0.70
0.54 (.061)
0.59 ( < .001)
RACE × POLIDEOLOGY
9.2
9.9
0.37
0.66
0.62 ( < .001)
0.64 ( < .001)
Appendix
Table 11: Identity-swap ceiling per attribute type, base vs. instruction-tuned Mistral (40 questions per type, all same-type cell pairs). Swap = movement of the predicted distribution under a full identity replacement, as a percentage of that type’s total prediction error. WD = mean absolute error to survey truth (lower is better). Dir. = fraction of pairs where group A ’s prediction is closer to A ’s own truth than to B ’s, with the sign-test p ; 0.50 is a coin flip.
Large language models (LLMs) show considerable potential in simulating human attitudes and preferences. Prior work finds that LLM-generated responses can compress the range of attitudes found within populations and misrepresent particular subgroups in ways that vary across models and topics. We introduce Population Fidelity, an evaluation framework that distinguishes key conditions required for a set of LLM-generated responses to represent a population. It incorporates three dimensions: group-level accuracy, the amount of between-group variation, and the structure of that variation. We demonstrate the framework's utility in two ways. First, we reproduce a prior study of "machine bias" in LLM survey responses and apply the framework to its models and more recent ones, showing that poor representation reflects not only insufficient between-group variation but also variation assigned to the wrong groups. Second, we evaluate one proposed approach to improving models' population representativeness: cultural fine-tuning. We find that cultural fine-tuning can improve alignment with the survey center without improving the representation of within-population differences, a distinction that measures of aggregate agreement do not capture. We argue that representing a population requires models to reproduce several features of human attitudinal variation simultaneously. Our framework organizes these features and provides reusable code, data, and trained models for evaluating population fidelity across substantive domains and assessing proposed alignment methods.
Neemias B. da Silva, Martin Lukk, Ali Sutani +5
University of Toronto, Canada · Federal University of Technology – Paran´a, Brazil
Predicting how a population will answer a new question is a long-standing goal. Statistical methods succeed at the level of the mass but falter at the level of the individual. Large language model simulators inherit this gap. They recover a population's central tendencies while flattening its heterogeneity, and they carry social biases and prompt brittleness that distort individual predictions. This paper introduces Anacreon, an audience simulation model that targets the individual level within a narrow, well-specified domain. Anacreon learns an authorship embedding that separates individuals, clusters a real qualitative corpus around seed people, and trains a dedicated adapter for each cluster, a mixture of minds, on a Gemma~4 12B base. It harvests demographics, psychological traits, and survey responses from public text, and augments each record with a chain-of-emotion. It reduces prompt brittleness by shuffling response options and reduces positive bias by balancing the training distribution. On a large, externally sourced survey, Anacreon reaches a state-of-the-art ordinal alignment of 0.775, the individual-level accuracy measure on which the field has converged, with a small residual bias. The work is a step toward drawing aggregate insight from faithfully simulated individuals.
Large language models (LLMs) are increasingly used to simulate social survey responses, yet their outputs exhibit systematic biases: marginal distributions are skewed, response variance is poorly calibrated, and predictor-outcome relationships are attenuated. We ask a simple question: given a small pilot sample of human responses, can an LLM recover the statistical characteristics of a broader population? We decompose recovery along three axes: structural fidelity, marginal fidelity, and individual fidelity. Using a COVID-19 misinformation survey as a case study, we benchmark three families of approaches: prompting, rectification, and fine-tuning. The findings suggest that fine-tuning on small pilot samples offers a balanced approach for achieving multiple forms of fidelity, but the levels of such fidelity can vary across subsamples, potentially threatening pluralistic alignment.
Eun Cheol Choi, Youngrae Kim, Prabhu Pugalenthi +2