Distributional alignment

Overview

The goal is that, for a question and a population group, the model's probabilities over the answer options match the share of that group who would pick each option. This is different from getting one answer right: a model can pick the modal answer and still miss how much a group disagrees internally. Suh et al. measure this with a Wasserstein distance (WD) over ordinal answer values, where lower is better 2502.16761 §3.3.

The main tension is between steering a model with a prompt and training it on survey data. The paper reports that prompting alone rarely reproduces the spread of human answers 2502.16761 §1, §4.2. Its own method is a fine-tuned variant that targets whole answer distributions 2502.16761 §3.1.

A second paper asks a related question from the other side. Tjuatja et al. do not try to match a group's answers. They test whether a model's answers move under survey-wording changes in the same direction as human answers do 2311.04076 §1, §2.1. Their finding is that a model with good opinion match does not necessarily show human-like response biases 2311.04076 §5.

A third paper works at the level of single respondents. AlKhamissi et al. give a model a demographic persona and score how often its answer matches the answer that one real respondent gave, for the World Values Survey in Egypt and in the US 2402.13231 §4.2, §4.5. This measures agreement with individuals, not with a group's distribution, so its numbers are not comparable with the WD values above.

A fourth paper, Argyle et al., conditions the model on a first-person backstory built from one real respondent's survey answers. Each backstory gives one simulated subject, and the paper checks group-level vote shares and associations between survey items against the real sample 2209.06899 §4, §6. It was run on one model only, GPT-3 Davinci 2209.06899 §2.

A fifth paper, Lee et al. (KorNAT), builds a benchmark that scores each multiple-choice answer by the share of a national survey that chose it. It rewards a model for picking a popular answer, and it does not test how the model's answers spread 2402.13605 §4.

The phrase has two other meanings in machine learning, and neither is about survey answers. Hazarika et al. align the distributions of text, visual and acoustic representations with a central-moment-discrepancy loss 2005.03545 §3.5.1. Wang et al. align source and target image features for unsupervised domain adaptation. They match both the overall feature distribution and each class's conditional distribution, and weight the two using estimates from the data 1807.07258 §3.4. Both align representations or features, so their results say nothing about how a human group answers a survey.

Variants

Steering with prompts

Describe the group in the prompt and read the option probabilities for the answer letters. The paper tests three zero-shot formats (QA, BIO and PORTRAY) and a few-shot format with five example questions, chosen by embedding similarity 2502.16761 §4.1, app. D. Best zero-shot WD is 0.138 on OpinionQA and 0.160 on SubPOP-Eval, both for Llama-3-70B with QA prompts 2502.16761 tab. 1. Card: Suh et al., 2025.

The paper also compares base and chat models. With Llama-2-7B, zero-shot WD on OpinionQA is 0.173 for the base model and 0.308 for the chat model 2502.16761 app. C.2. The authors use base models for this reason.

Fine-tuning on group response distributions (SubPOP-FT)

Train with LoRA on pairs of (steering prompt and question, human distribution over the options), minimising the forward KL from the human distribution to the model 2502.16761 §3.1, app. B. LoRA rank is 8 and alpha is 32 2502.16761 app. B. The reported WD is 0.094 to 0.106 on OpinionQA and 0.096 to 0.121 on SubPOP-Eval across the four base models 2502.16761 tab. 1. Gains also hold for subgroups absent from training: the mean relative improvement across unseen age groups is 44.7% 2502.16761 §4.3. Card: Suh et al., 2025.

Training data are a few thousand multiple-choice questions with group-level response shares, which the paper builds from public survey microdata 2502.16761 §3.2, app. A.3. The paper reports NVIDIA A100 80GB hardware and gives no per-run time 2502.16761 app. B.

Persona simulation scored by agreement

The model gets a persona built from six fields (region, sex, age, social class, education level and marital status), then a survey question with numbered options 2402.13231 §4.2, fig. 2. The paper uses 30 questions from World Values Survey wave 7, four paraphrases each, and 303 personas per country whose demographics match across the two surveys 2402.13231 §4.1, §4.2. Each answer is scored twice: hard agreement is an exact match, and soft agreement gives partial credit on ordinal items 2402.13231 §4.5. Averaged over English and Arabic prompts, GPT-3.5 gets 48.61 soft and 25.99 hard on the Egypt survey, and 64.86 soft and 39.29 hard on the US survey 2402.13231 tab. 3. Prompting in the dominant language of the surveyed country raises soft agreement for GPT-3.5 and AceGPT-Chat on both surveys 2402.13231 tab. 2. Card: AlKhamissi et al., 2024.

Anthropological Prompting 2402.13231 §4.6, app. I adds a seven-point framework from anthropological field methods and asks the model to reason in one paragraph under it before giving the option number. For GPT-3.5 with English prompts on the Egypt survey, soft agreement moves from 0.4834 with a five-sample vote to 0.5102 with one response per question, and hard agreement from 0.2443 to 0.2838 2402.13231 tab. 4. The authors report larger gains for underrepresented social classes and education levels, shown only in a figure 2402.13231 §5.6, fig. 5. This comparison covers one model, one language, one survey and one run, with no statistical test.

Demographic backstories (silicon samples)

Argyle et al. write a first-person account for each ANES respondent, built from fields such as ideology, party and church attendance, and put it before the question 2209.06899 §5, app. 3. The authors call the resulting set of simulated respondents a "silicon sample". For the 2012, 2016 and 2020 vote questions, the model's probability of each candidate is read from token probabilities, with no sampling, and averaged over respondents 2209.06899 §6, app. 3. Mean probabilities differ from the human means by 0.013 (2012), 0.045 (2016) and 0.060 (2020) 2209.06899 §6. Whole-sample tetrachoric correlations with the human vote are 0.90 to 0.94, but for independents they are 0.41 (2016) and 0.02 (2020) 2209.06899 tab. 1. The paper does not test whether each simulated respondent matches their own source 2209.06899 app. 4. Card: Argyle et al., 2022.

Benchmark scored by national survey shares

KorNAT has two parts. The social-value part asks opinion questions, drawn from Korean news, and scores a model's pick by the share of a 6,174-person survey that chose that option. The mean of those shares is the SVA score 2402.13605 §3.1, §4. Two coarser versions merge the agree and disagree options (A-SVA), or replace contested questions with a neutral label (N-SVA) 2402.13605 §4. The paper's maximum achievable SVA is 0.450, and an All-Neutral policy scores 0.190 on SVA 2402.13605 tab. 1. The best listed model on SVA is PaLM-2 at 0.331 ± 0.007 2402.13605 tab. 1. Each answer is one option, so the score does not check how the model's answers spread across options, unlike WD. Prompting with "How would someone from Korea respond" raises SVA for every model except Claude-1 2402.13605 tab. 2. Card: Lee et al., 2024.

Probing response biases (evaluation, not steering)

This variant does not change the model. It checks whether the model reacts to survey wording the way people do. Each probe is a pair of questions: an original, and an edited version that should trigger a known human response bias. The five biases are acquiescence, allow/forbid wording, response order, odd/even scales and opinion floating. Three non-bias edits (key typo, middle random, letter swap) serve as controls, because people are known to be robust to them 2311.04076 §2.1, app. A.2. Each version is sampled 50 times at temperature 1, and the shift in answer shares is tested against zero with a one-sample t-test 2311.04076 §2.2, §2.3. Card: Tjuatja et al., 2023.

The paper reports that no model shows human-like behaviour on every bias, and that every model shows significant shifts on some typo control 2311.04076 §3.1. RLHF chat models show smaller bias shifts than their base models and larger typo-control shifts 2311.04076 §3.2. Full per-model numbers are in 2311.04076 app. A.3.

Other methods

Modular Pluralism (Feng et al., 2024) is compared in the paper with one-hot error rates 2502.16761 tab. 1. No card exists for it, so its method is not described here.

When to use which

Implementation sketch

Training step for one (prompt, question, group) example, and the ordinal WD used for evaluation. The response-bias probe effect is also shown. Notes on where the variants differ are in the comments.

# Training loss for one example: steering prompt + question, human dist
# [arxiv:2502.16761 §3.1] [app. B]
# prompt_tokens (T,), option_tokens (K,) = ids of " A", " B", ...
# human_dist (K,) sums to 1

def training_loss(prompt_tokens, option_tokens, human_dist):
    # Next-token logits at the position that predicts the answer letter
    logits = model(prompt_tokens)[-1]           # (vocab,)
    # Keep only the option letters and renormalise over them
    model_dist = softmax(logits[option_tokens]) # (K,)
    # Forward KL(human || model), summed over options [§3.1]
    return sum(human_dist * (log(human_dist) - log(model_dist)))

# Ordinal WD between human and model distributions over options
# [arxiv:2502.16761 §3.3] [app. B]
# Options carry ordinal values (e.g. "Very likely" = 1)

def ordinal_wd(human, model, ordinal):
    # Sort options by ordinal value
    human, model, ordinal = sort_by(ordinal, human, model)
    cdf_h = cumsum(human)
    cdf_m = cumsum(model)
    # Weight each CDF gap by the spacing between ordinal values
    gaps = ordinal[1:] - ordinal[:-1]
    total = sum(abs(cdf_h[:-1] - cdf_m[:-1]) * gaps)
    # Divide by the ordinal range so values lie in [0, 1]
    return total / (max(ordinal) - min(ordinal))

# Effect of one bias probe on one question pair, in percentage points
# [arxiv:2311.04076 §2.3] [tab. 2]
# letters_orig, letters_edit: 50 sampled answer letters each
# orig_set, edit_set: the letters that the bias predicts for each version

def bias_effect(letters_orig, letters_edit, orig_set, edit_set):
    # Count the answers that fall on the predicted letters in each version
    hits_orig = count(letters_orig, orig_set)
    hits_edit = count(letters_edit, edit_set)
    # 50 samples per version; scale to percentage points
    # The sign and letter sets differ by bias; check tab. 2 before use
    return (hits_orig - hits_edit) / 50 * 100

# Across question pairs, test the mean effect against zero with a
# two-sided one-sample t-test [§2.3]. Controls use the same calculation
# on the non-bias edits.

The forward-KL target is a distribution, not a one-hot label. Training on a one-hot label is a different objective, and the paper reports it as the weakest of the target encodings it tests 2502.16761 app. C.1. Add a small epsilon inside the logarithms, as the code does train_utils.py. The paper does not state the number of epochs, learning-rate schedule, warmup or validation split, so those need tuning 2502.16761 app. B.

Contradictions

• Reported reductions. The text gives a relative WD reduction of 32 to 46% on OpinionQA and 39 to 42% on SubPOP-Eval against the best baseline 2502.16761 §4.2. Computing the same ratio from Table 1 gives about 32 to 40% on OpinionQA and 34 to 42% on SubPOP-Eval 2502.16761 tab. 1. The table values are the ones to cite.
• The "46%" figure. The mean of 46.7% in §4.3 is a gap-closure measure, not a WD ratio. Table 2 defines "relative improvement" as the share of the gap between zero-shot WD and the human lower bound that fine-tuning closes 2502.16761 §4.3, tab. 2. The two measures are not interchangeable.
• WD normalisation. Appendix B gives the WD as an unnormalised sum of CDF differences 2502.16761 app. B. The code divides by the ordinal range survey_utils.py. The reported uniform upper bound of 0.178 fits the normalised form. This is an inference from the magnitudes.
• Refusal option. The worked example lists "Refused" as an option 2502.16761 §3.1, fig. 2. The data script's docstring says refusal is excluded from the target prepare_finetuning_data.py, but the script appends the refusal rate as the last target entry prepare_finetuning_data.py. Whether refusal enters the loss depends on the option tokens; the paper does not say.
• Learning rate and batch size. The paper's Llama-2-7B learning rate is 2e-4 and batch size 256 2502.16761 app. B. The code's defaults are 1e-4 and 32 training.py.
• Modular Pluralism in Table 1. Its 0.285 and 0.279 are WD values, while its 55.6% and 55.2% are one-hot error rates from the original paper 2502.16761 tab. 1. They are not the same metric.
• Different metrics across papers. Suh et al. report WD between group distributions 2502.16761 §3.3. AlKhamissi et al. report hard and soft agreement with single respondents 2402.13231 §4.5. The soft score is partial credit, not a distance. Argyle et al. report mean vote probabilities, tetrachoric correlations and Cramér's V 2209.06899 §6, app. 4. Lee et al. report the mean survey share of the chosen option 2402.13605 §4. Do not compare their numbers.
• Vanilla baseline in Table 4. The Table 4 vanilla row (0.4834 soft, 0.2443 hard) matches neither Table 2's Egypt English row (47.08 / 23.42, in percent) nor the unfiltered Egypt English row in appendix A (52.69 / 30.17) 2402.13231 tab. 2, tab. 4, app. A. The setup for that row is not stated.
• Cross-national prompting in KorNAT. The text says both prompting variants improve scores for every model except Claude-1 2402.13605 §5.2.2. In Table 2, Gemini Pro's A-SVA and N-SVA sit below its baseline under both variants 2402.13605 tab. 2. The USA-prompt rows for HyperCLOVA X and Gemini Pro are identical in every cell, which the paper does not explain. This page quotes the table values only.
• What counts as matching humans. Suh et al. take lower WD to group response shares as the goal, and report that their fine-tuned model reproduces the intergroup disagreement pattern for education levels not in training 2502.16761 §4.3, fig. 4. Tjuatja et al. report that representativeness of human opinion distributions does not track bias-consistency 2311.04076 §5. AlKhamissi et al. report that agreement with individual respondents is higher for the US survey than for the Egypt survey across all four models 2402.13231 §5.1, tab. 3. These are author findings on different tests. Neither the Suh et al. card nor the Tjuatja et al. card cites the other paper, and no result here settles which test matters for a given use.
• Bias probe numbers. The paper's text says Llama 2 70b (base) shows significant perturbation shifts on three of five biases, while its table shows one such shift for that model 2311.04076 §3.1, app. A.3. Use the table.

Papers

• Suh et al., 2025: LoRA fine-tuning on group-level survey distributions (SubPOP), evaluated with ordinal WD on OpinionQA and an out-of-distribution survey.
• Tjuatja et al., 2023: tests whether LLMs shift under survey-wording edits like humans do, using paired bias and typo-control questions across nine models.
• AlKhamissi et al., 2024: persona prompting on World Values Survey items in Egypt and the US, scored by hard and soft agreement with individual respondents; introduces Anthropological Prompting.
• Argyle et al., 2022: "silicon samples" from first-person backstories of ANES respondents, checked against US vote shares and item associations.
• Lee et al., 2024: KorNAT, a Korean benchmark that scores multiple-choice answers by the survey share of the chosen option, with common-knowledge items.
• Wang et al., 2018: MEDA, unsupervised domain adaptation that aligns marginal and class-conditional feature distributions. Listed only for the domain-adaptation sense of "distribution alignment" described in the Overview.
• Hazarika et al., 2020: MISA, a multimodal sentiment model that aligns text, visual and acoustic representations. Listed only for the unrelated sense of "distribution" described in the Overview.