data/analysis/iaa/ANALYSIS.md

# Inter-Annotator Agreement & Alternative-Annotator Test

_Generated by `legex-analysis-report` from the CSVs in this directory — do not edit by hand; numbers always reflect the current CSVs._

Regenerate the whole chain with `scripts/reproduce_paper.sh`.

---

## 1. Scope

- Countries with ≥2 annotators: **8** — br, ch, de, ge, sg, tw, uk, us
- Annotators: **11** (primary + 10 secondary: 359f544380, 40dd94f4cc, 5c9b11ec0c, 93839740f5, 9bbad8ca9e, ab2d3cfed5, b36683f5be, c7cd8dc26a, cf5a561621, dd79b903af)
- Annotator pairs (country × pair): **24**

Countries: **br** Brazil, **ch** Switzerland, **de** Germany, **ge** Georgia, **sg** Singapore, **tw** Taiwan, **uk** United Kingdom, **us** United States.

## 2. Human–human agreement

> **Per-variable agreement.** Percent agreement is reported for every variable, using the same value-matching as the evaluation (ISO-date / number-format aware; `0` and empty treated alike). For the two **nominal ISIC** fields — the only variables with a fixed controlled vocabulary — we additionally report **Cohen's κ**. For the other variables the category space is unbounded (free text) or continuous (dates, counts, money, ratios): there κ's chance correction collapses toward percent agreement (as the number of categories → ∞, expected agreement pₑ → 0 and κ → observed agreement) and awards no partial credit for near-misses, so percent agreement is the appropriate summary. Correlation coefficients are deliberately not used — for these labels a wrong value is wrong, not partially correct. Cell detail: `kappa_audit.csv`.

_n = paired case comparisons (shared cases × annotator pairs). We report ±1 SE = √(p(1-p)/n) in percentage points, a descriptive precision marker. This is not a significance test._

### 2.1 By variable

| Variable | Type | n | % agreement | Cohen's κ |
| --- | --- | --- | --- | --- |
| `defendant_no1_ISIC1_industry_category` | nominal | 614 | 53.9% ±2.0 | 0.426 |
| `plaintiff_no1_ISIC1_industry_category` | nominal | 614 | 47.2% ±2.0 | 0.316 |
| `legal_subject_judgement` | free text | 614 | 2.4% ±0.6 | — |
| `trial_end_date` | date | 614 | 74.8% ±1.8 | — |
| `trial_start_date` | date | 614 | 70.2% ±1.8 | — |
| `plaintiffs_all_count` | count | 614 | 84.7% ±1.5 | — |
| `defendants_all_count` | count | 614 | 76.9% ±1.7 | — |
| `party_compensation_awarded_nominal` | monetary | 614 | 89.4% ±1.2 | — |
| `court_cost_awarded_nominal` | monetary | 614 | 86.0% ±1.4 | — |
| `dispute_value_nominal` | monetary | 614 | 65.3% ±1.9 | — |
| `plaintiff_loosing_share` | ratio | 614 | 72.5% ±1.8 | — |

### 2.2 By country

| Country | Pairs | n | % agreement |
| --- | --- | --- | --- |
| br | 3 | 68 | 61.1% |
| ch | 3 | 90 | 76.4% |
| de | 3 | 70 | 71.4% |
| ge | 3 | 68 | 51.7% |
| sg | 3 | 68 | 55.9% |
| tw | 3 | 70 | 71.0% |
| uk | 3 | 90 | 57.1% |
| us | 3 | 90 | 76.9% |

### 2.3 By pair

| Country | Pair | n | % agreement |
| --- | --- | --- | --- |
| br | 93839740f5 – ab2d3cfed5 | 19 | 65.5% |
| br | 93839740f5 – primary | 19 | 56.9% |
| br | ab2d3cfed5 – primary | 30 | 60.9% |
| ch | 5c9b11ec0c – ab2d3cfed5 | 30 | 71.8% |
| ch | 5c9b11ec0c – primary | 30 | 73.6% |
| ch | ab2d3cfed5 – primary | 30 | 83.6% |
| de | 40dd94f4cc – ab2d3cfed5 | 20 | 73.2% |
| de | 40dd94f4cc – primary | 20 | 75.5% |
| de | ab2d3cfed5 – primary | 30 | 67.6% |
| ge | 359f544380 – dd79b903af | 19 | 55.0% |
| ge | 359f544380 – primary | 20 | 53.6% |
| ge | dd79b903af – primary | 29 | 48.3% |
| sg | c7cd8dc26a – dd79b903af | 20 | 47.7% |
| sg | c7cd8dc26a – primary | 27 | 59.6% |
| sg | dd79b903af – primary | 21 | 58.9% |
| tw | ab2d3cfed5 – cf5a561621 | 20 | 67.7% |
| tw | ab2d3cfed5 – primary | 30 | 67.9% |
| tw | cf5a561621 – primary | 20 | 79.1% |
| uk | ab2d3cfed5 – b36683f5be | 30 | 54.8% |
| uk | ab2d3cfed5 – primary | 30 | 62.7% |
| uk | b36683f5be – primary | 30 | 53.6% |
| us | 9bbad8ca9e – ab2d3cfed5 | 30 | 76.4% |
| us | 9bbad8ca9e – primary | 30 | 76.7% |
| us | ab2d3cfed5 – primary | 30 | 77.6% |

## 3. Alternative-annotator test

> **Alternative Annotator Test** (Calderon et al. 2025, [arXiv:2501.10970](https://arxiv.org/abs/2501.10970)): leave each human annotator out in turn and score, per instance, both the candidate and the excluded annotator against the remaining annotators; a one-sided test per annotator asks whether the candidate's advantage probability trails the human's by less than ε = 0.2 (the expert-annotator tolerance), under Benjamini–Yekutieli FDR control at q = 0.05. `passes` = winning rate ≥ 0.5. Requires ≥ 3 independent annotators per country; free-text fields are excluded. ρ is the advantage probability — how likely the candidate annotates as well as or better than a randomly chosen human. The *non-trivial* variant drops instances every expert left empty: an empty prediction ties those for free, so the gap between the two columns shows how much of a pass rests on empty cells. Untestable cells (too few non-empty judgements) are excluded from the denominators.
>
> These numbers come from the **authors' reference implementation** ([github.com/nitaytech/AltTest](https://github.com/nitaytech/AltTest)) executed on the LEGEX data via `scripts/alt_test_reference.py`. See the README section "Alternative Annotator Test (AAT)" for how to run it. `legex-iaa` does not produce these CSVs.

### 3.1 How ω and ρ are computed

_Definitions from Calderon et al. (2025), as implemented in the authors' `alt_test`.
`values_agree` is the tolerant comparator LEGEX passes in as the scoring function._

```text
One jurisdiction, one candidate f, human annotators H = {1..M}, and instances i
(here: one (judgment, variable) cell over the 10 structured fields).

LEAVE-ONE-OUT. For human j and every instance i the other humans also labelled,
let A(i,-j) be the remaining humans' labels and

    s_f(i,j) = score( f(i),    A(i,-j) )      candidate vs. the other humans
    s_h(i,j) = score( h_j(i),  A(i,-j) )      held-out human vs. the same humans

    score(p, A) = (1/|A|) * SUM_{a in A} values_agree(p, a)     in {0, 1/2, 1}

ADVANTAGE PROBABILITY of the candidate against human j. Note the ">=", which
credits every tie to the candidate:

    rho_j = (1/n_j) * SUM_i  1[ s_f(i,j) >= s_h(i,j) ]

PER-ANNOTATOR TEST. With d_i = 1[s_f < s_h] - 1[s_f >= s_h], so E[d] = 1 - 2*rho_j:

    H0: E[d] >= epsilon        vs.        H1: E[d] < epsilon

one-sided paired t-test (Wilcoxon signed-rank when n_j < 30), the M p-values
corrected by Benjamini-Yekutieli at q = 0.05. Rejecting H0 is therefore
equivalent to rho_j being significantly greater than

    (1 - epsilon) / 2  =  0.4        for the expert tolerance epsilon = 0.2

VERDICT.

    omega = |{ j : H0_j rejected }| / M          winning rate
    rho   = (1/M) * SUM_j rho_j                  advantage probability
    "f may substitute a human annotator"  <=>  omega >= 0.5
```

Two consequences worth keeping in view when reading §3.2. First, ρ is a
**≥**-comparison, so a candidate that merely matches the held-out human on an
instance is scored as winning it. Second, with ε = 0.2 the hypothesis test
clears at ρ_j > 0.4, not at 0.5. Both are deliberate: the alt-test asks whether
a candidate can *substitute* a human annotator, not whether it is *better* than
one. §3.4 separates the two.


### 3.2 Headline: pooled per jurisdiction (paper numbers)

_One alt-test per jurisdiction; instance = (judgment, variable) cell over the 10 structured fields, so each annotator contributes ~190+ effective instances and the paired t-test applies without the paper's n<30 caveat._

| Candidate | Country | ω | ρ | ω (non-triv) | ρ (non-triv) |
| --- | --- | --- | --- | --- | --- |
| gpt-5.4-mini | br | 1.00 | 0.90 | 1.00 | 0.94 |
| gpt-5.4-mini | ch | 1.00 | 0.89 | 1.00 | 0.97 |
| gpt-5.4-mini | de | 0.33 | 0.80 | 0.33 | 0.78 |
| gpt-5.4-mini | ge | 1.00 | 0.82 | 1.00 | 0.84 |
| gpt-5.4-mini | sg | 1.00 | 0.86 | 1.00 | 0.87 |
| gpt-5.4-mini | tw | 1.00 | 0.86 | 1.00 | 0.87 |
| gpt-5.4-mini | uk | 1.00 | 0.81 | 1.00 | 0.80 |
| gpt-5.4-mini | us | 0.00 | 0.78 | 0.00 | 0.74 |
| gemini/gemini-3.1-flash-lite | br | 1.00 | 0.93 | 1.00 | 0.92 |
| gemini/gemini-3.1-flash-lite | ch | 1.00 | 0.90 | 1.00 | 0.93 |
| gemini/gemini-3.1-flash-lite | de | 1.00 | 0.84 | 0.33 | 0.80 |
| gemini/gemini-3.1-flash-lite | ge | 1.00 | 0.86 | 1.00 | 0.87 |
| gemini/gemini-3.1-flash-lite | sg | 1.00 | 0.88 | 1.00 | 0.90 |
| gemini/gemini-3.1-flash-lite | tw | 1.00 | 0.86 | 1.00 | 0.86 |
| gemini/gemini-3.1-flash-lite | uk | 1.00 | 0.82 | 1.00 | 0.79 |
| gemini/gemini-3.1-flash-lite | us | 0.00 | 0.75 | 0.00 | 0.69 |
| harvey | br | 1.00 | 0.91 | 1.00 | 0.87 |
| harvey | ch | 1.00 | 0.93 | 1.00 | 0.93 |
| harvey | de | 0.67 | 0.83 | 0.67 | 0.77 |
| harvey | ge | 1.00 | 0.84 | 1.00 | 0.84 |
| harvey | sg | 1.00 | 0.92 | 1.00 | 0.91 |
| harvey | tw | 1.00 | 0.85 | 1.00 | 0.82 |
| harvey | uk | 1.00 | 0.92 | 1.00 | 0.92 |
| harvey | us | 0.33 | 0.78 | 0.00 | 0.74 |
| legora-1 | br | 1.00 | 0.91 | 1.00 | 0.87 |
| legora-1 | ch | 1.00 | 0.97 | 1.00 | 0.97 |
| legora-1 | de | 0.00 | 0.70 | 0.00 | 0.57 |
| legora-1 | sg | 1.00 | 0.85 | 1.00 | 0.82 |
| legora-1 | tw | 1.00 | 0.88 | 1.00 | 0.85 |
| legora-1 | uk | 1.00 | 0.90 | 1.00 | 0.87 |
| legora-1 | us | 0.00 | 0.70 | 0.00 | 0.62 |
| legora-2 | br | 1.00 | 0.92 | 1.00 | 0.87 |
| legora-2 | ch | 1.00 | 0.96 | 1.00 | 0.95 |
| legora-2 | de | 0.00 | 0.69 | 0.00 | 0.55 |
| legora-2 | sg | 1.00 | 0.86 | 1.00 | 0.84 |
| legora-2 | tw | 1.00 | 0.88 | 1.00 | 0.85 |
| legora-2 | uk | 1.00 | 0.91 | 1.00 | 0.88 |
| legora-2 | us | 0.00 | 0.71 | 0.00 | 0.64 |

### 3.3 Per-field diagnostic (cells passed / testable)

| Candidate | ρ̄ (all) | Pass (all) | ρ̄ (non-triv) | Pass (non-triv) | br (all · non-triv) | ch (all · non-triv) | de (all · non-triv) | ge (all · non-triv) | sg (all · non-triv) | tw (all · non-triv) | uk (all · non-triv) | us (all · non-triv) |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| gemini-3.1-flash-lite | 0.86 | 47/80 | 0.85 | 40/69 | 9/10 · 6/7 | 7/10 · 7/10 | 7/10 · 4/7 | 5/10 · 6/10 | 5/10 · 6/10 | 6/10 · 6/9 | 3/10 · 2/8 | 5/10 · 3/8 |
| gpt-5.4-mini | 0.84 | 40/80 | 0.85 | 35/69 | 6/10 · 5/7 | 6/10 · 7/10 | 4/10 · 3/7 | 5/10 · 6/10 | 6/10 · 5/10 | 5/10 · 4/9 | 3/10 · 2/8 | 5/10 · 3/8 |
| harvey | 0.87 | 54/80 | 0.85 | 38/69 | 7/10 · 4/7 | 8/10 · 7/10 | 6/10 · 4/7 | 6/10 · 4/10 | 8/10 · 6/10 | 6/10 · 4/9 | 7/10 · 5/8 | 6/10 · 4/8 |
| legora-1 | 0.84 | 45/70 | 0.80 | 29/59 | 7/10 · 4/7 | 9/10 · 7/10 | 5/10 · 2/7 | – · – | 5/10 · 4/10 | 6/10 · 4/9 | 8/10 · 5/8 | 5/10 · 3/8 |
| legora-2 | 0.85 | 46/70 | 0.81 | 34/59 | 7/10 · 4/7 | 8/10 · 8/10 | 6/10 · 2/7 | – · – | 6/10 · 6/10 | 6/10 · 5/9 | 9/10 · 7/8 | 4/10 · 2/8 |

> Per-cell winning rates and advantage probabilities are in `alt_test_reference_<model>.csv`; an empty cell there means the (country, field, variant) combination was untestable.

### 3.4 Substitutable vs. better: win / tie / loss decomposition

> ρ collapses the leave-one-out comparison of §3.1 into one number, and its `≥` hands every tie to the candidate. This section keeps the same comparisons and reports the counts instead: per held-out human and instance, whether the candidate scored **better than**, **the same as**, or **worse than** that human against the two remaining humans. Restricted to judgments all three experts labelled, so every comparison has exactly two references and a score is 0, ½ or 1. `ρ (alt-test)` is the reproduced advantage probability (ties → candidate); `ρ (ties split)` counts a tie as half a win for each side. Source: `alt_test_decomposition.csv` from `scripts/alt_test_decomposition.py`, which reproduces the reference ρ of §3.2 to within 0.02.

| Candidate | Country | n | Candidate better | Tie | Human better | ρ (alt-test) | ρ (ties split) |
| --- | --- | --- | --- | --- | --- | --- | --- |
| gemini-3.1-flash-lite | br | 570 | 74 (13%) | 463 (81%) | 33 (6%) | 0.94 | 0.54 |
| gemini-3.1-flash-lite | ch | 900 | 53 (6%) | 758 (84%) | 89 (10%) | 0.90 | 0.48 |
| gemini-3.1-flash-lite | de | 600 | 37 (6%) | 470 (78%) | 93 (16%) | 0.84 | 0.45 |
| gemini-3.1-flash-lite | ge | 570 | 65 (11%) | 427 (75%) | 78 (14%) | 0.86 | 0.49 |
| gemini-3.1-flash-lite | sg | 600 | 68 (11%) | 465 (78%) | 67 (11%) | 0.89 | 0.50 |
| gemini-3.1-flash-lite | tw | 600 | 38 (6%) | 488 (81%) | 74 (12%) | 0.88 | 0.47 |
| gemini-3.1-flash-lite | uk | 900 | 87 (10%) | 650 (72%) | 163 (18%) | 0.82 | 0.46 |
| gemini-3.1-flash-lite | us | 900 | 59 (7%) | 617 (69%) | 224 (25%) | 0.75 | 0.41 |
| gemini-3.1-flash-lite | **all three** | 5640 | 481 (9%) | 4338 (77%) | 821 (15%) | 0.85 | 0.47 |
| gpt-5.4-mini | br | 570 | 72 (13%) | 445 (78%) | 53 (9%) | 0.91 | 0.52 |
| gpt-5.4-mini | ch | 900 | 46 (5%) | 759 (84%) | 95 (11%) | 0.89 | 0.47 |
| gpt-5.4-mini | de | 600 | 34 (6%) | 452 (75%) | 114 (19%) | 0.81 | 0.43 |
| gpt-5.4-mini | ge | 570 | 75 (13%) | 391 (69%) | 104 (18%) | 0.82 | 0.47 |
| gpt-5.4-mini | sg | 600 | 50 (8%) | 467 (78%) | 83 (14%) | 0.86 | 0.47 |
| gpt-5.4-mini | tw | 600 | 34 (6%) | 483 (80%) | 83 (14%) | 0.86 | 0.46 |
| gpt-5.4-mini | uk | 900 | 83 (9%) | 648 (72%) | 169 (19%) | 0.81 | 0.45 |
| gpt-5.4-mini | us | 900 | 60 (7%) | 642 (71%) | 198 (22%) | 0.78 | 0.42 |
| gpt-5.4-mini | **all three** | 5640 | 454 (8%) | 4287 (76%) | 899 (16%) | 0.84 | 0.46 |
| harvey | br | 570 | 72 (13%) | 451 (79%) | 47 (8%) | 0.92 | 0.52 |
| harvey | ch | 900 | 59 (7%) | 780 (87%) | 61 (7%) | 0.93 | 0.50 |
| harvey | de | 600 | 46 (8%) | 455 (76%) | 99 (16%) | 0.83 | 0.46 |
| harvey | ge | 570 | 79 (14%) | 399 (70%) | 92 (16%) | 0.84 | 0.49 |
| harvey | sg | 600 | 78 (13%) | 473 (79%) | 49 (8%) | 0.92 | 0.52 |
| harvey | tw | 600 | 55 (9%) | 466 (78%) | 79 (13%) | 0.87 | 0.48 |
| harvey | uk | 900 | 139 (15%) | 693 (77%) | 68 (8%) | 0.92 | 0.54 |
| harvey | us | 900 | 66 (7%) | 639 (71%) | 195 (22%) | 0.78 | 0.43 |
| harvey | **all three** | 5640 | 594 (11%) | 4356 (77%) | 690 (12%) | 0.88 | 0.49 |
| legora-1 | br | 540 | 68 (13%) | 434 (80%) | 38 (7%) | 0.93 | 0.53 |
| legora-1 | ch | 900 | 59 (7%) | 818 (91%) | 23 (3%) | 0.97 | 0.52 |
| legora-1 | de | 570 | 49 (9%) | 352 (62%) | 169 (30%) | 0.70 | 0.39 |
| legora-1 | sg | 600 | 74 (12%) | 432 (72%) | 94 (16%) | 0.84 | 0.48 |
| legora-1 | tw | 600 | 57 (10%) | 480 (80%) | 63 (10%) | 0.90 | 0.49 |
| legora-1 | uk | 900 | 128 (14%) | 679 (75%) | 93 (10%) | 0.90 | 0.52 |
| legora-1 | us | 900 | 71 (8%) | 560 (62%) | 269 (30%) | 0.70 | 0.39 |
| legora-1 | **all three** | 5010 | 506 (10%) | 3755 (75%) | 749 (15%) | 0.85 | 0.48 |
| legora-2 | br | 510 | 65 (13%) | 408 (80%) | 37 (7%) | 0.93 | 0.53 |
| legora-2 | ch | 900 | 62 (7%) | 804 (89%) | 34 (4%) | 0.96 | 0.52 |
| legora-2 | de | 600 | 50 (8%) | 362 (60%) | 188 (31%) | 0.69 | 0.39 |
| legora-2 | sg | 600 | 72 (12%) | 440 (73%) | 88 (15%) | 0.85 | 0.49 |
| legora-2 | tw | 600 | 56 (9%) | 484 (81%) | 60 (10%) | 0.90 | 0.50 |
| legora-2 | uk | 900 | 131 (15%) | 686 (76%) | 83 (9%) | 0.91 | 0.53 |
| legora-2 | us | 900 | 72 (8%) | 570 (63%) | 258 (29%) | 0.71 | 0.40 |
| legora-2 | **all three** | 5010 | 508 (10%) | 3754 (75%) | 748 (15%) | 0.85 | 0.48 |

**What is in the “Tie” bucket.** A tie only means *same score against the same two references*, so it merges several different situations. Split by score level, and independently by whether the candidate actually produced the held-out expert's answer:

| Candidate | Ties | Same answer as expert | Different answer, equal score | at 1 (all agree) | at ½ (experts conflict) | at 0 (both differ) |
| --- | --- | --- | --- | --- | --- | --- |
| gemini-3.1-flash-lite | 4338 | 3757 (87%) | 581 (13%) | 2930 (68%) | 901 (21%) | 507 (12%) |
| gpt-5.4-mini | 4287 | 3654 (85%) | 633 (15%) | 2888 (67%) | 855 (20%) | 544 (13%) |
| harvey | 4356 | 3926 (90%) | 430 (10%) | 2986 (69%) | 972 (22%) | 398 (9%) |
| legora-1 | 3755 | 3437 (92%) | 318 (8%) | 2639 (70%) | 796 (21%) | 320 (9%) |
| legora-2 | 3754 | 3446 (92%) | 308 (8%) | 2665 (71%) | 770 (21%) | 319 (8%) |

A tie at ½ is only possible when the two reference experts contradict each other — that caps every achievable score at ½, for the candidate and the held-out expert alike. The two references disagree in 1543 of 5640 comparisons (27%; a property of the human labels, identical for every candidate). Note that reference disagreement is *not* the same thing as a tie: ties also arise, and in fact more often, where the two references agree and the candidate simply matches them.

**Reading.**

- **gemini-3.1-flash-lite** — 77% of the 5640 comparisons are ties. 87% of those ties are real agreement (candidate gave the held-out expert's answer); the other 13% are comparisons where candidate and expert gave *different* answers that happened to score the same, and ρ credits every one of them to the candidate. On the 1302 comparisons that actually discriminate, the human wins 63% (821 vs 481). Dropping instances whose reference is empty throughout leaves ρ (ties split) at 0.46.
- **gpt-5.4-mini** — 76% of the 5640 comparisons are ties. 85% of those ties are real agreement (candidate gave the held-out expert's answer); the other 15% are comparisons where candidate and expert gave *different* answers that happened to score the same, and ρ credits every one of them to the candidate. On the 1353 comparisons that actually discriminate, the human wins 66% (899 vs 454). Dropping instances whose reference is empty throughout leaves ρ (ties split) at 0.47.
- **harvey** — 77% of the 5640 comparisons are ties. 90% of those ties are real agreement (candidate gave the held-out expert's answer); the other 10% are comparisons where candidate and expert gave *different* answers that happened to score the same, and ρ credits every one of them to the candidate. On the 1284 comparisons that actually discriminate, the human wins 54% (690 vs 594). Dropping instances whose reference is empty throughout leaves ρ (ties split) at 0.48.
- **legora-1** — 75% of the 5010 comparisons are ties. 92% of those ties are real agreement (candidate gave the held-out expert's answer); the other 8% are comparisons where candidate and expert gave *different* answers that happened to score the same, and ρ credits every one of them to the candidate. On the 1255 comparisons that actually discriminate, the human wins 60% (749 vs 506). Dropping instances whose reference is empty throughout leaves ρ (ties split) at 0.45.
- **legora-2** — 75% of the 5010 comparisons are ties. 92% of those ties are real agreement (candidate gave the held-out expert's answer); the other 8% are comparisons where candidate and expert gave *different* answers that happened to score the same, and ρ credits every one of them to the candidate. On the 1256 comparisons that actually discriminate, the human wins 60% (748 vs 508). Dropping instances whose reference is empty throughout leaves ρ (ties split) at 0.45.

This is what the alt-test is and is not evidence for. The tie rate is high and mostly genuine, so on this data the models are largely *indistinguishable* from an additional expert — which is exactly the substitutability claim ω and ρ are designed to support, and §3.2 supports it. It is not evidence of superiority: once ties stop counting as wins, ρ sits at chance, and on the comparisons that separate the two the human expert is still ahead. "Can this model replace a human annotator?" and "is this model better than a human annotator?" are different questions, and only the first one is being tested.

## 4. Headline extraction metrics

> Recall = TP / (TP + Mismatch + Missed) over cells the expert filled; precision = TP / (TP + Mismatch + Hallucinated); hallucination = invented values on empty-gold cells. Buckets from `legex/evaluation.py`; per-cell source `../per_column.csv`. n = evaluated label cells; recall and precision carry ±1 SE over their gold-filled / emitted denominators. The per-field grids (§4.2–4.5) break each metric out by variable across models; their `n` is the metric's model-independent denominator (gold-filled for recall, gold-empty for hallucination) and is omitted for precision (emitted; model-dependent) and F1 (composite).

### 4.1 Overall (all countries, summed across fields)

| Model | n | Accuracy | Recall (filled) | Precision | Hallu. rate | F1 |
| --- | --- | --- | --- | --- | --- | --- |
| gemini-3.1-flash-lite | 17017 | 61.5% | 57.8% ±0.5 | 57.4% ±0.5 | 30.3% | 0.576 |
| gpt-5.4-mini | 17006 | 58.5% | 58.7% ±0.5 | 54.2% ±0.4 | 41.9% | 0.563 |
| harvey | 15158 | 61.7% | 51.5% ±0.5 | 64.9% ±0.5 | 16.3% | 0.574 |
| harvey-2 | 15323 | 61.1% | 48.3% ±0.5 | 68.6% ±0.5 | 11.4% | 0.567 |
| legora-1 | 13827 | 65.0% | 52.5% ±0.5 | 73.6% ±0.5 | 8.7% | 0.613 |
| legora-2 | 13981 | 65.0% | 52.7% ±0.5 | 73.3% ±0.5 | 9.1% | 0.613 |

### 4.2 Recall (filled) by field (all countries)

| Field | n | gemini-3.1-flash-lite | gpt-5.4-mini | harvey | harvey-2 | legora-1 | legora-2 |
| --- | --- | --- | --- | --- | --- | --- | --- |
| `court_cost_awarded_nominal` | 501 | 63.9% | 65.5% | 57.9% | 57.0% | 70.1% | 70.4% |
| `defendant_no1_ISIC1_industry_category` | 1075 | 58.0% | 64.7% | 49.2% | 33.7% | 55.5% | 50.7% |
| `defendants_all_count` | 1505 | 76.9% | 73.8% | 71.6% | 71.8% | 66.6% | 65.8% |
| `dispute_value_nominal` | 708 | 56.4% | 57.1% | 47.0% | 33.1% | 34.7% | 39.7% |
| `legal_subject_judgement` | 1541 | 3.6% | 4.9% | 3.9% | 0.7% | 1.8% | 2.2% |
| `party_compensation_awarded_nominal` | 364 | 71.4% | 67.3% | 66.9% | 63.1% | 79.1% | 79.7% |
| `plaintiff_loosing_share` | 1323 | 71.3% | 69.9% | 71.4% | 69.7% | 69.3% | 70.8% |
| `plaintiff_no1_ISIC1_industry_category` | 865 | 54.1% | 53.9% | 41.8% | 31.3% | 36.8% | 36.9% |
| `plaintiffs_all_count` | 1532 | 88.8% | 85.4% | 74.9% | 77.6% | 70.5% | 72.4% |
| `trial_end_date` | 1487 | 67.6% | 66.9% | 65.0% | 65.0% | 77.8% | 77.0% |
| `trial_start_date` | 916 | 26.2% | 41.6% | 13.3% | 15.1% | 27.3% | 27.2% |

### 4.3 Precision by field (all countries)

| Field | gemini-3.1-flash-lite | gpt-5.4-mini | harvey | harvey-2 | legora-1 | legora-2 |
| --- | --- | --- | --- | --- | --- | --- |
| `court_cost_awarded_nominal` | 82.9% | 72.9% | 85.2% | 83.7% | 94.7% | 94.8% |
| `defendant_no1_ISIC1_industry_category` | 50.6% | 52.1% | 55.8% | 51.1% | 70.6% | 65.1% |
| `defendants_all_count` | 76.6% | 80.3% | 85.0% | 84.6% | 85.7% | 88.5% |
| `dispute_value_nominal` | 45.6% | 42.3% | 45.5% | 46.7% | 63.0% | 63.2% |
| `legal_subject_judgement` | 3.6% | 4.9% | 4.8% | 1.3% | 3.0% | 3.7% |
| `party_compensation_awarded_nominal` | 74.1% | 55.9% | 77.2% | 75.9% | 80.2% | 79.7% |
| `plaintiff_loosing_share` | 74.1% | 68.6% | 76.7% | 85.2% | 90.4% | 85.6% |
| `plaintiff_no1_ISIC1_industry_category` | 35.5% | 35.2% | 49.2% | 48.2% | 54.0% | 55.8% |
| `plaintiffs_all_count` | 89.1% | 89.8% | 88.6% | 89.6% | 94.5% | 93.4% |
| `trial_end_date` | 68.3% | 71.1% | 91.8% | 85.9% | 87.8% | 88.2% |
| `trial_start_date` | 58.8% | 32.4% | 57.1% | 67.4% | 78.7% | 80.7% |

### 4.4 Hallucination rate by field (all countries)

| Field | n | gemini-3.1-flash-lite | gpt-5.4-mini | harvey | harvey-2 | legora-1 | legora-2 |
| --- | --- | --- | --- | --- | --- | --- | --- |
| `court_cost_awarded_nominal` | 1046 | 4.1% | 8.3% | 1.9% | 0.8% | 0.9% | 0.7% |
| `defendant_no1_ISIC1_industry_category` | 472 | 65.9% | 74.7% | 37.3% | 27.4% | 22.4% | 28.5% |
| `defendants_all_count` | 42 | 90.5% | 56.1% | 48.6% | 62.2% | 37.1% | 18.4% |
| `dispute_value_nominal` | 839 | 44.0% | 53.8% | 32.9% | 20.4% | 12.3% | 12.9% |
| `legal_subject_judgement` | 6 | 83.3% | 100.0% | 83.3% | 0.0% | 16.7% | 16.7% |
| `party_compensation_awarded_nominal` | 1183 | 6.6% | 13.6% | 4.7% | 4.9% | 4.2% | 4.5% |
| `plaintiff_loosing_share` | 224 | 36.6% | 55.2% | 33.3% | 15.9% | 11.4% | 16.3% |
| `plaintiff_no1_ISIC1_industry_category` | 682 | 79.5% | 80.5% | 25.4% | 18.8% | 16.9% | 14.8% |
| `plaintiffs_all_count` | 15 | 100.0% | 71.4% | 83.3% | 66.7% | 28.6% | 35.7% |
| `trial_end_date` | 60 | 50.0% | 44.1% | 12.3% | 14.0% | 13.5% | 13.2% |
| `trial_start_date` | 631 | 9.7% | 61.3% | 4.4% | 3.3% | 3.6% | 3.6% |

### 4.5 F1 by field (all countries)

| Field | gemini-3.1-flash-lite | gpt-5.4-mini | harvey | harvey-2 | legora-1 | legora-2 |
| --- | --- | --- | --- | --- | --- | --- |
| `court_cost_awarded_nominal` | 0.722 | 0.690 | 0.689 | 0.679 | 0.806 | 0.808 |
| `defendant_no1_ISIC1_industry_category` | 0.540 | 0.578 | 0.523 | 0.406 | 0.621 | 0.570 |
| `defendants_all_count` | 0.768 | 0.769 | 0.777 | 0.777 | 0.750 | 0.755 |
| `dispute_value_nominal` | 0.504 | 0.486 | 0.463 | 0.387 | 0.447 | 0.488 |
| `legal_subject_judgement` | 0.036 | 0.049 | 0.043 | 0.009 | 0.023 | 0.028 |
| `party_compensation_awarded_nominal` | 0.727 | 0.611 | 0.717 | 0.689 | 0.797 | 0.797 |
| `plaintiff_loosing_share` | 0.727 | 0.692 | 0.740 | 0.767 | 0.784 | 0.775 |
| `plaintiff_no1_ISIC1_industry_category` | 0.429 | 0.426 | 0.452 | 0.379 | 0.438 | 0.444 |
| `plaintiffs_all_count` | 0.889 | 0.875 | 0.812 | 0.832 | 0.807 | 0.816 |
| `trial_end_date` | 0.679 | 0.690 | 0.761 | 0.740 | 0.825 | 0.822 |
| `trial_start_date` | 0.362 | 0.364 | 0.216 | 0.247 | 0.405 | 0.406 |

## Appendix

### Landis–Koch (1977) κ scale (for interpreting the ISIC κ)

| κ | Strength |
| --- | --- |
| < 0.00 | Poor (worse than chance) |
| 0.00 – 0.20 | Slight |
| 0.21 – 0.40 | Fair |
| 0.41 – 0.60 | Moderate |
| 0.61 – 0.80 | Substantial |
| 0.81 – 1.00 | Almost perfect |

### Provenance

- Pairwise agreement & kappa: `legex/analysis/iaa.py` (`pairwise_agreement`, `write_kappa_audit_csv`).
- Alt-test: authors' reference implementation ([github.com/nitaytech/AltTest](https://github.com/nitaytech/AltTest)) run via `scripts/alt_test_reference.py` → `alt_test_reference_*.csv` (see README).
- Alt-test win/tie/loss decomposition: `scripts/alt_test_decomposition.py` → `alt_test_decomposition.csv`.
- Tolerant comparator: `legex/evaluation/comparison.py` (`values_agree`, `normalise`).
- Headline buckets: `legex/analysis/aggregate.py` over `legex/evaluation.score_country`.
- This report: `legex/analysis/report.py`.