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Add MFQ-2 per-zone p90 respondent ellipses to ipsative map
respondent_profiles now returns countries alongside profiles; plot_ipsative_pca gains respondent_zones -> a p90 Gaussian ellipse per IW zone of the projected Atari respondent cloud (edge-only, no scipy). mfq2 uses these real-respondent ellipses; the other instruments keep country-mean hulls. Journal notes the finding: individual profiles overlap across cultures (within >> between variance), so only the country-mean hull reproduces the Economist's clean zone blobs. Co-Authored-By: Claudypoo <288921227+claudypoo@users.noreply.github.com>
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wassname
@@ -725,3 +725,27 @@ stronger steering. The binding constraint on a joint-coherent C across all five
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instruments is the side instruments' -C neutral-degeneracy (profile pins to 3.0,
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already at C=1; pmass stays ~1.0), a model property, not an ordinal coherence
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break. C=1 stands as a valid, coherent real coefficient.
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## 2026-07-04 — Inglehart-Welzel zone overlays on the ipsative maps (Economist comparison)
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Prompted by the Economist's "Godless hippies" chart placing AI models on the WVS
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Inglehart-Welzel cultural map. Added two zone overlays to plot_ipsative_pca:
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country-mean convex HULLS (all instruments) and, for mfq2 only, per-zone p90
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respondent ELLIPSES (real Atari individuals). Caller owns the IW taxonomy +
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name/ISO2 normalizer (scripts/plot_steer_showcase.py), fails loud on unmapped
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countries; the corrupt big5 "(nu" row (n=369, country unidentifiable from the
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aggregate CSV) is excluded with a warning.
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Finding: the two methods answer different questions and only the hull matches the
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Economist look. The country-mean hull separates zones cleanly (between-country
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signal), because society means are low-variance. The individual-respondent p90
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ellipse is HUGE and overlaps every neighbour -- within-culture variance dominates
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between-culture variance in MFQ-2 foundations (the standard Atari/Graham result),
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so at the person level the zones are not separable. What still separates at the
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individual level is the zone CENTROID (labelled): African-Islamic top, Confucian
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by Japan, Latin America left, the Europes right, English-Speaking lower-centre.
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So the Economist's clean "zone blobs" are hulls over country dots, not contours
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over people; a person-level contour honestly shows the overlap the country-mean
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view hides. Secondary caveat: several mfq2 zones are single-country in the Atari
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19 (Confucian=Japan, Orthodox=Russia, Protestant=Switzerland), so those ellipses
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are one country's spread wearing a zone label.
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@@ -104,6 +104,13 @@ ECONOMIST_OUTLIERS = {"China", "South Korea", "United States", "Great Britain",
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"Nigeria", "Pakistan", "Sweden"}
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def _zone_of(country: str) -> str | None:
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"""IW zone of a verbatim country string, or None for a known-corrupt row. KeyErrors (fail loud)
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on an unrecognised country so a normalization bug can't silently drop it."""
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canon = _COUNTRY_CANON.get(country, country)
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return None if canon is None else IW_ZONE[canon]
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def zones_for(countries: list[str]) -> tuple[dict[str, list[str]], set[str]]:
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"""Group verbatim country strings by IW zone + the subset to emphasize. Fails loud (KeyError)
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on a country absent from the taxonomy so a name-normalization bug can't silently drop a dot from
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@@ -112,12 +119,12 @@ def zones_for(countries: list[str]) -> tuple[dict[str, list[str]], set[str]]:
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dropped: list[str] = []
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emph: set[str] = set()
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for c in countries:
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canon = _COUNTRY_CANON.get(c, c)
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if canon is None:
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z = _zone_of(c)
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if z is None:
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dropped.append(c)
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continue
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groups.setdefault(IW_ZONE[canon], []).append(c)
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if canon in ECONOMIST_OUTLIERS:
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groups.setdefault(z, []).append(c)
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if _COUNTRY_CANON.get(c, c) in ECONOMIST_OUTLIERS:
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emph.add(c)
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if dropped:
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logger.warning(f"excluded known-unmapped countries from zone hulls: {dropped}")
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@@ -269,16 +276,23 @@ def plot_ordinal(run_dir: Path, out: Path, name: str, vec_label: str, C: float,
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# fit the ipsative PCA on it (better-conditioned, the true envelope). Other instruments have no raw
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# per-person data, so scatter a marginal resample from each country's published mean+sd as the haze
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# while keeping the PCA basis on the society means M.
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# mfq2 has real per-respondent data -> draw a p90 respondent ELLIPSE per zone (grounded in
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# people) and drop the country-mean hull. Other instruments have only society means -> the
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# country-mean convex HULL is the best-available zone blob.
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_, emph = zones_for(countries)
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if name == "mfq2":
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respondents, haze = T.maps.respondent_profiles(dims, instr.scale_max), None
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resp_countries, respondents = T.maps.respondent_profiles(dims, instr.scale_max)
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haze, zones = None, None
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respondent_zones = [_zone_of(c) for c in resp_countries]
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else:
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respondents, haze = None, human_haze(instr)
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zones, respondent_zones = zones_for(countries)[0], None
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traj = {c: _frac(prof_c[c], instr.scale_max) for c in coh_cs}
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zones, emph = zones_for(countries)
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figm = T.maps.plot_ipsative_pca(instr, dims, countries, Mfrac,
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_frac(base, instr.scale_max), _frac(pos, instr.scale_max),
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_frac(neg, instr.scale_max), respondents=respondents, haze=haze,
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traj=traj, zones=zones, emphasize=emph, labels=labels)
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traj=traj, zones=zones, emphasize=emph,
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respondent_zones=respondent_zones, labels=labels)
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figm.axes[0].set_title(f"{instr.display}: humans vs LLMs steered for {vec_label}", fontsize=10)
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paths = [T.maps.save_both(figm, out / name, "map_pca_ipsative")]
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plt.close(figm)
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+33
-7
@@ -25,6 +25,7 @@ from pathlib import Path
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import numpy as np
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import matplotlib.pyplot as plt
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from matplotlib.patches import Ellipse
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from .instrument import Instrument
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@@ -42,11 +43,12 @@ MFQ2_FOUNDATION_ITEMS = {
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}
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def respondent_profiles(foundations: list[str], scale_max: int = 5) -> np.ndarray:
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def respondent_profiles(foundations: list[str], scale_max: int = 5) -> tuple[list[str], np.ndarray]:
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"""Per-respondent MFQ-2 6-foundation profiles (each foundation = mean of its 6 raw 1-5 items),
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returned as 0-1 FRACTION (same scale as `M` in plot_ipsative_pca) in `foundations` order.
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Rows with any NA in the keyed items are dropped (fail-fast, no imputation). MFQ-2 only --
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keying is MFQ2_FOUNDATION_ITEMS. Source: data/atari_study2_raw.csv (Atari et al. 2023 Study 2)."""
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returned as (countries, X) where X is a 0-1 FRACTION matrix (same scale as `M` in
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plot_ipsative_pca) in `foundations` order and `countries[i]` is respondent i's country. Rows with
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any NA in the keyed items are dropped (fail-fast, no imputation). MFQ-2 only -- keying is
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MFQ2_FOUNDATION_ITEMS. Source: data/atari_study2_raw.csv (Atari et al. 2023 Study 2)."""
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raw_path = DATA / "atari_study2_raw.csv"
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rows = list(csv.DictReader(raw_path.open(newline="")))
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cols = rows[0].keys()
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@@ -55,13 +57,14 @@ def respondent_profiles(foundations: list[str], scale_max: int = 5) -> np.ndarra
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raise KeyError(f"keying columns absent from {raw_path.name}: {missing}")
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def cell(v: str) -> float:
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return np.nan if v in ("NA", "", "-99") else float(v)
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out = []
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out, countries = [], []
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for r in rows:
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prof = [np.mean([cell(r[c]) for c in MFQ2_FOUNDATION_ITEMS[f]]) for f in foundations]
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if not np.isnan(prof).any():
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out.append(prof)
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countries.append(r["country"])
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X = np.array(out) # (n_resp x K), raw 1-5
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return (X - 1) / (scale_max - 1) # -> 0-1 fraction
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return countries, (X - 1) / (scale_max - 1) # -> 0-1 fraction
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# range-plot palette + geometry (shared with the experiment's prior fig_profile_sweeps look)
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CLOUD_GREY = "0.78" # individual respondents (subtle backdrop)
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@@ -216,6 +219,7 @@ def plot_ipsative_pca(instr: Instrument, dims: list[str], countries: list[str],
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traj: dict[float, np.ndarray] | None = None, traj_incoherent: set | None = None,
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boots: dict | None = None,
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zones: dict[str, list[str]] | None = None, emphasize: set[str] | None = None,
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respondent_zones: list[str] | None = None,
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labels: tuple[str, str, str] = ("baseline (c=0)", "honest (c=+2)", "dishonest (c=-2)")):
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"""Ipsative culture map. M is societies x K (0-1 fraction); base / pos / neg are the length-K
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fraction vectors for the base model and its two steer poles (or None). `labels` is the legend
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@@ -235,7 +239,10 @@ def plot_ipsative_pca(instr: Instrument, dims: list[str], countries: list[str],
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each zone with >=3 members gets a shaded convex hull (echoes the Economist WVS map's zone blobs),
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testing whether moral-foundation space recovers the WVS clusters. `emphasize` is a subset of
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`countries` labelled bold-first so named outliers (China, US, Sweden...) always survive the
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label-collision drop. Returns the Figure."""
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label-collision drop. `respondent_zones` (length = rows of the projected cloud, i.e.
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`respondents` when `haze` is None) is each respondent's IW zone; each zone with enough respondents
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gets a p90 Gaussian ellipse of its cloud (the real-respondent analogue of a zone hull, mfq2 only).
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Returns the Figure."""
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try:
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import textalloc as ta
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except ImportError:
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@@ -256,6 +263,25 @@ def plot_ipsative_pca(instr: Instrument, dims: list[str], countries: list[str],
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Pi = (cloud @ Pc - mu) @ Vt[:2].T
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ax.scatter(Pi[:, 0], Pi[:, 1], s=4, c="#8f8a7e", alpha=0.14, edgecolors="none",
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zorder=1, rasterized=True)
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# Per-zone p90 respondent ellipse (mfq2 only): the real-respondent analogue of a zone hull.
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# A 90%-mass contour of the bivariate-Gaussian fit to each zone's projected cloud; the radius
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# is the chi-square(2 dof) 0.90 quantile, sqrt(4.605)=2.1459 (hardcoded to avoid a scipy dep).
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if respondent_zones is not None:
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assert len(respondent_zones) == Pi.shape[0], "respondent_zones must align with the cloud rows"
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zr = np.asarray(respondent_zones)
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for zname in dict.fromkeys(respondent_zones): # stable order, unique
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zp = Pi[zr == zname]
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if len(zp) < 30: # too few respondents -> unreliable contour
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continue
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cen = zp.mean(0)
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evals, evecs = np.linalg.eigh(np.cov(zp.T))
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ang = np.degrees(np.arctan2(evecs[1, -1], evecs[0, -1]))
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w, h = 2 * 2.1459 * np.sqrt(np.maximum(evals[::-1], 0))
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zcol = ZONE_COLORS.get(zname, "#888888")
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ax.add_patch(Ellipse(cen, w, h, angle=ang, facecolor="none",
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edgecolor=zcol, alpha=0.75, lw=1.4, ls="--", zorder=1.6))
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ax.text(cen[0], cen[1], zname, fontsize=8.5, color=zcol, ha="center",
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va="center", style="italic", fontweight="bold", zorder=2, alpha=0.9)
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# Inglehart-Welzel zone hulls: a shaded convex blob per zone with >=3 member societies, drawn
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# UNDER the society dots (zorder<3). The zone name sits at the hull centroid in grey, echoing the
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# Economist WVS map. A 2-member zone has no polygon, so it's shown as its connecting segment.
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