Chapters in part 3
Click a chapter to open its detailed mind map.
Seeing, knowing, enabling
Mind map of chapter 17: objectivation requires three distinct gestures — seeing (assembling a material), knowing (making it intelligible), enabling (turning it into an instrument). The chapter sets the invariant form of the material (a table of criteria and evaluations), names APMC the use made here of MCDA tools, defines what a criterion is, and lays out the itinerary of the part.
Building the material
Mind map of chapter 18: the chapter establishes three things and three only — the structure of the table (columns = criteria built from the seventeen variables, rows = repeated evaluations grouped in blocks), the filling rules (common orientation and scale fixed before collection, written instructions, context L attached to each evaluation), and preprocessing (repairing, transforming, qualifying — never silently).
The test set
Mind map of chapter 19: lacking collection, the test set is built by hand and frozen. The contrast between the two regimes plays out on the triplet, with arbitrary values — L_d at (80, 35, 50), L_p at (30, 75, 60); closure and recognition are inverted, the translation requirement stays neutral. Ten criteria on [0, 100], all read "more is better". The axioms of Part II fix the direction of the contrasts, the amplitude is a choice — and that is where the fictional character of the table resides.
Scores
Mind map of chapter 20: a score is never collected data but a constructed value, presupposing an operator and declared weights. Two species by direction — the score of a criterion, the score of an evaluation — and two profiles. The chapter follows only the column direction: rows are what reveal columns. The operator retained is the discrete upper median, because it stays on the collection scale. No aggregate suffices alone: the minimal pair associates position and dispersion.
Comparing criterion by criterion
Mind map of chapter 21: monocriterion means never combining two criteria into a single number. The gap Δ_j gives the local preference — L_p wins on nine criteria, L_d on C_1 alone, with no ties. The sign is not enough: an indifference threshold decides below which amplitude a gap will not be read, and it is decided, not read off the data. Dispersion answers two distinct questions — internal agreement within a block, separation between blocks. The signs read together establish that the two regimes are incomparable: an arbitration is required, and everything hinges on C_1.
Multicriteria comparison
Mind map of chapter 22: multicriteria compresses one notch further, and we lose track of which criterion won the verdict. The identity U(w) = Σ w_j Δ_j links the weighted sum to the monocriterion gaps: weighting does not replace criterion-by-criterion reading, it weighs it. More than 71 % of the weight on C_1 is needed to reverse the ranking. The weighted sum is compensatory; letting criteria vote gives L_p by nine votes to one, and the two rules do not tip at the same point — the gap between thresholds measures exactly what compensation permits. No aggregation family escapes Arrow's theorem.
Simulating
Mind map of chapter 23: the frozen table suggested four false things — that the retained evaluation was the evaluation, that the weights went without saying, that the world was neutral, that a single evaluator was looking. Simulating means redoing N times the gesture made once. Redrawing evaluations never reverses the conclusion; reopening the weights spreads it without displacing it, with 0.11 % of deliberate reversals; only context makes the comparison undecided — under media polarisation, nearly one draw in four places L_d ahead. Hence a hierarchy of fragilities: facts, priorities, state of the world.
Factor analysis
Mind map of chapter 24: a table is two clouds, and the duality scheme — table, metric, weights — is the common frame that PCA and CA fill in two ways. PCA calls structure linear association, CA calls it dependence: zero correlation does not imply independence, zero inertia in CA does. On the table, PCA carries 84.9 % of the inertia on one axis opposing nine criteria to the primacy of common law alone — the single crossing of chapter 21, recovered geometrically. The PCA/CA convergence at +0.94 is a coherence check, not a discovery. Ten criteria measure roughly one.
Discriminant analysis
Mind map of chapter 25: the inertia of a partitioned cloud decomposes exactly, I_T = I_B + I_W, and 72.8 % of the inertia lies in the gap between blocks. Fisher's criterion maximises the ratio of separation to dispersion; with two groups the solution is the line of centres reweighted by internal stability. Separating is not spreading: the discriminant axis correlates only at 0.86 with the first factorial axis, and the criterion that carried the latter receives the smallest coefficient here. The most useful criterion is the one that separates least on its own — because it separates differently. Hence the distinction between marginal and conditional contribution.
Automatic clustering
Mind map of chapter 26: the three methods of the part differ by the information they receive — factor analysis receives the table and returns axes, discriminant analysis also receives the groups, clustering receives only the table and returns the groups. Clustering requires four decisions: proximity, quality criterion, construction strategy, stopping rule. Minimising I_W and maximising I_B are one problem. The procedure converges to a local minimum: the starting point decides the end point. A computed partition has no general reason to recover a declared one; here it does, and the structure is stable where the detail is not.
Bayesian modelling
Mind map of chapter 27: six command and environment parameters — closure, institutional recognition, translation requirement, encounter arrangements, structural segregation, effective primacy of common law — act, through effective mixing, on an audit vector. The objects of the network do not share the same status: edges and their directions come from Part II and can only be discussed by going back there; the quantities are numerical conventions, and sensitivity analysis answers to them alone. The chapter discovers nothing and can discover nothing: it checks that the probabilistic engine restates what the axioms said. Three uses: predicting, diagnosing, measuring the reduction of uncertainty.
From the simulator towards a shared observatory of laïcité
Mind map of chapter 28: the LaïciScope observatory is the first public version of the platform embodying the whole method of the book. V1 is open, free, anonymous, GDPR-compliant, entirely executed in the browser — none of the analytical content is collected server-side. Four sub-spaces: sourced conversation, deterministic causal atlas, probabilistic Bayesian network, analysis and comparison. The book's sandbox is delivered ready to handle: two regimes, two experts, two contexts, ten criteria, 160 rows. Every project is exportable with its proof of computation — a result without documentation of the chain that produced it is explicitly refused.
Conclusion of Part III
Mind map of chapter 29: Part III made the arbitrations explicit — criteria, scores, weightings, scenarios. Dominance is rare, incomparability is normal: it signals real trade-offs. Context and uncertainty can reverse a conclusion, and robustness is measured. The four re-readings of the same material differ by what they receive: the table alone yields axes or groups, the table plus a partition yields a separating axis, the axioms yield degrees. In a model backed by an axiomatics, not everything is contested in the same place. A shared observatory is legitimate only if it presents its results as conditional.