Writing a voting rule into the training objective

Definition · Jürgen Habermas, Between Facts and Norms (1992)

This concept locates legitimacy in the exchange of reasons among equals: participants justify their views to each other, free of coercion, and remain able to change their minds. Counting votes or averaging preferences does not produce it, because the reasoning is what does the work.

Analysis

Every member of this family swaps one tallying rule for another — a maximal lottery (NEW-S36), the Nash equilibrium of a preference model (NEW-S38), maximin over a mixture of reward models (NEW-S37), proportional representation of the evaluator distribution (NEW-S41), a pessimistic median of MLEs (NEW-S154), or a literal majority ballot in Democratic AI (NEW-S158). All of them run on judgments already harvested from people who never meet each other, and no stage exists at which anyone defends a comparison, hears an objection, or revises a rating. Democratic AI is the sharpest case: real humans do vote, and the vote is the whole of the legitimacy claim, which is precisely the substitution Habermas denies. The analytical papers (NEW-S40, NEW-I3, NEW-S154) study properties of counting rules, so they inherit the same restriction.

Definition · Jean-Jacques Rousseau, The Social Contract (1762)

This distinction separates what is good for a public in common from the sum of what its members privately want. Aggregating private wants, however fairly, does not produce the former, since the two can and often do diverge.

Analysis

The input to every rule here is a private want — a labeler's comparison between two outputs, or in NEW-S158 a player's judgment of a redistribution rule that sets his own payoff — and the papers differ only in how those wants are weighted: worst-off, Condorcet, proportional, median. Rousseau's distinction turns on the input rather than the weighting, since the general will requires citizens to judge what is good in common, and nothing in the pipeline asks for that judgment or could tell it apart from self-interest. NEW-S41 is the clearest illustration: proportionality is a promise to mirror the population's private distribution faithfully. NEW-S40 proves a formal cousin of the gap — aligning to everyone must override some individual's private ethics — but treats it as an impossibility for tallying, not as a reason to seek a different object.

Definition · John Rawls, A Theory of Justice (1971)

This device requires that rules be chosen without knowledge of which position the chooser will occupy under them, e.g., rich or poor, majority or minority. Not knowing generally pushes the chooser to protect the worst-off position, since it may turn out to be their own.

Analysis

MaxMin-RLHF writes the veil's characteristic output straight into the loss: it clusters raters into groups and maximizes the worst-off group's reward, so a majority's mild gains cannot buy a minority's loss. What is entirely missing is the device itself — the maximin objective is imposed by the designer, not reached by choosers deprived of knowledge of their position, and every rater in every paper reports from their own standpoint with their group membership inferred rather than hidden. Democratic AI runs the inversion: players vote on redistribution rules knowing exactly what each rule pays them, and an egalitarian mechanism is one of the baselines their self-interested votes defeat. Claimed is IMPLIED because MaxMin-RLHF sells its objective in the egalitarian-justice vocabulary the veil underwrites, and NEW-S158 names a Rawlsian-style baseline, while no source asserts position-blind choice.

Definition · T. M. Scanlon, What We Owe to Each Other (1998)

This test holds a principle justified only if no individual could reasonably reject it, and it is applied person by person rather than in aggregate. One sufficiently strong objection therefore outweighs many mild preferences, which is the case averaging handles wrongly.

Analysis

MaxMin-RLHF has the structural shape Scanlon's test demands: the group with the lowest reward sets the objective, so no accumulation of mild approvals can outweigh it. Two things are missing. The unit is a latent cluster discovered by fitting a mixture, not a person, and the strength of an objection enters only as a scalar reward value rather than as a reason anyone could state and have answered; nobody is given standing to reject anything. And the rest of the family runs the other way — maximal lotteries, Nash equilibria, proportional alignment and Democratic AI's majority-vote training objective all let many weak preferences beat one severe complaint by construction, which NEW-S154 sharpens by showing how far a single participant's report can be made to matter or not matter at all.

Social choice theory brings formal limits with it. Arrow's theorem shows that no voting rule can turn individual rankings into a group ranking while meeting a small set of basic fairness conditions at once. These works import that result into alignment, which establishes what aggregation cannot be expected to deliver.

Democratic theory has constitutional design and it has ratification, but it assumes a rule is drafted by someone and then put to the people. Here the rule is searched for by reinforcement learning with the vote as the objective function, and the electorate is simulated during training so that candidate mechanisms can be tested against modelled players before real ones vote. Neither Rousseau nor Rawls nor Habermas describes a legislator that proposes and discards institutions at that rate, or a public modelled closely enough to be optimized against.