Six dimensions rather than two: what is gained, what is lost

On a single line, two people located at the same point are deemed to think the same thing. As soon as an axis is added, one discovers that they may frankly disagree about the relation to authority, about the level at which the decision should be taken or about the place given to collective norms.

The gain is not cosmetic. It makes it possible to account for common combinations that a single line must treat as anomalies: a strong demand for social protection combined with distrust of supranational institutions, or great tolerance about ways of life combined with a high expectation of public order.

It also changes the nature of what can be said to someone. On a line, one can only place them nearer to or further from a camp. On several dimensions, one can show them where they take a side, where they hesitate, and where they part company with those who otherwise resemble them.

The reliability of a measurement depends on the number of items feeding it. At constant questionnaire length, adding a dimension means taking questions away from the others, and therefore measuring each axis with a little less certainty. There is a point beyond which one gains in apparent fineness what one loses in real solidity.

The second cost is cognitive. A position on two axes is read at a glance on a plane; a position on six cannot be visualised directly. Intermediate representations are then needed, radar or bars, and one must accept that none shows everything at once.

The third cost is that of interpretation. The more dimensions there are, the more small gaps there are that have no statistical significance and that the reader will nonetheless comment on. An honest model must state below what gap nothing should be concluded.

A dimension deserves to exist if it separates people whom the other dimensions conflate. If it merely duplicates another, it inflates the description without teaching anything: two strongly correlated axes tell the same story twice.

It must also be stable: questioned twice a few weeks apart, the same person should end up in the same place, allowing for noise. An unstable dimension measures mood or recent news rather than a conviction.

The choice of six is therefore in no way magical, and any serious model should be able to say why it settles on that number. The right question to put to a typology is not how many axes it uses, but what each one makes it possible to distinguish that the others do not.

Two-dimensional representations, often an economic axis and an authoritarian one, have a considerable merit: they are read instantly and allow many people to be compared at a single glance. No six-dimensional representation offers that.

The reasonable use therefore consists in combining the two: a two-axis view to situate oneself, and a dimension-by-dimension reading to understand. Setting them against each other would be a mistake; they do not answer the same question.

Three questions are enough to judge the seriousness of a typology. What does each dimension measure, and with how many items? What variation is observed when the same person retakes the test? And below what gap does the model refuse to conclude?

A model that answers none of the three is not necessarily wrong, but it asks to be taken on trust. A model that answers them, even modestly, allows the reader to know what they are holding.