Utility Functions

A utility function is a direction. It is what an effort points at, the star that says this way and not that way. Everything a person does, everything an institution does, is bent toward some such point, whether or not the point was ever named.

A direction cannot be averaged.

That is the whole of it. Averaging finds a center. The typical, the mean, the thing a spread surrounds. It works on quantities that have a center. Direction has none. Average two people who want different things and you do not get a third thing worth wanting. You get the vector between them, which points where neither would go, and usually nowhere. Add enough wants that pull against each other and they cancel. The centroid of a crowd's directions has almost no length. It points at the middle of the disagreement, which is a place no one was trying to reach.

This is why you cannot design by committee. A committee tries to find a direction by aggregation. It averages the wants of the room into a single arrow. But direction is not what averaging returns. The room produces a centroid, the centroid is short, and the effort built on it moves without pointing anywhere. It stays busy and it arrives nowhere, and everyone inside can feel the nowhere without being able to name it.

Choosing a direction is not a computation. It is the first act. Intelligence stating what matters, the seeing that says here. It cannot be handed to aggregation, because aggregation is the second act, the finding of centers, and there is no center here to find. One person who sees can point. A thousand who vote cannot produce a pointing, and this is not a slight against the thousand. It is a theorem. Arrow proved it in 1951: no procedure can aggregate individual rankings into a collective ranking while satisfying even a short list of conditions any fair procedure must meet. The impossibility is not in the voters. It is in the arithmetic. Voting settles many things well, who governs, who is accountable, what a group will consent to. What it cannot manufacture is a direction, because direction was never the kind of thing aggregation returns.

So a utility function is right or wrong before any of its results are in. A right one is a direction that someone saw and holds, single and coherent, kept honest by contact with the world. A wrong one is the centroid. Worse than the centroid is a direction manufactured elsewhere and installed, agreed to without ever being seen. The manufactured kind does the most damage, because it wears the look of alignment while pointing nowhere. A room can be made to nod at a goal that none of them can see. The nodding is not seeing. The arrow is still short.

What we have now, almost everywhere, is the short arrow. Knowledge sits in silos, held by people and institutions that share no direction and are worked into the appearance of one. A civilization optimizing hard and arriving nowhere, because the thing it optimizes was averaged out of a billion wants that never pointed the same way.

The correction is not a new goal to install. That is only one more manufactured arrow. The correction is a single seeing, actually pointed, and the refusal to average it away.