In a comment to Can we hold intellectuals to similar public standards as athletes? I said that one of the largest problems with using prediction accuracy (EG prediction markets) as the exclusive standard by which we judge intellectuals would be undervaluing contributing to the thought process.

Here, I propose a modification of prediction markets which values more types of contributions.

Arguments as Models

In many cases, a thought/argument can be reformulated as a model. What I mean by this is a formally described way of making predictions.

Adding models to prediction markets could increase their transparency; we want to create an incentive for traders to explain themselves.

A model has a complexity (description length; the negative log of its prior probability). We generally have more respect for predictions which come from models, in contrast to those which don't. And, given two models, we generally have more respect for the simpler one.

So, to adjust prediction markets to account for models, we would want something which:

Values making good predictions over everything else;
Values models over opaque predictions;
Values simple models more.

But how can we trade off between modelling and predictive accuracy?

Time Travel Markets

As I've discussed before, one of the major differences between prediction markets and Bayesianism is that prediction-market traders only get credit for moving the market in the right direction, which introduces a dependence on when a prediction is made: if you make an accurate prediction at a time when everyone else has already arrived at that conclusion, you don't get any credit; whereas, if you make an accurate prediction at a time when it's unpopular, you'll get a lot of credit for that.

That's a problem for model-makers. An explanation is still useful, even after all the facts needing explanation are agreed upon.

This is a generalization of the problem of old evidence.

Solomonoff induction solves the problem of old evidence for Bayesians as follows: a new hypothesis which explains old evidence is evaluated as if it were in our set of hypotheses from the beginning. (After all, it would have been in the Solomonoff prior from the beginning; it was only absent from our calculations because we are forced to approximate Solomonoff.) The prior probability is based on the complexity of the hypothesis; the updates are whatever they would have been....