Most sociological mathematical models are formed by thinking about the relationships involved qualitatively, then building models that are simple, have those qualitative aspects, and can be worked with. Then you can gather data, compare the models to the data, and revise the models.

Take the Cobb-Douglas model of a production function. It was pulled out of someone's mind (not their ass) in just such a manner. Perhaps by luck, it never needed to be revised, because it turned out to model real data very well.

The use of a "bias function" is the really questionable thing here. Is what is really going on that people add imputed believability to someone who is biased, or can you get the same results just by saying that people agree with people who agree with them? You can't get the same results easily in this case, because moderates don't make the same kind impassioned defense of other moderates. You could suppose opinions are not evenly-distributed and conclude that moderates would do that, if there were more of them. Or you could explain the data as signalling group affiliation rather than having to do with belief.

Whatever explanation you prefer, putting it in math (when done well) distinguishes these different parts of the argument and makes these critical points more apparent.

(Some models are built by looking at a lot of data and noticing patterns, like Zipf's law. Some, more often found in physics, are built from the ground up, like E=mc^2. Those are better, if we can make them.)