It's worth noting that "we" is ill-defined here.

Supposing that what this site does successfully improves rationality among its participants, then we should expect that someone like me who has only been here for a few months would be less rational than the folks who have been around for years and benefiting from the site.

But a discussion of politics here would not exclude me, so even in that scenario we would expect such a discussion not to lead to convergence.

The proper empirical test, I suppose, would be to identify cohorts based on their tenure here, and conduct a series of such conversations within each such cohort -- say, once a year -- and evaluate whether a given cohort comes closer to convergence from year to year.