Common-knowledge arbitrage

Hypothesis 1: Ask people what they think about a stock or a political issue, and also what they think “most people” think. Where these guesses are the same, predictions about the outcome will be right. Where they differ, outcomes will have more upsets.
There are a few places where I would ultimately want to see this perspective go. One would look at advertising and other goal-oriented broadcasts as aimed at strategically creating a difference between what people think and what they think others think. Another would try to predict changes in finance markets based on these differences. This perspective will be useful in any domain where people don’t merely act on what they think, but on the differences with their estimate of common knowledge. It will also be useful in domains where people’s expressed opinions differ from their privately held ones.
Hypothesis 2: Holding everything else still, average opinion and the average of estimates of public opinion will tend toward being equal.
If this second guess is true, a systematic significant difference between the average opinion and the average estimate of public opinion could provide an objective measure of propaganda pressure, one that could be used to assign a number to the strength of social pressure that is being applied by a goal-oriented agent working on a population through the mass media ecosystem.
But maybe that is too conspiracy theory-ey, and too top-down. The same measure could indicate a bottom-up dynamic. Take a social taboo that is privately ignored but still publicly upheld. In such a domain, it will be common for expressed opinions to differ from held opinions, which will drive a consistent non-zero difference between average opinion and average received opinion. Over a dozen taboos, those with a large or growing divergence will be those that are most likely to become outmoded. Anecdotally, I’m thinking here of the surprise, and surprisingly-robust, changes in opinion and policy around controlled substances, most striking in California.
Hypothesis 3: This is a little idle, but I would also guess that people with larger differences tend to be less happy, particularly where the differences concentrate on highly-politicized topics. Causation there could go either way — I’d guess both way.
This subject has some relationship to some extensions to Schelling’s opinion models and to my dissertation work (on surprising group-scale effects of “what you think I think you think I think” reasoning).

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