I read over this model recently to implement it in Flocc. I'm not very familiar with fixed point analysis, so I skipped over that section. It's a very straightforward model, with agents defined by their opinion on an issue — for, against, or neutral. Agents are contained in a non-spatial environment without any network connections. With each tick, each agent randomly chooses one other agent to interact with (as in conversation or debate). Depending on their relative opinions, different outcomes may occur:
- If the first agent has a neutral opinion, nothing happens (presumably they just discuss the weather).
- If the first has a non-neutral opinion and the second has a neutral opinion, there is a probability
p(in my implementation I called this theconvinceparameter) that the second will take the first's opinion, as if persuaded by a strong argument. However, it is also possible that the second can take the opposite of the first's opinion (dependent on therepelparameter), as if they were not only not convinced but dissuaded by the first's argument, or perhaps turned off by other factors (bad breath?) - If the two agents have the opposite opinion, there is a probability (
doubt) that the second will revert to a neutral opinion — not entirely convinced by the first, but willing enough to see the merits of the first's opinion that they no longer fully hold their prior belief. - Finally, if the two agents have the same opinion, there is a small chance (
convince * repel * doubt) that the second will revert to a neutral opinion, as if just noticing flaws in the argument supporting their opinion through interacting with the first agent.
The paper describes how different parameters lead to different dynamics of public opinion — the proportion of the group for, against, or neutral on the issue. It uses a baseline value of 0.5 for convince: When a non-neutral agent encounters a neutral agent, there is a 50% likelihood that the second will take the first's opinion.
- With small
repel= 0.2 and largedoubt= 0.5, after 100 rounds or so, one opinion generally takes hold and spreads to become the dominant opinion of the group, reaching upwards of 80% holding that opinion. - With large
repel= 0.5 and smalldoubt= 0.1, public opinion becomes locked in a stalemate, with a very small percentage holding neutral opinions and for and against holding close to 50%. This is the case no matter the starting distributions: For example, if two-thirds of the agents begin for and only one-third against, after 200 or so rounds public opinion becomes deadlocked. This is because therepelparameter acts as a check on any dominant opinion. As one opinion starts to become more widespread, more agents with that opinion interact with neutral agents than do agents with the opposite opinion, and since neutral agents have a high likelihood of being repelled, they join the other side, creating a negative feedback loop acting against any dominant opinion.
This model focuses solely on the dynamics of rational debate, assuming that 1. opinions are discrete and objective, 2. participants in a debate do so on equal ground, and 3. agents are not influenced by factors outside of debate (i.e. public opinion as measured by polls, media representations, etc.). Interestingly, this doesn't imply that debate is necessarily rational, in that the likelihood of an agent being convinced, repelled, or doubting itself is assumed to be some fixed global parameter quite separate from the issue being debated or the strengths/weaknesses of argument. One way to explore this would be to instead model these parameters as emergent from some qualities distributed over the agents (i.e. skill at rhetoric, status...). I agree with the model's view that there's nothing inherently agreeable or objectionable in an opinion, insofar as it's a qualitative belief rather than a statement of fact ("There are too many cats" vs. "There are 1,000 cats"). Even extreme or seemingly unjust opinions are usually grounded in some material basis, so it's implicit in this model that any opinion up for debate has enough material justification to be an acceptable issue for debate (the Overton window).
The model suggests that, for minority opinions to gain ground, it may be useful to shift the style of discourse, such that in general debate is more likely to repel the undecided. While this hurts both sides, it does so unequally, since it hurts the majority opinion more and can bring about a stalemate. In this, of course, I'm thinking of Trump's rhetoric and how prominent Democrats have tried (mostly unsuccessfully) since 2016, at times, to imitate it. Trumpism — insofar as it's a coherent ideology at all — is certainly a minority opinion (see the results of the 2016 and 2020 popular votes), but it's likely that the divisiveness and even offensiveness of Trump and Trump-style rhetoric has been a net positive. While Never Trump Republicans are turned off by it, there are also people on the left and in the center repelled by mainstream Democrats trying to keep up with Trump. It's also notable, then, that Joe Biden (and other centrist Democrats more broadly) in 2020 have sought a return to normalcy and an end to a 'grim era of demonization,' if it's likely that less controversial/repellent modes of debate help opinions held by the majority.