# A. Ishii trust and suspicion model with many agents

Recently one of the well-known researchers in the field has proposed an interesting opinion dynamics model, which aims to explain polarization and group formation in human societies [1]. His model is based on two antipodal concepts in human interactions: trust and suspicion.

In this post we present you with an app, which uses \( 100 \) agents. Obviously, it would not be reasonable to enter \( \mathbf{D} \) by hand for such number of agents. So we have used random strategy to fill in \( \mathbf{D} \).

While, obviously, there is a large choice of possible fill in strategies we have decided to use a random fill in strategy with the following assumptions:

- All relationships are symmetric (reciprocal). Both agents either trust or distrust each other.
- Relationship is trusting with probability \( 1 - p_s \) and distrusting with probability \( p_s \).
- Relationship strength is distributed according to half-normal distribution with standard deviation \( \sigma \sqrt{1 - 2 / \pi} \). Sign is added depending on relationship status.

So what do we find using such \( \mathbf{D} \)?

For Type I model, society quickly approaches radical opinions. If \( p_s \) is small, then all agents have large positive or negative opinions (quickly approaching respective infinity). If \( p_s \) is large, then half of the agents converge towards positive opinions, the other half converges to negative opinions. Transition between these two modes appears to be rather sharp.

For Type II model, society either converges to consensus at some intermediate value if \( p_s \) is small, or polarizes itself for large \( p_s \).

Try to discover the dynamics yourself using the app below. Note that this app plots logarithmic density of opinions within \( O_i \in [-10,10 ] \) interval. If opinions fall outside this range, they are shown at the edges (as if they were \( \pm 10 \)).

**Acknowledgment.** This post was written while reviewing literature relevant to the planned activities in postdoctoral fellowship ''Physical modeling of order-book and opinion dynamics'' (09.3.3-LMT-K-712-02-0026) project. The fellowship is funded by the European Social Fund under the No 09.3.3-LMT-K-712 ''Development of Competences of Scientists, other Researchers and Students through Practical Research Activities'' measure.

## References

- A. Ishii. Opinion Dynamics Theory Considering Trust and Suspicion in Human Relations. In: Group Decision and Negotiation: Behavior, Models, and Support, Lecture Notes in Business Information Processing, 351: 193-204. Springer, 2019. doi: 10.1007/978-3-030-21711-2_15.