Multiple Majority Rule model (MMR) is designed to model a three state system where there are two main opinions and an undecided population. The model includes a bias that can favour one opinion over another.
Adopter: This parameter represents the percentage of nodes that start
as adopters. Its
value is between zero and one.
Rejector: This parameter represents the percentage of nodes that start as rejectors. Its value is between zero and one.
If the sum of Adopter and Rejector is one, the MMR model behaves as a two-state system. However, if the sum of these two parameters does not sum to 1, the difference between the sum and one represents the undecided population, which models a three-state system.
Bias: Given the case where a Q-group contains two equal majorities, the bias value represents the probability that the Q-group will change their opinion to the adopter state. This value should only be set inclusively between zero and one.
Qgroup: It represents a group of people of size Q, which is a value from one to the maximum number of nodes. This is the group whose opinion is being influenced in each iteration.
Let us assume there is a population consisting of 0.45 of rejectors, 0.30 of adopters, making undecided 0.25. Assume every node has 4 interactions on average hence the Q-group should be set to 4. In this simulation, if the bias is set to 0.8 it is expected for the adopter population to take over the majority even though the rejector population had a head start in population.