One approach I want to try is using a model like above. The intersection between the two sets would represent a compromise decision, and the x-value for the compromise membership peak can then be used to calculate agent decision. Using this the autonomy scale would be represented as the peak membership to a given preference for the agent shown in blue, while the width of the agent memberships would represent sociotropy.
Agent decision in this case would be the either the self preference or the intersection, whichever has a higher membership value
This would allow modeling behavior for sociotropy and autonomy such that
Even though this toy model is not feasible due to the fact that the compromise peak is always lower than the autonomy peak value, a comparison of the areas of the agent preference vs compromise triangles can be used. Another approach can be checking the ratio of the compromise peak to the agent peak.
Implementation of the simple roundup model is straigtforward enough. The expected distribution of groups' decisions is the same as the distribution of a series of coin flips with the number of coins equal to the group size.
For the implementation with the Sociotropy-Autonomy Model, it is reasonable to expect a beta distribution depending on the ratio between autonomy and sociotropy, as well the actual values for each variavle. For instance, a high autonomy to sociotropy rate would mean an agent makes decisions similar to the naive roundup model, disregarding group preferences. Vote distributions in simulations where all agents have such a ration could be expected to have a distribution like below:
In simulations where all agents have a low autnomy to sociotropy ratio, on the other hand, distributions can be expected to favor consensus votes: agents would be most likely to follow along the first suggestion, leading to an overwhelming majority of consensus votes and little conflict such as below
If the autonomy-sociotropy ratio approaches the same value, on the other hand, the distribution can be expected to look mostly uniform like a beta distribution with both parameters at 1.
Decided I can release this as a generalized group decision-making simulator. For this I started by adding generalized decision making models (unimplemented) as well as case-specific parameter generators.
Added actor to manage data dumps. Right now it simply shows a Spark dataframe but the ultimate goal is to have it generate some preliminary analysis to make visualization easier.
Now model instances are initialized with uniform random preferences and Gaussian weights to showcase Harvey's original example, see the branch on the Github repo
An implementation based on the naive model above is now up on the GitHub repo
Groups often behave differently than expected given the behavior and preferences of their members.
Abilene Paradox is one of the most famous examples of this: a group can reach a consensus none of its members want.
An agent-based network model can represent such a group.