An Opinion Space to represent Social Interactions

Following my recent presentation for the Experimental Psychology Society meeting in Oxford, I will write about how I came up to conceive the Opinion Space and how I use it now to represent social interactions.

The idea came to me during a project using support vector machines, algorithms in machine learning that represent data points (called instances) in a multi-dimensional geometric space. Separation of categories and learning in this multivariate space is easier than along each individual dimension constituting the space. These sort of machine learning algorithms are great for representing complex data. The signal of different sensors along the scalp, if taken alone, is very weakly indicative of a certain brain state. Taking multiple sensors into account at the same time however (hence “multivariate“) allows us to discern patterns that are not found otherwise.

Social interaction is similar in nature to the problems studied in neuroscience, in respect to its complexity and non-linearity. When two people interact (for example when you talk to friend), they affect each other in very unpredictable ways and with no clear direction of cause and effect. The exchange opinions, views and believes. Each of the individuals in the interaction affects the other (either willingly or not) but is at the same time influenced by the other. By representing social interaction as movements along a higher dimensional space – the Opinion Space -we can understand better the mechanisms, describe better the phenomena and predict better the behaviour of human interaction.

How do we construct an Opinion Space?
Each dimension of the space (feature) is one person’s belief or opinion about a certain variable of interest (e.g. is it going to rain tomorrow? Is the restaurant to the left or to the right going to be better?) or decision (e.g. shall I take my umbrella with me? Shall I try the restaurant on the right-hand side of the road or the one on the left-hand side?). In my research I typically measure the confidence associated with the variable of interest to gauge the strength of the participant’s opinion.

We can now construct from these orthogonal axes a Cartesian space, that we have called Opinion Space, where the information state of the group is represented as a single point along this space. This full Opinion Space is characterised by two agreement quadrants and two disagreement quadrants. We can simplify things to reduce this full space to a more parsimonious version that gets rid of subject’s identity (Yellow and Blue in the video above) and the choice identity (left and right in the video above). We now care only about whose opinion was supported by the strongest confidence (x-axis)? How’s the other person relate to this opinion (y-axis)? Does it agree or disagree? With what level of confidence?

We can now represent the state of the group’s opinion at each moment in time as a point along the space. As soon as one of the two participants change their mind or their confidence as a function of the social interaction, the group’s state will shift to a different point along the Space. We can now track the group’s opinion state as the the trajectory along the Opinion Space.

This method is incredibly useful to compare different social contexts or communication systems, as it allows to quickly visualise the dynamics of opinion formation and social influence. It is also effective to predict the future state of the group give the past and present trajectory. Finally, a simple expansion to more than two dimensions can be used to represent groups composed by more than two members.

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