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The Mathematics of Affect Control Theory

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Michael Deng

on 30 October 2012

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Transcript of The Mathematics of Affect Control Theory

The Mathematics of Affect Control Theory Optimal Behavior
and Identity Emotions Re-identification Self and Identity Attributes Event (Un)Likelihood We need to pull out behavior terms
and non-behavior terms Emotions are a function of a person’s situational identity and their historical identity– it registers how an event makes one seem as compared to how one is supposed to be Three factors influence an individual’s adoption
of a particular identity:

(1) the individual’s efforts to actualize self

(2) the space-time positioning of the individual within society’s institutional structure

(3) alter-casting by influential others Emotions correspond to how events affect the self (bad events make one feel bad).

People conduct themselves to keep transient impressions of themselves close to their identities.

People experience especially good or potent or lively emotions when events make them seem more good or potent or lively than their identity warrants.

One's situational role identity influences the extent to which transient impressions of self translate into more extreme emotions, since it acts as the overall multiplier Re-identification must take account of emotion because emotion is used to check whether the behavior signals if they feel confirmed or disconfirmed by an event.

When someone has a particular mood or emotion during/after an event, an observer tries to make an inference about the identity of the actor. (eg. A person who seems extremely happy at the pain of others would be considered a sadist). Attributes are trans-situational particulizers of identity.
Similar to emotions, an attribute profile is defined as:

And the attribute profile required in order to convert the person’s identity into the event profile is:

Participating in the same happening in the same way could imply different traits for people with different identities. Thus, lesser deflections indicate events that are more likely to occur, while greater deflections indicate events that are less likely. Spark (cc) image by nuonsolarteam on Flickr (cc) image by nuonsolarteam on Flickr After decomposing into behavioral
and nonbehavioral terms 2002 March (cc) image by jantik on Flickr Settings can be included in the analysis by adding E,P, and A terms for settings to the fundamentals and transients

Self-directed action can be included in the analysis by removing the E, P, and A terms for objects from the fundamentals and transients Settings and Self-Directed Action The same procedure can be repeated for an optimal action, yielding: And also for an optimal object, yielding: We define r, ρ, and ε to be the EPA profile of the role identity, the event state, and the emotion respectively: Amalgamating mood and identity: We can define unlikelihood as:

And in terms of preexisting transients: Developing a Model of Identity Selection Create an identity profile for an individual The recently experienced self An individual tries to minimize the inauthenticity of the experienced-self, S.

The ideal identity would be a perfectly self-actualizing identity only if the experienced-self has zero inauthenticity at time 0. The recently experienced-self ordinarily is associated with some degree of inauthenticity. The weights of the recently experienced-self determine whether the system is stable or oscillatory A Quick Example: Goodness/badness of predicted acts dependent primarily on actor’s fundamental goodness/badness: Good actors engage in good behaviors, neutral in neutral or slightly good, and bad in bad.

Actor’s transient modulates these tendencies. Transient neutralization of good actor exaggerates good of the actor’s actions, and neutralization of a bad actor exaggerates the badness of behavior.

Stigmatized object-persons elicit behaviors that are less extreme than behaviors towards valued object-persons.

Transient neutralization of an object relative to object’s fundamental causes behavior to be more extreme Another One Aprpropriate emotionality effect:

When Oe is positive, an actor is re-identified positively when his/her behavior matches the emotionality, and is re-identified negatively when behavior does not.

When Oe is negative, an actor is re-identified positively only when behaving agreeably and not displaying unpleasant emotionality. An actor is reidentified negatively if behaving disagreeably or if displaying unpleasant emotionality.

Thus the effect dominates when the actor is behaving toward a good object. (cc) photo by medhead on Flickr Interact Analyses Use dictionary sentiments and set current impressions equal to sentiments

For an unspecified behavior, simulation starts with calculated optimal behavior Calculate deflection and impressions with impression formation equations Predict emotions based on both initial sentiment and impression based on current action.

Selects closest modifier and display corresponding expression on face.

Optimal behavior equation determines what the interactants will do next Optimization equation for unknown actor and object determines re-identification
Attribute equation uses re-identification to find modifier that explains action Impression Formation ABO equations deal with actions specified in terms of actor, behavior, and object person.

ABOS equations deal with actions specified in terms of actor, behavior, object person, and setting.

AB equations deal with self-directed actions specified in terms of actor and behavior.

MI equations predict the outcomes of combining a modifier with an individual’s identity. In some cultures, different equations apply for emotions as opposed to personal attributes. A Tabular Method Program Interact reads impression formation equations in a tabular format that facilitates mathematical analysis Selection matricies are constructed from the Z-expressions given in the tabular representations of impression-formation equations.

Standard computational algorithms are used in Interact for matrix algebra. Multiplications involving zero-one matricies are computed with the zero-one matrix in Boolean form. Predicting Without Occurring
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