Event Likelihood

In affect control theory, a deflection, D, measures whether conditions generated by an event confirm or disconfirm past experience as represented in the following schematic definition.

(1)

Since absolute values are troublesome in analysis, this conception is translated to

(2)

and more specifically to

(3)

where f represents a fundamental sentiment established in a personal or cultural history, and t represents a transient impression that exists as a result of an event. The subscript, i, indicates that the sentiments, impressions, and deflections in an event have a number of different aspects.

The subjective likelihood (L) of an event is defined by the formula

(4)

where c is an arbitrary constant, w stands for summation weights, and D_i are deflections for actor (A), behavior (B), and object (O) on the response dimensions of evaluation (e), potency (p), and activity (a). That is, i indexes over A_e, A_p, A_a, B_e, B_p, B_a, O_e, O_p, O_a (and also over S_e, S_p, S_a when settings are being considered).

Equation (4) means that an event seems more likely when it generates smaller deflections. Alternatively an event seems more unlikely (U), uncanny, or unique as deflections are larger - a proposition that has been verified empirically (Heise and MacKinnon, 1987). This interpretation corresponds to the following equation.

(5)

or, from equation (3),

(6)

or, writing out the terms in the summation and expanding the square,

(7)

where an overline signifies measurement of a fundamental, and a caret signifies measurement of a post-event transient.

All fundamentals can be collected in a vector, and all transients in another vector, as follows:

(8)

(9)

and the weights can be organized in a diagonal matrix:

(10)

whereupon equation (6) becomes

(11)

If weights for all terms are equal to 1.0 (and this presumption has been found adequate for simulations of social interaction [Heise, 1985]) then W is an identity matrix, and (11) becomes

(12)

On the other hand, in principle weights might differ from term to term for fundamentals, transients, and cross-products, in which case the summation still is a quadratic form, but not necessarily the one corresponding to squared differences, shown in (7). This generalization is incorporated because it relates to a later derivation.

(13)

Indeed, at this point it is easy to generalize the quadratic form further by including first-order terms.

(14)

where V_f and V_t each is a vector of weights. The notion is that a sense of unlikeliness might spring directly from some of the states produced by an event as well as from comparing resultant states to past experience.

The transients existing after an event can be predicted from the transients that precede the event (Smith-Lovin, 1987a):

(15)

M is the matrix of prediction coefficients estimated in impression-formation research. Vector t contains pre-event transients along with interaction terms that have been found to have predictive value in empirical analyses. The following composition of t follows the report of Smith-Lovin (1987a), but specification of interactions for predicting affective outcomes remains an open issue, especially across cultures.

(16)

Substituting the value of tau given in (15), equation (14) becomes:

(17)

Terms involving pre-existing transients now can be isolated in a vector along with the fundamentals as follows.

(18)

Equation (18) indicates that the unlikeliness-uncanniness-uniqueness of a future event can be determined entirely in terms of quantities that exist before the event occurs, namely, cultural definitions (f), parameters describing psychological processes (M, W, and V), and circumstances produced by recent events (t).