Numerical Illustration

    In this section, I show how the equations are applied by presenting a simplified version of the model dealing with evaluation alone and ignoring many interaction effects. In this simple model the vector of fundamentals, f', corresponding to equation (8) is merely

(116)

and the vector of post-event transients, t', for equation (9) is

(117)

    Impression-formation equations estimated only for the evaluation dimension, ignoring potency and activity effects and many interaction terms, are as follows.

(118)

Thus the M' matrix in equation (15) is

(119)

and the vector t' in (15) is

(120)

The vector z_�' in equation (20) is

(121)

The diagonal of matrix I_� in equation (21) is

(122)

The selection matrix S_� in (25) becomes

(123)

while the g_� vector in (26) is

(124)

Thus the solution for the optimal behavior defined by equation (36) is

(125)

which reduces to

(126)

or

(127)

    The bar graph in Figure 1 shows how predictions vary as a function of actor and object fundamentals and transients. The graph shows that the goodness or badness of predicted acts is dependent mainly on the actor's fundamental goodness or badness. Relative neutralization of an actor's transient status exaggerates the goodness of the actor's actions when dealing with a positively-evaluated object, and this particular feature of the predictions was confirmed in a laboratory experiment (Wiggins and Heise, 1988). Negative fundamental evaluations of object persons lead to behaviors that are evaluatively less extreme than behaviors toward non-stigmatized object persons.

    In a similar way the solution corresponding to equation (46) for an optimal actor can be reduced to

(128)

The equation above distinguishing fundamentals and transients indicates that object fundamentals are not a consideration in actor reidentification. For example, an actor who engaged in a given behavior on another theoretically would be judged the same, regardless if the other were a hero who has been made to seem neither good nor bad (transient E=0), or if the other were a villain who has been made to seem neither good nor bad.

    Interact simulations of actor reidentifications set transients equal to fundamentals for both behaviors and objects, as shown in equation (41), in which case (128) becomes

(129)

This reveals that object evaluations (ranging between �4.3) never can reverse the judgment of an actor's character generated by the actor's behavior. However, the reidentification of an actor is more extreme with a good object and less extreme with a bad object.

    The solution for an optimal object person as given in equation (54) reduces to

(130)

Here again transients are distinguished from fundamentals though that has not been the practice in the past.

    The bar graph in Figure 2 reveals considerable complexity in object reidentifications with no factor having a uniform overall effect. Focus just on the cases where the behavior transient equals the behavior fundamental. If the actor is positive and the behavior is positive, then the predicted re-evaluation of the object is positive. (This effect is even more extreme when the actor has a temporarily depleted status: apparently, a recipient is assumed to be particularly good if an actor tries to regain self-esteem by acting favorably toward the recipient.) A good act by a stigmatized actor makes the recipient seem bad: if an evil actor acts nicely toward a person, then the recipient of action must be evil, too. If the actor is good and the behavior is bad, then the object is seen as bad - someone who gets treated badly by a good person must deserve it. If the actor is bad and the behavior is bad, then the object is seen as someone good, as if we presume that bad people prefer to abuse good people.

Emotions and Reidentification

    I turn now to the matter of reidentification in the presence of displayed emotions. The solution for reidentification with information on emotion - equations (47), (98), and (99) - is too sensitive to variations in coefficients to expect realistic results in this illustration where coefficient estimates are biased by dealing only with the evaluation dimension. However, the illustration offers some insight into how the emotion-reidentification solution works.

    An equation for predicting evaluation of a modified identity from evaluations alone is

(131)

so the arrays in equation (63) reduce to the following: vector d is [-0.50], matrix P is [0.42], matrix F is [0.46], and matrix Q is [0.11]. Thus (63) itself reduces to

(132)

where P_e is the predicted evaluation of an emotion corresponding to the fundamental self evaluation, F_e, and the transient self evaluation, T_e.

    Substituting the above one-dimension estimates of F and Q_e, equation (87) becomes

(133)

and substituting the one-dimension estimates of d and P equation (88) becomes

(134)

Thereby the matrix of constants in (98) for the quadratic part of the solution becomes

(135)

and the matrix of constants in (99) for the linear part of the solution becomes

(136)

Now substituting quantities into (47) we get the formula for predicting the evaluation of the reidentified actor when taking account of her displayed emotion. Since the inverted matrix now is a scalar it is shown in the equation below simply as a denominator.

(137)

or

(138)

or

(139)

or, assuming behaviors are processed with transients equal to fundamentals

(140)

    Many of the predicted evaluations of actors obtained with (140) are beyond the possible range of actual measurements: -4.3 to +4.3, even with inputs within the �4.3 range. This is the instability problem analyzed earlier, and it seems more pervasive with (140) than when the model is analyzed by simulations using all three EPA dimensions. Thus, evidently, the potency and activity dimensions generally contribute to stability. Also, the worst cases of blow-up involve emotions in the -1 to +1 range, but most real emotions are more polarized than this. That is, the kinds of emotions that actually occur tend to produce the more realistic solutions.

    The best thing someone can do is act nicely (E=2.5) toward a good person (E=2.5), and this results in a positive reidentification (3.5 or higher) if any positive emotion is displayed, whereas the reidentification is negative (-6.0) if the displayed emotion is definitely negative (E=-2.5). On the other hand, the worst thing someone can do is act nefariously (E=-2.5) toward a good person (E=2.5), and in this case any positive emotion yields a prediction of stigmatization (-6.0 or less) whereas a definitely negative emotion yields a positive reidentification (4.3). These effects arise from the last two terms in the numerator of equation (140) which show that the evaluative appraisal of the event is conditioned by emotion displayed.

    According to (140), though, emotion displays have little effect on the judgment of evaluatively ambiguous actions. A good act toward an evil person leads to slightly positive reidentifications regardless of whether the action is accompanied by a display of good or bad emotion - as if the actor is credited for good conduct and allowed to feel positive about a good act or to feel negative about interacting with an evil character. Similarly, a person engaging in a wicked act toward a bad person is stigmatized even though there is some justice in the event, and the prediction is negative regardless of the emotion displayed. Finally, neutral acts provide little basis for dramatic positive or negative reidentifications regardless of emotion displays.

    Thus this one-dimension analysis suggests that appropriate or inappropriate emotion displays affect reidentification mainly if an actor is behaving nicely or badly toward a good person.