First Law of Thermodynamics
The First Law of Thermodynamics relates the differences in the internal energy of a system at equilibrium to the difference between the heat transfer and the work done (Knight, 2007).
Kinematics of a Particle With Constant Acceleration
The equations relating the three basic quantities of particle kinematics (position, velocity, and acceleration) are explained in terms of differences in time, differences in displacement, and velocity in acceleration (Knight, 2007).
Relevance of Physical Models
What is the relevance of these physical examples for human communication science? First, these examples show the successful application of a model (Lave & March, 1993); these examples are literally textbook cases. Second, these examples are parsimonious: The variables and relationships that are included fit within a framework that implicitly dismisses variables that are deemed irrelevant. Compare these examples with studies in the communication discipline that add a potpourri of variables, seemingly without limit (see Pacanowsky, 1976, for an example of a line of research that, although a caricature, fits into the “no variable need be excluded” category and appears all too realistic).
Third, the physics examples all specify the measurement rules—the metrics—that apply to all included variables; these metrics are balanced in the sense that the units on one side of the equation generate the same units as the other side. Thus, the units on both sides work out to be the same (created by what is referred to as dimensional analysis).
These examples are only a few that could be used to show the success of models based on discrepancy. In the following, we start with a simple discrepancy model, a model applied to beliefs, and then examine the extent to which theory and research have extended, modified, and complemented the simple ideas about discrepancy and belief change.
A Linear Model
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The simplest form of change induced by discrepancy would be linear. If we define the relevant change induced by a message as the difference between the position adopted by the individual after message receipt (P1) and the individual’s premessage position (P0), then belief change = (P1–P0). The linear function relating change to discrepancy is
where ∀ is a constant of proportionality. This model has several different names, including the linear discrepancy model, the linear balance model, the distance-proportional model (Anderson & Hovland, 1957), and the proportional change model (e.g., Danes, Hunter, & Woelfel, 1978); the model is also consistent with the logic of Anderson’s (1974) information integration theory.
We may rewrite Equation 1 as follows:
Equation 2, which is mathematically equivalent to Equation 1, highlights another aspect of this model: Because (1 - ∀) and ∀ sum to 1, we see that the new position (P1) is the weighted sum of the initial position (P0) and the position advocated in the message (PA). This model can be directly applied to the receipt of more than one message, either simultaneously or sequentially; the latter case is addressed in the following.
Using the “contribution to alma mater” example, if the linear discrepancy model were correct and we arbitrarily set ∀ = 1⁄3 (the meaning of ∀ is discussed in detail two sections later in this chapter), then
So, the new position adopted by the individual would be a contribution of $40.00.
Assumptions
This model has several assumptions. The first set of assumptions reflects general issues of attitude and belief change studies:
A.0. The subjects [i.e., individuals who are involved in the investigation] are capable of attending to and comprehending the messages.
A.1. The subjects’ attitudes [and beliefs] and the relevant messages may be placed on a unidimensional [quantitative] continuum.
A.2. Each equation is static, and thus assumes that an equilibrium value for the dependent variable has been achieved prior to or simultaneously with [its measurement].
A.3. … parameters in the attitude [and belief]change models … are identical for all subjects given the same facilitating or inhibiting factors represented by the equivalent experimental conditions. (bracketed material added; Fink, Kaplowitz, & Bauer, 1983, n20, pp. 416–417)
Assumptions A.0, A.2, and A.3 are typical assumptions in experimental attitude and belief change research, although these assumptions are generally implicit. Assumption A.1 is particularly relevant to discrepancy models: Attitude or belief positions may be implicit in messages and in the message recipient, but the model requires that they be made explicit. If the information is not explicit, this assumption may be interpreted in two different ways: (1) All messages and positions can be quantified, even if they are not quantified explicitly in a message or by the message recipient. So, if you are asked to donate to your alma mater, you may respond as if your initial position (P0) was $10.00, although you may not have been aware of that number, and a message like “Please donate to our alma mater” may be interpreted by you to mean “donate $100.00.” (2) An alternate interpretation is to suggest that the message position, the recipient’s initial position, and the new position are qualitative (categorical); in that case, belief change would be better modeled by logistic regression, a catastrophe model (Flay, 1978; Latané & Nowak, 1994; van der Maas, Kolstein, & van der Plight, 2003), or a cellular automata model (Corman, 1996); due to space limitations, these models are not discussed further, but suffice it to say that the linear discrepancy model is incompatible with this second possibility.
Assumption A.2 means that the time interval between message receipt and P1is long enough for the individual to integrate the message in his or her set of beliefs; the actual time interval has been estimated using a dynamic model, discussed next.
A different assumption concerns the range of values for ∀. Many authors, including, for example, Hunter, Levine, and Sayers (1976), assume that 0 < ∀ < 1 (Assumption A.4). This assumption means that (for 0 < ∀) there can be no boomerang effect: A message cannot cause a person to change an attitude or belief in a direction opposite to that which was advocated. This assumption also means that (for ∀ < 1) the person cannot adopt a position more discrepant than that which was advocated. In the following section, we examine the effect of various values of ∀ that disregard Assumption A.4.
Message Repetition
We can use the linear discrepancy model recursively. If the same message is given repeatedly with enough time for each message in the sequence to be integrated (Assumption A.2), one can take Equation 1 and change the 0 subscript to 1 and the 1 to 2, and we have
(P2–P1) = ∀(PA–P1).
Or, in general,
(Pτ − Pτ − 1) = ∀(PA–Pτ − Pτ−1),
where τ is the number of repetitions. Note that we have another assumption here, namely (Assumption B.0) that the model, and more specifically the value of ∀, is unchanged by repetition.
Given assumptions A.1-A.3 and B.0, if ∀ = 0 (which disregards A.4), the person’s initial position is unchanged by repetition: If P0 = 0 and PA = 100, repetition of the message leaves all subsequent positions (P1,P2, etc.) = 0.
In Figures 6.1., 6.2., and 6.3., the effect of repetition is shown with other values of ∀. Figure 6.1. shows that if 0 < ∀ ≤ 1, repetition causes the individual to move toward the position advocated (here, 100). With 0 < ∀ < 1, an individual’s position approaches 1.00 asymptotically; with ∀ = 1, the individual adopts the position advocated (PA = 100) after the first message and remains at that value with additional repetitions of the message.
Figure 6.1 Effect of Number of Repetitions on Belief Position, by Different Values of Alpha: 1.00, 0.75, 0.50, 0.25. P0 = 0, PA = 100
Figure 6.2. shows that when ∀ > 1.00, the trajectory of belief positions oscillates due to message repetition. With ∀ = 1.50, we see that the newly adopted positions oscillate with damping (the decrease in oscillation amplitude), alternately overshooting and undershooting the position advocated, with the absolute value of the difference from the position advocated getting sma
ller and smaller. With ∀ = 2.00, message repetition causes the position adopted to alternate between a position of 200 (for an odd number of repetitions) and a new position of 0 (for an even number of repetitions). Not shown in Figure 6.2. is what happens if ∀ > 2.00: In that case, the oscillations explode, increasingly moving away from the position advocated.
Figure 6.2 Effect of Number of Repetitions on Belief Position, by Different Values of Alpha: 2.00, 1.50. P0 = 0, PA = 100
Figure 6.3. shows the effect of a negative value for ∀. In this case, repetition causes the positions adopted by the individual to move increasingly away from the position advocated, always in a negative direction.
What Is ∀?
The value ∀ has so far been mysterious. Clearly ∀ is the ratio of the change achieved by a message (P1–P0) to the change advocated by the message (PA–P0): It is the slope of the line relating these two quantities. However, neither of these descriptions of ∀ relates it to the study of belief change.
Figure 6.3 Effect of Number of Repetitions on Belief Position, Alpha = -0.50. P0 = 0, PA = 100
Let’s consider Berlo’s (1960; see also Shannon & Weaver, 1949) four aspects of communication: source, message, channel, and receiver. Imagine a thought experiment (Gedankenexperiment) in which we hold the message, channel, and receiver constant, and vary only the source. In other words, we have two or more sources, and we have empirically determined the receiver’s P0 and the message’s PA. After giving the message and having the receiver integrate the message with other attitudes and beliefs (Assumption A.2), we measure P1, which allows us to estimate ∀. We would expect that some sources are more effective than others, and that these more effective sources are associated with higher values of ∀, which is consistent with findings regarding source credibility (Aronson, Turner, & Carlsmith, 1963; Hovland & Weiss, 1951; Jaccard, 1981). In this case, ∀ is source credibility: Credibility means believability, so rather than say that properties of a source, as assessed by a scale, provide an operationalization of credibility, we can say that such measures may be indicators of credibility, but, in our hypothetical example, the value of ∀ is the source’s level of credibility.
Our next thought experiment holds source, channel, and receiver constant, and varies the message. By the same logic as previously noted, in this case ∀ is message persuadability or message effectiveness. Continuing this logic, if we hold the source, the message, and the receiver constant, ∀ becomes channel effectiveness. Finally, if we hold the source, the message, and the channel constant, ∀ is receiver persuadability or, more derisively, gullibility.
Of course, in an actual investigation (1) we may never completely hold these factors constant, (2) these factors may interact in predicting belief change, and (3) there may be factors to consider other than or as a component of source, message, channel, and receiver. For example, greater ego involvement (a receiver characteristic) should reduce belief change (Freedman, 1964; Jaccard, 1981; Zimbardo, 1960), which should reduce ∀, whereas stronger arguments (a message characteristic) should increase ∀ (Petty & Cacioppo, 1986).
Another interpretation of ∀ is to consider it as the ratio of the weight of the message position (PA) divided by the weight of the message position plus the weight that exists for the effects of prior messages (which becomes the weight of P0). Because the coefficients for P0 and PA sum to 1 (see Equation 2), (1 - ∀) reflects the ratio of the weight of the initial position (P0) divided by the weight of the message position plus the weight of the initial position. Algebraically,
and
so that
(see Fink et al., 1983; Saltiel & Woelfel, 1975). By this interpretation, the greater the weight of the message position, the more belief change is achieved. On the other hand, holding the weight of a new message position constant, the more massive (“weightier”) a receiver’s initial position, the less the belief change induced by a new message. The weight of the initial position can reflect the number of or involvement with prior messages while taking into account the processes of forgetting, which should reduce the weight, and activation, which may increase or restore the weight to a previous higher value.
Summarizing this discussion, the value of ∀ is composed of factors that inhibit (low values of ∀) or bolster (high values of ∀) belief change; in any given investigation, its composition reflects the factors that vary the most across the comparisons to be assessed. The linear model assumes that ∀ is a constant, and this assumption is investigated further.
Message Order
The linear discrepancy model makes specific predictions about the way that combinations of messages produce belief change. If we retain Assumption A.2, we can consider whether a message that is extremely discrepant followed by a message that is moderately discrepant is more or less effective than if the messages were in the opposite order.
In the following example, let P0 = 0, ∀ = 0.50, PE (the position of an extremely discrepant message) = 100, and PM(the position of a moderately discrepant message) = 40. The analysis of the two message orders looks like this:
We see that, with the assumptions that were made, the moderate message followed by the extreme message is more effective than the messages in the reverse order.
Summarizing this section, we see the linear discrepancy model makes clear predictions about several aspects of belief change: the effect due to a single message, the relation of communication factors (e.g., source, message, channel, receiver) to the model’s single parameter (∀), the effect of message repetition, and the effect of message order. The model has nonobvious implications; for example, the same equation, used to assess message repetition, generates incremental upward motion toward an asymptote, oscillatory motion that damps out, oscillatory motion that does not damp out, oscillatory motion that is unstable, and accelerating motion away from the position advocated. We now examine how various theories relate to this model.
Theories Regarding Discrepancy
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Social Judgment Theory
M. Sherif and Hovland (1961; C. W. Sherif & Sherif, 1967; C. W. Sherif, Sherif, & Nebergall, 1965) created social judgment theory, which is based on the idea that beliefs are perceived, and therefore judged, the way that physical quantities are perceived and judged. The usual analogy (referred to as the contrast principle) considers how a hand first put in cold water, after adapting to that temperature, when put in lukewarm water feels hot, whereas a hand first put in hot water, after adapting to that temperature, when put in lukewarm water feels cold. In other words, the initial location (i.e., cold or hot water) acts as an anchor that leads to a misperception of how hot or cold the subsequent location (i.e., lukewarm water) is. C. W. Sherif et al. (1965) proposed that an individual’s initial beliefs or attitudes determine how a position in a message is perceived. If the position in the message is close to the individual’s initial position (i.e., it is within the individual’s latitude of acceptance), the message position is perceived to be closer than it actually is, and therefore the message seems not very discrepant (i.e., it is assimilated). If the position in the message is far from the individual’s initial position (i.e., it is within the individual’s latitude of rejection), the message position is perceived to be further than it actually is, and therefore the message seems very discrepant (i.e., it is contrasted). The less discrepant the message appears, the more change it induces. Therefore, messages within the latitude of acceptance are effective in bringing about belief or attitude change, whereas messages within the latitude of rejection are ineffective in bringing about such change. (C. W. Sherif et al. also posit a latitude of noncommitment, in which no distortion of the message position is perceived.)
The implication of the social judgment approach is that the relation of discrepancy and belief change should not be linear: A message that is as discrepant as possible but still within the individual’s latitude of acceptance should be most persuasive. Messages within the latitude of acceptance would be expected to cause change similar to that
expected by the linear discrepancy model, whereas messages in the latitude of rejection should bring about less change. Overall, the curve representing the relation of discrepancy to belief change should be an inverted-U, first increasing to the point of maximum change and then decreasing; see Figure 6.4. In the terminology of the linear discrepancy model, ∀ (the slope) is not a constant: At low levels of discrepancy it is positive, and then at high levels of discrepancy it becomes negative.
Social judgment theory complicates this simple picture by adding the effects of two other variables. First, source credibility is expected to interact with discrepancy: In general, the greater the credibility, the greater the belief change (a main effect), but more important, the extremum of the curve (here, the maximum, which is the highest point on the y-axis) should occur at higher values of discrepancy the more credible the source. (Note: The extremum is not an inflection point.) Second, ego involvement—the idea that the issue is personally important to the message recipient—is also expected to interact with discrepancy: The lower the involvement, the greater the persuasion (a main effect), and the extremum of the curve should occur at higher values of discrepancy the lower the involvement.
Figure 6.4 Hypothetical Relationship Between Discrepancy and Belief Change as Affected by Source Credibility, Consistent With the Social Judgment Approach and Cognitive Dissonance Theory. The Same Relationship Is Expected to Hold if Low Credibility Is Replaced With High Ego Involvement and High Source Credibility Is Replaced With Low Ego Involvement.
The SAGE Handbook of Persuasion Page 18
