Johannes Kottonau and Claudia Pahl-Wostl (2004)

Simulating political attitudes and voting behavior

Journal of Artificial Societies and Social Simulation vol. 7, no. 4
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Received: 18-Dec-2003    Accepted: 09-Jun-2004    Published: 31-Oct-2004

Abstract

Understanding the dynamics of attitude formation is a key issue in social psychology. The paper presents a computational model for simulating the formation and change of attitudes and the influence of the strength of attitudes on behavior. The main conceptual challenge was to capture not only the traditional attitude concept but the full concept of attitude strength. This required combining different theoretical approaches within an integrated modeling framework. The dynamics of political attitudes of German citizens were chosen as specific application area because of the considerable amount of empirical data available. The model was tested by simulating the effects of different voting campaign strategies on the outcome of an election. Uncertainties in model parameters were accounted for by using Monte Carlo simulations. The implications of specific theoretical assumptions were investigated by performing model simulations for different model structures.

The paper shows the potential of social simulation when it comes to bringing together different theoretical approaches. The integration within a model exposes gaps and inconsistencies and allows formulating hypotheses for further empirical investigations.

The model has a modular structure and provides a rich repository for other modelers who are working in the field of attitude simulation.

Keywords:

Attitude Formation, Social Simulation, Voting Behavior

Introduction

1.1

What counts in elections are not only converted citizens but also activated citizens (Berelson, Lazarsfeld and McPhee 1954). That is, only party (or candidate) supporters that finally cast their vote on voting day have a measurable effect on the direction of politics. The relevant questions are therefore: how does a converted citizen become an activated citizen? How does a weak attitude without behavioral consequences become a strong attitude with behavioral consequences? The latter question addresses the well-known problem of the attitude-behaviour relationship (Fazio 1986, Fazio, Powell and Williams 1989, Kraus 1995, Zanna and Fazio 1982).

1.2

During the last two decades, attitude strength has become a focal issue in the fields of attitude psychology and theories of public opinion (Doll and Ajzen 1992, Eagly and Chaiken 1998, Petty and Krosnick 1995). Strong attitudes of an individual can be defined as attitudes which are extreme, consistent (non-ambivalent), and important to the holder (held with a high level of involvement). In contrast, weak attitudes are tempered, ambivalent, and unimportant to the holder (held with a low level of involvement). The most important characteristic of strong attitudes is that they are considerably more predictive of behaviour than weak attitudes (Fazio and Williams 1986, Krosnick and Abelson 1992, Krosnick, Boninger, Chuang, Berent and Carnot 1993). The research on attitude strength was initiated in the late 1980s. It was invigorated in the 1990s after empirical studies had almost unanimously pointed out the difficulty of explaining and predicting behaviour from the traditional way of measuring attitudes.

1.3

As a complement to empirical studies on attitude strength, this paper presents a computational simulation model of the mental structures and processes underlying the formation and change of the components of attitude strength. Computational models of the formation and change of strength-related attitudinal substructures are missing in attitude research. Although there are several computational models of attitude change (Hegselmann, Müller and Troitzsch 1996, Latane, Nowak and Liu 1994, Mosler, Schwarz, Ammann and Gutscher 2001, Nowak, Szamrej and Latane 1990, Nowak, Vallacher, Tesser and Borkowski 2000, Regenwetter, Falmagne and Grofman 1999), this is the first computational model of the formation and change of the strength of attitudes and the dynamic interrelationship between several components of attitude strength. The model is applied to a practical example, the dynamics of voting behaviour. The Political Attitude Strength Simulation model (the PASS model, from here on) simulates the individual time traces of the attitude extremity, the attitude ambivalence and the attitudinal involvement of individual artificial citizens prior to voting day.

1.4

The most salient benefits of simulating mental representations related to attitude strength are the following:

• at each time step the model distinguishes between certain citizens that communicate univalent arguments and uncertain citizens that communicate ambivalent arguments. That is, not every attitude exchange does a priori persuade the communication partners. The persuasive effect on the side of the receiver is dependent on the certainty of the citizen representing the source.
• on voting day the model distinguishes between citizens with a relatively high level of attitude strength (participating in the elections) and citizens with a relatively low level of attitude strength (abstaining from the elections).

1.5

The cost of tackling the problem of simulating attitude strength has been to implement the complexities of the strength-related components into the computer model. For example, in order to simulate the temporal formation of the attitudinal ambivalence component, it is required that at least two psychological responses towards the attitude target are kept separate.

1.6

All citizens are embedded in a virtual social network. At the start of each model run an artificial citizen network is generated, based on empirical network data.

1.7

Two simulated political parties provide the basic information input for the attitude formation and change process. Starting from an individual initial attitude towards the parties, every simulated citizen changes her attitude in response to the coverage from the mass media, the activities of the parties, and the content of the interpersonal communication.

1.8

Thus, the PASS model provides a number of innovative steps in

• combining existing procedural models of serial information integration in the political science with models of attitude strength in social psychology
• combining the individual process of political attitude formation with models of interpersonal communication in ego-centric political discussion networks
• allowing to compare the importance of theoretical assumptions such as the speed of memory decay or the effect of the confirmation bias on bolstering attitudes.

1.9

The following model description may thus be used as a rich repository for other modellers working on the issue of attitude or public opinion formation who may be interested to use parts of the model and/or extend it. Consequently, the paper provides the full mathematical expressions for utmost transparency of our ideas.

1.10

The model is implemented in the JAVA-based simulation environment called Quicksilver (Burse 2000). Quicksilver consists of a set of Application Programmers Interfaces (APIs), a set of tools for the creation and execution of models, and a set of tutorial examples and examples of completed projects (for downloading, see http://sourceforge.net/projects/java4u/).

1.11

The model provides an example for the strengths of agent based social simulation. In order to understand the phenomenon of interest it was necessary to make use of theories from different specialized fields. The development of a computional model offers a framework for theory integration where gaps and contradictions become evident. Simulations can support theory testing and the derivation of new hypotheses that can be investigated in empirical research. This potential of agent based social simulation is not yet fully explored. We hope that our paper will stimulate further work in this direction.

Model description

2.1

The paper proceeds in a top-down manner. In the first part, the central actors and processes on the social level are portrayed. On the mental level, the second part describes the cognitive units and the cognitive processes of revising the citizen's attitude if new evidence is encountered.

The social level

2.2

Since the formation of attitudes has been documented to be an inherently social phenomenon (Lenart 1994), it is indispensable to include the social level in a model of citizen behaviour. The model comprises of three different types of social actors: the party strategists, the mass media, and the citizens.

Figure 1. Overview of the social level. The center of the graph depicts a citizen network representing five citizens c1 to c5. In each time step, the citizens perceive a fraction of persuasive messages from the "campaign arena" depending on their habitual interest in the elections (the light ring denotes "perceived" messages, whereas the dark ring denotes "lost" resp. not perceived messages). In each time step, the strategists SA and SB and the mass media M post a specific number ni of persuasive messages on the campaign arena according to their temporal campaign strategy.

The strategists and the mass media represent external sources of persuasive messages released in the form of TV news and spots, newspaper articles and ads, brochures, bumper stickers etc. These persuasive messages permanently affect the attitude formation and communication process of the citizens (see figure 1).

Two Contradicting Information Sources

2.3

Two opponent strategists constitute the competitive setting in the model. They represent parties like the Democrats and Republicans in the USA or temporary party blocks like the CDU-CSU-FDP Parteilager and the SPD-Grüne Parteilager in Germany. To keep the model general, the two parties or party blocks are just called party A and party B in the remainder of this paper.

2.4

At the start of the simulation ( H days previous to voting day), the parties make the strategic decisions of choosing between different degrees Ψ of accumulating campaign resources toward voting day (see figure 2).

2.5

The strategists are assumed to be completely ignorant and independent of the decision-making of the competitor. The design of independence has been selected to systematically explore the whole space of possible strategy encounters between party A and party B even if the extremes are quite unrealistic (e.g. Ψ = 0 or Ψ = 64). As a second modeling assumption, both parties have an identical budget Y and an identical level of permanent advertising activities ρ. The budget restriction is essential to isolate the effects of different temporal resource allocations from the effects of simply varying the campaign spending.

2.6

Apart from the parties, the mass media are the second actor type present in the public sphere. This actor is used to model the non-commercial coverage in the newspapers, television, broadcast, and the Internet. Importantly, their coverage is not supposed to be neutral. Rather, the predominance of coverage on party A or party B reflects the current campaign activities of the parties. This automatic amplification effect of party activities is explicitly modeled, since parties have proven to be successful in deliberately launching pseudo-events designed to become news stories in the mass media (Schmitt-Beck and Pfetsch 1994).

Release of persuasive messages

2.7

In each time step, the parties A and B put a certain number of persuasive messages on a virtual "campaign arena" according to their accumulation strategy. For some simple examples with only one parameter, the degree of accumulation Ψ, see figure 2). To be sure, the temporal regime of persuasive messages is exogenous to the model and can be chosen arbitrarily complex (multi-peak or even data-based) by the modeler.

2.8

The number of released persuasive messages n_r,j(t_k) is a relative measure of the level of campaign activities of party j. At the end of each time step t_k, all persuasive messages on the campaign arena are cleared for the new persuasive messages released within the next time step. Figure 2:.

Figure 2. Increasing degrees Ψ of accumulating half of the budgeted party advertising activities (light area) during one year before voting day. The other half of the budget (dark area) is spent for permanent party advertising activities (baseline campaigning)

2.9

The mass media M put a more or less one-sided coverage for and against both parties on the campaign arena. They accumulate at the degree of Ψ = 2.0 assuming a relatively permanent, but slightly increasing coverage towards voting day. The coverage from the media is distorted according to the automatic amplification effect of party activities. The modeler can set the maximum distortion level ω of the media coverage. For example, if ω = 0.15 and party A is extremely active while party B is totally inactive, the distortion of the media coverage A:B is maximal at the level of (0.5 + ω) : (0.5 - ω) = 65:35. In less extreme cases, the distortion is somewhere between the maximum distortion and the 50:50 neutral coverage.

The Citizens

2.10

The simulation comprises of a population of citizens in a social network. The citizens' minds are boundedly rational in a double sense: i) they do not have access to all information available on the campaign arena and ii) the information integration process is biased itself. The biases this model takes into account in the integration process are the availability bias (Tversky and Kahnemann 1974) due to the decay of memory content, the confirmation bias (Klayman 1995) due to the tendency of bolstering attitudes, and the homogeneity bias (Berelson, Lazarsfeld and McPhee 1954, Schenk 1995) due to the relatively homogeneous social networks of political discussants. The specific mental processes will be discussed in the section "The cognitive level".

Citizen perception

2.11

Citizens differ in their degree of interest in the elections. The individual number of persuasive messages n_p,c(t_k) perceived out of the whole set of inputs n_r,tot(t_k) on the campaign arena is proportional to the individual level I_c(t_k=0)=I_0,c of habitual interest into elections of citizen c (eq. 1) (Schmitt-Beck 2000, Semetko and Schönbach 1994, Zaller 1992). The somewhat counter-intuitive picture from the literature is that people in general (not only the apartisans) are not particularly selective in choosing TV channels and newspapers according to their attitudes. Possible accounts for this finding are that i) the advertising activities of the parties in the public sphere (like posters in the streets) are inadvertently and unwillingly perceived by all types of citizens, and ii) political attitudes are probably not the only criterion people base their selection of TV channels and newspapers (Huckfeldt and Sprague 1993, Schmitt-Beck 2000, Zaller 1992). For these reasons, we do not model the process of perception as selective. Yet, selectivity is modeled in the process of judgement (confirmation bias) and in the process of communicating within relatively homogeneous social networks.

(1)

2.12

The credibility of a particular persuasive message from the public sphere depends on its source. It is assumed to be higher for the mass media than for the parties since citizens generally consider the media as more independent and trustworthy (Eagly, Wood and Chaiken 1978).

Citizen communication

2.13

Embedded in a social network, citizens exchange their current views about the parties. The probability p_ex,c(t_k) of initiating an interpersonal exchange of attitudes at time step t_k increases with the citizen's involvement at t_k-1 (eq. 2) (Schmitt-Beck 2000, Zaller and Feldman 1992). The constant ς _c is the general tendency of citizen c to begin an attitude exchange (the personal communicativeness).

(2)

2.14

Considering a widely accepted norm of conduct, the simulated target citizen responds even if her/his current involvement is very low. The content of the exchange both on the side of the person beginning the exchange and the person responding depends on the attitude certainty of the participants (see revision step 7). If the citizen belongs to the subset of "certain" citizens, his/her argumentation is modeled as one-sided. If the citizen belongs to the subset of "uncertain" citizens, his/her argumentation is modeled as double-sided (Latane 1981). In the case of one-sided argumentation, the citizen tells the valence of his/her current attitude. In the case of double-sided argumentation, the citizen expresses his/her ambivalence by telling arguments for and against both parties. The credibility ε_c(t_k) of the communication partner is derived from her/his involvement I_c(t_k-1) in the last time step (eq. 3) and normalized between 0.0 and 1.0 by the constant const₁.

(3)

Citizen voting behaviour

2.15

According to the dominant effects of strong attitudes on behaviour (Bargh, Chaiken, Govender and Pratto 1992, Bassili 1995, Fazio and Zanna 1978, Fazio and Williams 1986, Jonas, Broemer and Diehl 2000, Krosnick 1988), the involvement, the ambivalence, and the extremity of a citizen's attitude are modeled as the determinants of participation in the election. Only the citizens with the strongest attitudes will participate in the elections. The percentage of participants is given by the level of the simulated turn out which is derived from the average attitude strength within the population on voting day (see the Appendix). The other citizens with weaker attitudes will "stay at home" and will not have an impact on the outcome of the election.

The cognitive level

2.16

This section describes the modeling assumptions underlying the integration of the persuasive messages from the campaign arena. Essentially, the task was to find a parsimonious set of (as far as possible) empirically verified mental structures and processes that link the temporal evolution of the citizen's memory to the temporal evolution of the citizen's attitude.

2.17

The main sources of empirically tested assumptions were the Receive-Accept-Sample (RAS) model (Zaller 1992) and the impression formation model developed by Lodge and his colleagues (Lodge 1995). In many views, these two models represent the "state-of-the-art" of information integration models in political psychology. In addition, our model encompasses an explicit treatment of the dimension of attitude strength (Krosnick and Petty 1995). This construct is missing in both the RAS and the Lodge model in spite of the fact that in the field of social psychology (and consumer psychology) the focus on attitude strength has already proved to be indispensable for thinking about the determinants of attitude stability and change.

2.18

The additional component of attitude strength requires the PASS model to explicitly simulate a minimal set of strength-related characteristics. We have somewhat arbitrarily concentrated on the citizen involvement, the attitudinal ambivalence, and the attitudinal extremity. However, we contend that these characteristics capture three important facets of attitude strength that are relevant in the context of voting behaviour. In the following section, an appropriate substructure of the attitude is presented which is capable of modeling the dynamics of these components of attitudinal strength.

2.19

Theories of mental accounting predict that the content in the citizen memory is organized around separate accounts (Henderson and Peterson 1992). The simplest form of mental accounting is the separation of a positive and a negative account towards the judgmental target. Therefore, the attitude is divided into the party A account and the party B account (see figure 5). Newly encountered persuasive messages are associated with one of these accounts according to their affective tag. The affective tag reflects the subjective impression of the main thrust of the arguments, pictures, slogans contained in the original persuasive message and is considered to be easily extractable under the condition of low citizen involvement (Lodge, McGraw and Stroh 1989) (see figure 3). The PASS model neglects the explicit simulation of the memory traces of the full original messages and focuses on the memory decay of the much more relevant affective extract (similar to the Lodge model).

2.20

The affective tags of the persuasive messages are pre-defined by the modeler. That is, all the extracts derived from the persuasive messages coming from party A are a priori assigned the affective tag A and all the persuasive messages coming from party B are a priori assigned the affective tag B. Similarly, if a persuasive message comes from the mass media and is univocal, the citizens supposedly find out the affective tag correctly. Sometimes, however, the persuasive message comes from ambivalent mass media coverage or from interpersonal communication with an uncertain citizen. In this case, the persuasive message is split into two contradicting sub-messages with the univocal affective tags A resp. B. To avoid doubling the impact of ambivalent messages, the judgmental weight of these sub-messages is halved.

2.21

In contrast to the Lodge model, a second attribute is derived from the original persuasive message: the credibility of the message source. Similar to the affective tag, this attribute is considered to be easily extractable even under low levels of involvement and to be much more decay-resistant. The underlying assumptions are i) that the source of every persuasive message is correctly identifiable and ii) that the citizens have subjective a priori credibility levels assigned to the different sources (Hovland and Weiss 1951).

2.22

The resulting essence of the persuasive message is called a Persuasive Message Extract (PME). Every PME combines the extracted affective tag and the credibility of the original persuasive message (see figure 3). The PMEs are the basic knowledge units in the PASS model.

Figure 3. At the moment of perceiving an Original Persuasive Message (OPM), its full content is translated into the Persuasive Message Extract (PME)

Steps of Integrating the Persuasive Message Extracts

2.23

The attitude of a citizen at a particular moment in time is the result of a bottom-up integration procedure starting from all the PMEs available at that particular moment in time. The following sections describe the sequence of steps of the integration procedure. Because of the basic assumption of low involvement, the processes revising the attitude are unconscious for most of the time (Kihlstrom 1987).

Figure 4. Overview of the temporal sequence of the various steps that are performed if a citizen has encountered new evidence. The numbers of the boxes correspond to the numbers of the steps used in the section headers in the text. The dashed lines denote the temporal evolution at the three levels of the Persuasive Message Extracts (PMEs), the citizen's attitude and the citizen. The arrows denote the inputs required for a particular step

2.24

In the PASS model, the sequence of revision steps is only performed if some new persuasive message has been perceived. Simulating the preference revision process as a bottom-up integration starting from some basic knowledge units is conceptually related to the Response Axiom of the RAS model (Zaller 1992) and more generally, to the attitudes-as-constructed perspective proposed in attitude theory (Tourangeau 1992, Wilson and Hodges 1992). The continuous revision of the attitude in the light of new evidence is a core element of the on-line relationship between memory and judgement (Hastie and Park 1986).

Figure 5. The attitude unit is divided into two basic memory accounts. Every account is associated to steadily growing sets of PMEs (circles at the end of the spokes) that have been perceived during the ongoing campaign. The affective valences A or B and the credibility ci of PME i are indicated as two small circles within the circle indicating the PME

Step 1: Revising the PME accessibilities

2.25

The temporal decay of human memory content is best approximated by a power law (Anderson and Schooler 1991, Wixted and Ebbesen 1991). Generally, the level I_c(t_p,m) of the involvement of citizen c at the moment t_p,m of perceiving a certain original persuasive message m mediates the accessibility a_i(t_k) of the PME i (eqs. 4a and 4b) (Burnkrant and Sawyer 1983, Greenwald and Leavitt 1984, Park and Hastak 1994). The accessibility of a PME at time step t_k is a measure of its probability to have an effect on the outcome of the attitude revision at time step t_k. If the citizen was in a highly involved mind set when perceiving the original persuasive message, the decay of the PME is slower than if the citizen was in a low involvement mind set. The process of decay is translated into the continuously decreasing accessibility of the PME. The constant υ_c determines the general memory decay speed of citizen c.

	(4a)
	(4b)

2.26

The three important model assumptions for modeling the accessibility of each PME are: First, the maximal accessibility of a PME is considerably higher in an interpersonal setting than in a setting of impersonal mass media or party campaigns (cf. weight of interpersonal communication ω_IPC in the Appendix). Two reasons can be found for this situation-dependent treatment: i) when communicating face-to-face, the recipient's attention and understanding can continuously be controlled and the message can easily be "customized" (Avery and McCain 1986, Katz and Lazarsfeld 1955); ii) the interpersonal setting provides numerous retrieval cues facilitating later retrieval of the communication act (Avery and McCain 1986).

2.27

Second, the citizen memory is not selective on congeniality, i.e. does not hold congenial PMEs (matching the valence of the current attitude) on higher levels of accessibility than uncongenial PMEs. The results from empirical studies on memory selectivity are still controversial. However, recent experiments point to the direction of non-selectivity (Eagly, Kulesa, Brannon, Shaw-Barnes and Hutson-Comeaux 2000).

2.28

Third, the PASS model adopts the assumption that memory traces that cannot be accessed by self-report and introspection anymore have an effect on the judgement (Greenwald and Banaji 1995, Kihlstrom 1987). In other words, the models does not ignore memory traces that would be subjectively felt as "forgotten" but revises the accessibility and credibility of every PME even if its accessibility is nearly zero. This allows for the simulation of the effect that a large number of old "forgotten" traces might out-balance a small number of fresh memory traces from recently encoded persuasive messages. Thus, the PASS is able to explicitly capture the nature of the citizen's unconscious.

Step 2: Revising the PME credibilities

2.29

People tend to bolster their previous attitudes if they encounter new evidence (Houston and Fazio 1989, Lord, Ross and Lepper 1979, Pomerantz and Chaiken 1995). This type of confirmation bias is expected to prevail if the perceiver is in a low-involved mind-set as supposed throughout the PASS model. According to the second axiom of the Receive-Accept-Sample model (RAS-A2) (Zaller 1992), the strength of the confirmation bias is positively related to habitual interest I_0,c into elections (eq. 5a). Basically, the confirmation bias increases or decreases the original credibility level c_0,i of the PME i. If the affective tag δ_i of PME i corresponds to the valence of the attitude in the last step t_k-1, the PME credibility is multiplied by the factor 1+ I_0,c . χ_c, where χ_c is the general need of confirmation of citizen c. If the affective tag of a PME does not correspond to the valence of the attitude in the last step t_k-1, the credibility of that PME is divided by the same factor. Equation 5b is the reformulation of eq. 5a if the RAS-A2 is absent, i.e. if the strength of the confirmation bias is independent of the individual level of I_0,c. The dependence is replaced by a constant, the average initial involvement I_0,avg. The different effects of implementing either eq. [5a] or eq. [5b] were investigated in Monte Carlo Experiments (see below).

(5a)

(5b)

Step 3: Revising the citizen involvement

2.30

The notion of political involvement is defined here as the "interest in public affairs validated by keeping informed and [is] expressed through participation in civic action" (Inkeles 1974). The specific level of citizen involvement I_c(t_k) regarding the upcoming elections during the simulated time period depends on the recent frequency of encoding persuasive messages related (eqs. 6a-c and figure 6).

(6a)

(6b)

(6c)

2.31

The summed accessibilities β_c(t_k) of the PMEs of both accounts provide a useful index that integrates both the recency and frequency of encoding PMEs in memory (Kokkinaki and Lunt 1997). At a specific individual threshold of accessibility β_att,c, the growth of involvement per time step is at its maximum, i.e. the citizen gets significantly aware and interested in the campaign. Another parameter ς_c varies the "sharpness" of the involvement increase around this threshold. With increasing total account accessibility, the involvement curve reveals the typical stimulus-response ceiling effect (McCombs and Shaw 1972, Semetko and Schönbach 1994).

Figure 6. If citizens perceive persuasive messages with some minimal frequency, the total accessibility of all PMEs β c(tk) in the accounts is steadily growing. This overall measure for the recent frequency of campaign activities in the campaign arena is translated into the citizen involvement. Each citizen has an individual threshold of accessibility β att,c that determines the moment of getting significantly attentive to the campaign activities

Step 4: Revising the response intensities, the attitude valence, and the attitude extremity

2.32

The total number n_A,c(t_k) of PMEs that are associated with account A of citizen c at time step t_k and the total number n_B,c(t_k) of PMEs that are associated with account B have to be separately translated into two antagonistic responses which form the building blocks of the final attitude (eqs. 7a and 7b). First, every PME i is assigned a weight according to its accessibility a_i(t_k) and its credibility c_i(t_k). Second, the weights of all PMEs are separately summed up for account A and account B, and added to the initial account accessibilities a_0A,c and a_0B,c, respectively. For each citizen c, this procedure yields two response intensities R_A,c(t_k) and R_B,c(t_k). That is, the more highly accessible and highly credible PMEs are associated with an account, the higher is its response intensity.

(7a)

(7b)

2.33

The relative imbalance of the initial account accessibilities represents the initial attitude (or party identification) of each citizen at the beginning of the simulated time window. The initial account accessibilities do not decay during the simulation since they represent the political pre-disposition previously established over years. The valence and the extremity of the attitude (both incorporated in A_v(t_k) with the valence = sign [A_v(t_k)] and the extremity = |A_v(t_k)|) are derived from a simple integration of the two antagonistic response intensities normalized on a scale between -1 (completely pro B) and +1 (completely pro A) (eq. 8). The implicit assumption underlying this normalization is that more extreme attitudes are more resistant against change (Feldman 1989).

(8)

Figure 7. Processes involved in the revision of the attitude Ac(tk) of citizen c at time tk after new evidence was encountered from the campaign arena. The two circles represent the two party accounts. The index i of each PME denotes its position within the temporal sequence of perception (high numbers for recent PMEs). The most recent PMEs are more accessible (bold lines), whereas older PMEs are less accessible (thin lines). Episodes that were perceived in situations of interpersonal communication (IPC) are most accessible. According to their accessibilities ai(tk) and credibilities ci(tk), the PMEs of each account are separately integrated into the response intensities RA,c(tk) and RB,c(tk). Finally, the response intensities are transformed into the attitude Ac(tk) and the party ambivalence Πc(tk).

Step 5: Revising the attitudinal ambivalence

2.34

Empirical studies suggest that the subjectively felt ambivalence during the election campaigns is a pivotal component of attitudinal strength (Cacioppo, Gardner and Berntson 1997, Erber, Hodges and Wilson 1995, Meffert, Guge and Lodge 2000). There are several quantitative models of ambivalence in the literature. We have selected the model from Thompson and Zanna (1995) because of its parsimony and frequent use in empirical studies (eqs. 9a and 9b). Thompson and Zanna propose that ambivalence is high if both responses have similar intensities and if the absolute intensities of both responses are high. Equation 10b is used for normalizing the ambivalence between -1 and 1 whilst maintaining a maximum sensitivity of Π_c(t_k) if Π_c^*(t_k) is between -3 (Π_c(t_k) = 0.1) and 3 (Π_c(t_k) = 0.9).

(9a)

(9b)

Step 6: Revising the attitudinal strength

2.35

The overall attitude strength α_c(t_k) is the product of the involvement I_c(t_k), attitudinal extremity |A_c(t_k)|, and attitudinal consistency (the inverse of the attitudinal ambivalence Π_c(t_k)). The reason for this conceptualization is the assumption that if one of the attributes approaches zero, the attitude strength approaches zero as well (eq. 10a). For example, if a citizen feels strongly involved in the election, but at the same time feels strongly ambivalent because of nearly identical response intensities, the overall attitudinal strength is supposed to be low.

(10a)

2.36

The attributes are more or less positively interrelated. Empirical studies suggest that high extremity commonly is related to low ambivalence, and involvement correlates with extremity (Krosnick, Boninger, Chuang, Berent and Carnot 1993). However, since the level of attitudinal strength is a relative measure, the multiplication just amplifies the relative differences within the population of artificial citizens with regard to attitude strength.

Step 7: Revising the attitudinal certainty

2.37

The number of ambivalent citizens was found to steadily decrease during the time before voting day at least for the German General Elections 1994. The percentage of non-respondents declined from 23% to 14% within the 40 weeks before voting day (Erhardt 1998). Since our simulation covers one year before voting day, we had to extrapolate the percentages for the weeks 52 to 41 using the simplest (linear) trend in the data (see figure 8).

Figure 8. Decreasing percentage Δ (tk) of uncertain citizens when asked which party they would vote for if voting day were today. Data (dots) from Erhardt (1998), extrapolation (line) by the author

2.38

In each time step, the model differentiates between citizens with certain attitudes and citizens with uncertain attitudes. The certainty ξ_c(t_k) of the attitude is determined by multiplying the attitudinal extremity and the attitudinal consistency (eq.10b]). In contrast to the full construct of attitudinal strength, the certainty construct does not contain the motivational component of involvement required for the distinction between citizens going to vote and citizens not going to vote.

(10b)

The state label "uncertain" is attached to the Δ(t_k) percent out of all citizens with the lowest certainty at time step t_k. Due to this categorization, an attitude of a particular citizen can flip between "certain" and "uncertain" several times during the simulated year depending on her/his position in certainty ranking.

Citizen typology

2.39

The Dalton citizen typology divides the electorate along the two dimensions of party identification strength and cognitive mobilization, encompassing the level of formal education and the level of interest in politics (Dalton 1984). As a useful idealization, we adopt the general character of the dimensions and the assumption of independence proposed by Dalton. We put habitual political interest as the only component contributing to the dimension of cognitive mobilization (see figure 9).

Figure 9. Citizen types distinguished in the model. The two dimensions are related to the Dalton (1984) typology of citizens.

Citizen initialization

2.40

This section describes the procedure required to set up an initial population of artificial citizens. All required data are taken from empirical studies conducted in the context of German General Elections.

2.41

The simulated populations encompass N = 100 citizens. In the first step of the citizen initialization, the party identification in terms of the initial valence and extremity of the attitude A_0,c is attributed to each citizen c. The underlying frequency distribution of different strengths of party identification was derived from data yielded in Germany in 1994 and 1998 (Falter, Schoen and Caballero 2000). In another study conducted in Germany, Schmitt-Beck (2000) demonstrates that in 1990 the strength of party identification is equally distributed in both Parteilager (CDU/CSU/FDP and SPD/Grüne). Reflecting the available evidence, the initial attitudes A_0,c in each model run are distributed as depicted in figure 10.

Figure 10. Distribution of initial attitudes among 100 citizens in the simulation experiments. Reading example: 17% of the citizens have an initial attitude extremity between 0.00 and 0.25 and a pro party A valence. When asked for their party identification, 14 % of them report that they do not identify themselves with any party, whereas only 3% translate the relatively small extremity into the answer "tempered partisan"

2.42

In the second step, different levels of habitual political interest I_0,c are attributed to the citizens independent of the extremity of the initial attitude. According to the aggregated ALLBUS dataset 1980-1998 (GESIS 1996), the frequencies of five different interest levels (not at all, low, medium, strong, very strong) can be approximated by a normal distribution. Since involvements are typically very low one year before voting day, the values attached to the citizens are normally distributed between 0.0 and 0.25. Thus, citizens with initial involvements between 0.0 and 0.125 are rather uninterested citizens, whereas citizens with initial involvements between 0.125 and 0.25 are rather interested citizens.

2.43

In the third step, the total initial accessibility β_0,c of the attitude is determined on the basis of the extremity of the initial attitude |A_0,c|, the initial involvement I_0,c, the maximum value β_0,max, and two constants const₃ and const₄ for keeping the maximal contribution from the initial involvement and the initial attitude equal (eq. 11).

(11)

2.44

The underlying assumption is that strong partisans with a high level of habitual interest in the elections have the most accessible attitudes. Strongly interested apartisans (with |A_0,c| close to zero) are assigned half of the maximum accessibility since they probably have, due to their interest, extended but two-sided knowledge about the parties in their minds (eq. 12). Weakly interested partisans have little but one-sided knowledge about parties. These citizens are assigned a medium level of initial accessibility as well. Apartisans with little interest in politics yield a minimum initial accessibility. Their attitudes are closely related to "non-attitudes" in the sense of Converse (1970).

2.45

In the last step, the initial accessibility β_0,c is divided into the two initial accessibilities of the basic party accounts a_0A,c and a_0B,c according to the initial attitude (eq. 13).

(12)

(13)

2.46

The other individual citizen characteristics (the speed of memory decay, the probability of beginning an attitude exchange and the weight of interpersonal communication, the level of the confirmation bias, the accessibility threshold, and the sharpness of this threshold) are uniformly distributed within the ranges presented in the Appendix. Most of the ranges have been found by performing Monte Carlo data sampling. One Monte Carlo sampling consisted of 36'000 model runs using the currently optimal guesses of the parameter ranges. The statistical parameters from each Monte Carlo data sampling were then compared with the available data or the assumptions presented in the Appendix. To improve the match between the input parameters and the statistical characteristics of the Monte Carlo data, additional data samplings with slightly different input parameters were performed again and again. Lacking an automatic parameter fitting procedure, corrections in the parameter ranges have been done manually (equivalent an inverse trial-and-error process). All the parameters were estimated running the model with intermediate degree of campaign resource accumulations (Ψ = 8, 16, or 32) that are considered to be closest to the real world practice (Finkel and Schrott 1995).

Results

3.1

The goal of this section is to demonstrate that the simulated citizen behaviour on the individual level is plausible in spite of the fact that the model parameters were estimated mainly on the aggregate level (see the Appendix). In fact, the dynamics of the one-year traces of the three components of attitude strength simulated here (extremity, involvement and ambivalence) and the trace of the overall attitudinal strength itself are quite insightful and comprehensible on the background of the implemented model assumptions (see figure 11). Furthermore, surveying the individual temporal traces of attitude valence and certainty of all the 100 simulated citizens, the more stable and the more volatile zones within the electorate become clearly visible (see figure 12).

Individual level

3.2

The example depicted in figure 11 is aimed at demonstrating the temporal effects of different types of interpersonal communication at the level of one particular citizen. In order to isolate the effects from interpersonal communication, the accumulation level of both parties is set at the level of Ψ = 0 (no accumulation). That is, over the simulated time period, the effects of the parties cancel each other out and are only visible as the allover micro-shakiness of the time plots. Because of the balanced party activities, the mass media coverage is neutral as well. However, since the credibility of the mass media is higher than the credibility of the party advertising, the impact of the mass media on the citizen's attitude is still visible as small perturbations in the traces (see bullets 1 and 3).

3.3

The citizen starts as a partisan temperately supporting party A (see the initial attitude at 0.37). The first significant event is when at time step 93 another citizen communicates with the citizen presented here (see bullet 2). The discussant is a supporter of party B with a relatively strong attitude and, consequently, is treated as "certain" in the model. This means that she will argue univalently for party A. Additionally, she is highly involved and therefore highly credible (this cannot be seen in the plot, but see eq. 3). Consequently, the PME derived from this uncongenial and univalent communication event abruptly pulls the attitude of the focal citizen on the side of party B. In other words, the citizen was efficiently convinced of the merits of party A changes from a tempered partisan to a partisan of party B. Simultaneously, the ambivalence drops due to the new level of consistency subjectively felt under the salient impression of the recent persuasive communication act. In the following time steps, the memory trace of the PME derived from the communication act slowly decays, and, accordingly, the subjectively felt level of ambivalence. Between communication act 2 and 5, there are no further persuasive attempts of party B discussants to keep the focal citizen on the side of the party B partisans. After some time (around time step 250, supported by two congenial PMEs from the mass media), the attitude has indeed returned to the initial level of extremity and valence. Put metaphorically, the anchor of the initial attitude has outrun the "ephemeral intermezzo" on the side of the partisans of party A.

3.4

Another interesting effect can be taken form the time plots in figure 11. At time step 180, the attitude crosses the zero-line (and the ambivalence is at its maximum, see bullet 4). Just after the zero-line is crossed, the credibilities of the PMEs attached to the party A account synchronously flip from suppressed to elevated and the credibilities of the PMEs attached to the party B account synchronously flip from elevated to suppressed (see eq. 5a and eq. 5b). Due to the working mechanism of the confirmation bias, the PMEs are seen in a different light from one moment to the other. Consequently, feeling "back home" near the initial attitude, the level of ambivalence drops and the attitude strength increases a little bit.

3.5

At time step 284, an attitude exchange with an uncertain discussant arguing pro and contra both parties (see bullet 5). The result is, at the moment of communication, that the ambivalence of the recipient is strongly elevated, whilst the attitude is far from responding as sensitively as in event 2 (univalent communication).

Figure 11. Time plots of the various characteristics of attitude strength (and attitude strength itself). The figure is an example of how the model's output on the level of one particular citizen. The x-axis is divided into the 365 days before voting day. The y-axis shows the relative values of the different attitude components. On day 93, this citizen gets in contact with a strong supporter from the opponent party. The initial attitude of the receiver is almost immediately converted (one has to know that the ambivalence of this citizen is relatively high compared to the average citizen in the model). However, the impact of this conversion is not lasting very long. After some 100 days the citizen might think: "Three months ago, I felt completely convinced by my colleague, but now I feel quite sure again that I have always been right."

Aggregate Level

3.6

Another look at the model dynamics is provided by figure 12. Party A does not accumulate (Ψ = 0) whereas party B does strongly accumulate (Ψ = 32). The 100 simulated citizens are aligned horizontally according to the valence and extremity of their initial attitude. The strongest partisans of party A are at the upper edge of each graph, whereas the strongest partisans of party B are at the lower edge. The apartisans are positioned around the zero-line. At every time step, the hypothetical vote of each citizen is depicted resulting in a trace over time. Dark states encode for votes pro party B, light states encode for votes pro party A. Blank states denote that this citizen would not have participated in the elections. The turnout underlying these examples was set at 82%. The emerging picture fits into one of the most stylized facts of citizen psychology. Obviously, the initial apartisans in the middle of the figure are mostly affected by the advertising activities. This is visible as frequent changes of the party preference (changing from dark to light states and vice versa) and long periods of undecidedness (blank states). These undecided voters have been identified as the main target group in political advertising (Moffitt 1999). Indeed, some weak partisans of party B are converted (their states becoming light). This process is observable after time step 50 (see box 1 in figure 12) and can be attributed to the early dominance of party A due to its zero accumulation strategy. The re-conversions of party B within the last two weeks before voting day are visible in box 2. An interesting effect is the rapidly growing uncertainty of the supporters of party B at the beginning of the model run (increasing number of blank traces).

Figure 12. Overview of the volatility of the electorate encompassing 100 citizens (the temporal trace of the preference of each citizen is represented as a horizontal line) during the 365 days before voting day. The vertical position of every citizen depends on his/her initial attitude valence and extremity (between -1 for extreme support of party B, +1 for extreme support of party A, and near 0 for apartisans). Blue color means that, on a particular day, this citizen is supporting party A, red color means that this citizen is supporting party B. In this example model run, party A is advertising relatively early, while party B concentrates on strong accumulation with a big final burst. Window 1 shows the early advertising of party A yielding a considerable number of initial apartisans near the zero extremity line, while window 2 documents the final burst of party 2 regaining almost all of these citizens shortly before voting day.

A First Sensitivity Analysis and Application of the Model

4.1

We have investigated the sensitivity of the optimal degrees Ψ of accumulating campaign resources (one possible model output) against two input parameters: one metrical parameter (speed of memory decay) and one structural parameter (the presence or absence of a model assumption). The focal model assumption is the second axiom of Zaller's Receive-Accept-Sample (RAS) model: "People tend to resist arguments that are inconsistent with their political predispositions, but they do so only to the extent that they possess the contextual information necessary to perceive a relationship between the message and their predispositions" (Zaller 1992, p. 44). In the context of the PASS model, the axiom means that citizens habitually more interested in politics are more resistant against uncongenial persuasive messages because they can access more knowledge (see eq. 1) to find out if a given message is congenial or uncongenial. Technically, the presence or absence of the RAS-A2 is implemented as a module of the citizen initialization process that can be switched on or off. If the module is on (presence of the RAS-A2), the individual strength of the confirmation bias χ_c is derived from the individual level of involvement I_0,c (see eq. 5a). If the module is off (absence of the RAS-A2), the strength of the confirmation bias is set independently of the individual involvement (see eq. 5b).

4.2

The evidence for relatively low levels of memory decay (between 0.0015 and 0.0035) originates from data gathered in a study on the effectiveness of TV ads in consumer product marketing (Zielske and Henry 1980). The evidence for relatively high levels of memory decay (between 0.0035 and 0.0055) is taken from a study on issue saliences in response to media coverage (Watt, Mazza and Snyder 1993) and a study on brand awareness depending on advertising intensity (West and Harrison 1997) (see the the Appendix for parameter estimation). Crossing the dimension of the decay parameter with the structural dimension of the RAS-A2 results in the following 2 × 2 matrix of the four experiments:

Table 1: Structural and parametrical attributes of the experiments 1 to 4
speed of memory decay	RAS-A2 absent	RAS-A2 present
high	experiment 1; Ψopt,1	experiment 2; Ψopt,2
low	experiment 3; Ψopt,3	experiment 4; Ψopt,4

4.3

In each experiment i, the optimal degree of accumulation Ψ_opt,i for party A is determined. The central hypothesis with regard to the outcomes is (see eq. 4.15):

(14)

4.4

Previous to explicating this hypothesis, it is important to remember that a high level of accumulation (for example 16 ≤ Ψ ≤ 64) means to release the majority of persuasive message relatively late within the time period of one year previous to voting day. In contrast, a low level of accumulation (for example 0 ≤ Ψ ≤ 8) means to release the majority of persuasive message relatively early (see figure 4.2 on p. 5).

4.5

The rationale of the hypothesis above is as follows: high memory decay speed will push the optimal degrees of accumulation towards high values since the traces of persuasive messages released early are rapidly forgotten. Low memory decay speed will push the optimal degrees of accumulation towards low values. Persuasive messages released early have the effect to persuade initially uncertain supporters of the opponent party (to bring them across the zero-line) and to prevent the initially uncertain supporters of the own party from crossing the zero-line. Once an initially uncertain supporter from the opponent party has crossed the zero-line, the confirmation bias reinforces this attitude conversion and helps to stabilize this attitude (increasing its extremity and decreasing its ambivalence). In the following, this effect is called the "early-conversion-and-stabilizing effect".

4.6

In contrast, if the speed of memory decay is high, the early-conversion-and-stabilizing effect cannot establish properly because the early released persuasive messages just peter out too rapidly in the citizens' memories. That is, the same temporal density of persuasive messages that is sufficient for the early-conversion-and-stabilizing effect to occur for a particular citizen under the condition of low memory decay does not produce this effect under the condition of high speed of memory decay.

4.7

Similar to low memory decay speed, the presence of the RAS-A2 will push the optimal degrees of accumulation towards low values. Citizens highly interested in politics perceive more persuasive messages from the campaign arena (see eq. 1) and evaluate them more carefully with regard to their congeniality (see eq. 5a). One year previous to voting day, there are citizens which moderately or strongly identify with a party and which are (at the same time) strongly interested in politics (see figure 9). If a party releases the majority of persuasive messages relatively early (low accumulation), these citizens will eagerly perceive these PMEs and, additionally to the sheer number of perceived PMEs, heavily weight them by means of their strong confirmation bias. Remember that according to the RAS-A2 the strength of the confirmation bias is dependent on the level of initial interest in politics. In other words, any party which is relatively late (high accumulation) will have the problem of these supporters which have been previously stabilized by the opponent. In the following, this effect induced by the RAS-A2 is called the "early-supporter-stabilizing effect".

4.8

If RAS-A2 is absent, the early released PMEs are still perceived eagerly by all the highly interested citizens but the initial supporters among them do not automatically have the tendency to discern congenial PMEs from uncongenial PMEs (by means of a higher credibility, see eq. 5a and 5b). In sum, advertising early is expected to be far less efficient, if RAS-A2 is absent.

4.9

The hypothesis (see eq. 14) can now be substantiated. In experiment 1, the structural effect (absent early-supporter-stabilizing effect) and the parameter effect (absent early-conversion-and-stabilizing effect) will be synergetic and push the optimal degree of accumulation towards high values. In experiment 4, the effects will be synergetic as well, but in the opposite direction, i.e. towards low values. In the experiments 2 and 3, the effects are expected to annihilate each other. Some medium degree of accumulation will be optimal. If, however, the model sensitivity against the memory decay speed dominates the model sensitivity against the presence or absence of the RAS-A2, the optimal degree of accumulation is expected be higher in experiment 2 than in experiment 3. If the structural sensitivity is dominant, the optimal degree of accumulation is expected to be lower in experiment 2 than in experiment 3.

4.10

We have conducted 36'000 model runs for each of the four experiments. This number was required for isolating statistically significant patterns. At the start of each run, the party A and party B were randomly assigned a certain degree of accumulation out of six possibilities (0, 2, 8, 16, 32, and 64, see figure 2). This resulted in a matrix of 6x6 = 36 possible strategy encounters between the parties. Consequently, for each of these encounters, 1'000 runs were collected. In each run, either party A or party B emerged victorious. In the runs ending in the indeterminate condition of equal numbers of party supporters on both sides (9% of all runs on average), the victory was randomly assigned to one of the parties. The specific number of victories of party A was counted separately for each strategy encounter and was transformed into the winning probability of party A for each of the 6x6 strategy encounters. Next, the probability estimates were transformed into ranking scores. Each combination of party strategies is scored according to its statistically significant (p=0.05) superiority to the other 35 strategy encounters (from the viewpoint of party A). In other words, if the winning probabilities of two strategy encounters do not differ significantly, their ranking scores are identical. As a reading example taken from experiment 1 in figure 13, the strategy encounter (party A = 0; party B = 2) is superior to six other strategy encounters, whereas the strategy encounter (party A = 32; party B = 64) is superior to 23 other strategy encounters.

Figure 13. Strategy ranking scores for the 6 × 6 strategy encounters in each of the four experiments. Generally, the higher the winning probability of party A under a specific strategy encounter of the opposite parties A and B, the higher is the relative ranking score for that strategy encounter (see text)

Discussion and Conclusions

5.1

The goal of this paper has been to develop an empirically grounded simulation model of the formation of political attitude strength within interpersonal discussion networks including the subsequent voting behaviour. The model so far encompasses existing theories from cognitive science and social psychology that are, mostly, supported by a number of empirical studies. In the first part of this section, the results from figure 13 are interpreted in order to answer the question of the sensitivity of the optimal accumulation degree Ψ_opt as a function of model parameters. In the second part, we suggest some avenues of reducing the complexity of the model while clearly pointing to the information lost. In the third part, the transfer of the political attitude model into a consumer attitude model is discussed.

Model Sensitivity

5.2

The most salient result from our first sensitivity experiments is that the model is only sensitive against the presence or absence of the second axiom of Zaller's RAS model (RAS-A2), if the speed of memory decay is assumed to be low. The reason for this pattern is that if memory decay speed is supposed to be high, the "early-supporter-stabilizing effect" from the RAS-A2 cannot establish because any stabilization is impossible under high memory decay speed. In contrast, under the condition of the low memory decay, the "early-supporter-stabilizing effect" is clearly established.

5.3

The experiments confirm the hypothesis that in experiment 1 and 4 (see table 1) the optimal degrees of accumulation are most extreme (although experiment 2 is very close to experiment 1). If both the decay speed is low and the RAS-A2 is present (experiment 4), low degrees of accumulation appear to be highly efficient since interested initial supporters can be stabilized and undecided citizens can be converted and stabilized. If the opposite party B does accumulate between the levels 2 and 32, the losses of effect in terms of memory decay seem to be negligible. If, however, the opposite party does strongly accumulate on the maximum level of 64, it is risky for party A not to accumulate at all (level 0 or 2). Under this condition, the maximum ranking scores are found at levels of 8 and 16. An interesting situation for party A arises if it is known that party B takes the otherwise optimal general strategy of party A, i.e. no accumulation (see the B0 segment). Then, the best thing party A can do is to accumulate between levels 8 and 32, but again, not on level 64.

5.4

In experiment 1, the general rule for party A is to accumulate just below the maximum, but not above, as is reflected by the inferior results at the accumulation level of 64. The more party B is accumulating, the more important is it for party A to imitate that strategy. The results of experiment 2 are qualitatively equivalent to the results of experiment 1. This illustrates the model's insensitivity against the presence/absence of the RAS-A2 if memory decay speed is high.

5.5

In experiment 3, ranking scores do not differ very much from each other and characterize a sort of trade-off "plateau" if both parties do not accumulate at the highest level of 64. Under the condition of these strategy encounters, the benefits from stabilizing attitudes and the benefits of recency effects on the PME accessibilities largely cancel each other out. The peak at A8-B32 is not visible in the winning probabilities and is probably caused by the small differences between the winning probabilities and the specific method of translating winning probabilities into ranking scores.

5.6

At first sight, it might seem that there is no clear answer to the initial question of the optimal degree of accumulation campaign activities towards voting day simply because the model is too sensitive against the model parameters of memory decay speed and the presence or absence of the RAS-A2. However, the current support from empirical studies is not equally strong for all of the four experiments. If we trust in the empirical studies suggesting that the resistance axiom from Zaller's Receive-Accept-Sample theory is true (Zaller 1992), we can direct our attention to the experiments 2 and 4 from the analysis. Furthermore, if the low memory decay speed supported only by one of the marketing studies (Zielske and Henry 1980) is neglected in the light of the other studies pointing unanimously to a higher speed of memory decay (Watt et al. 1993; West and Harrison 1997), the subsequent discussion can completely concentrate on experiment 2. Combining the RAS-A2 with a high memory decay speed seems to be the most relevant experimental setting for answering our initial question of optimal temporal resource allocation during political campaigns. In summary, looking at the ranking scores yielded in experiment 2, the answer that can be derived from the set of experiments performed in this section is to accumulate between at levels of Ψ = 8, Ψ = 16 or Ψ = 32 independently of the expected level of accumulation of the competitor. To illustrate this range of optimal degrees of accumulating, the average of the accumulation curves from figure 2 with Ψ = 8, Ψ = 16 and Ψ = 32 is depicted in figure 14. Please note that this result is sensitive to the assumption that memory decay is high and that the second Axiom of the Receive-Accept-Sample (RAS) theory is true.

Figure 14. The optimal degree of accumulating campaign resources towards voting day under the condition of high memory decay and the presence of the second axiom from the Receive-Accept-Sample (RAS-A2) model (Zaller 1992)

5.7

Our results are surprisingly coherent but not totally congruent with the real world practice. In the German General Elections, the "hot phase" of the elections starts between three and six weeks before voting day (Finkel and Schrott 1995). If in our model the threshold for perceiving the start of the hot phase is set at the threefold baseline activity level of 3 x 0.5 = 1.5 (an activity level that is assumed to be perceived as the start of the hot phase by almost every citizen, see figure 14), the current practice corresponds to accumulation levels of Ψ = 16 (the hot phase lasting six weeks, see figure 2), Ψ = 32 (the hot phase lasting four weeks), and Ψ = 64 (the hot phase lasting three weeks). In the light of our simulation results, this means that the practitioners generally have a good intuition about the optimal degree of accumulation with a slight tendency to accumulate too much.

Possibilities of simplification

5.8

There are several possibilities of simplifying the full attitude strength model (see table 2). First, whenever for some project the phenomenon of human attitude bolstering is not considered as essential, the mechanism of suppressing or elevating the credibilities of new persuasive messages can be omitted (see eq. 5a and 5b). However, without implementing some type of confirmation bias, the dramatic nature of the moment of conversion disappears (see figure 11, bullet 4); there will be a smooth crossing of the zero line. Without an implemented mechanism of confirmation bias, the common sense phenomenon of "seeing the same evidence from a different angle from one moment to the other" is not represented in the model. Every modeler has to verify if this feature is important for the specific purpose of the specific research project.

Table 2: Possibilities of simplifying the model by omitting specific model components. The modeler has to decide if the loss of psychological detail is relevant to her/his project
Omitted Model component	Loss of psychological detail
simulation of suppressing or elevating the credibilities of new persuasive messages depending on their congeniality of the receiving citizen	Human attitude bolstering "The opposite is not very credible." The dramatic nature of the moment of conversion "Since today I see everything from a different angle."
simulation of the temporal decay of persuasive messages	Recency effects typical for information integration under low involvement Antagonism between an initial attitude anchor and short-term conversion "One week ago, I felt completely convinced by my colleague, but now I feel quite sure again that I have always been right."
simulation of the ambivalence and involvement component of attitudes	Attitude-behaviour link "First, I feel very certain about my opinion and second, I am really curious in the outcomes of the election. So, for me it is obvious to participate in the election."
simulation of the involvement component of attitudes	Attention to advertisements I am really not interested in the elections. Even if I notice something about the parties, it is instantaneously forgotten". Communication behaviour "I am really curious in the outcomes of the election. I will start a discussion with Paul this evening." "I feel very sure about my opinion; it will be easy to convince Paul."

5.9

Second, whenever for some project the temporal decay of persuasive events is not regarded as essential, the process of memory decay has not to be simulated explicitly. For example, if involvement during attitude formation is extremely high (buying an extensive consumer product or not), recency effects can be neglected. However, without explicitly considering memory decay, the diminishing impact of an almost forgotten persuasion act (resulting in the short-term "excursion" to the opposite opinion, see the time span between bullet 2 and 4 in figure 11) cannot be simulated. Similarly, if the antagonism between an initial attitude anchor and short-term conversion is considered as central for the cognitive units of a given project, simulating memory decay is essential.

5.10

Third, whenever the attitude-behaviour link is not central for the focal project, the dynamical simulation of the ambivalence and involvement component can be replaced by constants. However, in projects aiming at consumer simulation or diffusion of innovation, the attitude-behaviour link is probably crucial, since after all, the actual purchase of the product is most relevant for the supplier. In the full PASS model, the changing levels of ambivalence and involvement are used to determine the following behaviour of the voters:

• communicating as a certain voter or as an uncertain voter at time step t_k
• communicating as a credible or an incredible voter at time step t_k
• participating in the election or "stay at home" at voting day

5.11

Clearly, if the PMEs are simulated as going into one single mental account, any information about ambivalence gets lost. Similarly, if the involvement is treated as a constant, i.e. if the involvement does not depend on the recent frequency of perceiving persuasive messages, the levels of involvement cannot be used to discern between PMEs that are perceived when the receiver has already been made attentive (high involvement) and PMEs that are perceived when the receiver is still inattentive (e.g. at the beginning of a campaign, when the first PMEs are used to "wake" up the citizens first).

Transferability to consumer psychology

5.12

The PASS model is generally suited for research projects that are targeted at simulating the formation of attitudes in social networks with individuals in a low-involved mind set. The model is not suited for all projects simulating attitudes that are formed under the condition of high involvement. Such projects would be attitude formation towards buying an expensive car or not, starting a new job or not, moving to a foreign country or not, adopting a new technology or not, or to contract insurance or not. For example, the assumptions of extracting only the affective content from original persuasive messages, of forgetting relatively rapidly, or of applying the "how do I feel heuristic" do not hold in these domains of high involvement human decision making. In these situations, the affective and holistic response is partly overwritten by a more cognitive, data-driven and systematic response (Bobrow and Norman 1975, Breckler and Wiggins 1991, Chaiken, Liberman and Eagly 1989, Dulany 1991, Epstein 1991, Petty and Cacioppo 1986). Processes of mental correction (Petty and Wegener 1993, Wegener and Petty 1997, Wilson and Brekke 1994) are activated to avoid cognitive biases that might be deleterious for the individual.

5.13

According to the low-involvement condition, the model could be easily adapted to the field of preconscious formation of attitudes towards low involvement consumer products like tooth paste or soap powder (Janiszewski 1988, Shapiro 1999, Shapiro and Krishnan 2001). Since the model was put forth in a two-party setting, it is applicable to simulate the effects of the advertising schedules of two competitive brands (e.g. Elmex vs. Colgate tooth paste). One of the most advanced (and award-winning!) models in the field of consumer product advertising (Naik, Mantrala and Sawyer 1998) does explicitly mention the requirement to extend the model by including competition between two products.

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