Toward a sustainable email marketing infrastructure

Toward a sustainable email marketing infrastructure

Available online at www.sciencedirect.com Journal of Business Research 61 (2008) 1191 – 1199 Toward a sustainable email marketing infrastructure ☆ O...

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Available online at www.sciencedirect.com

Journal of Business Research 61 (2008) 1191 – 1199

Toward a sustainable email marketing infrastructure ☆ Oleg V. Pavlov a,⁎, Nigel Melville b , Robert K. Plice c a

b

Worcester Polytechnic Institute, Worcester, MA, 01609, USA Stephen M. Ross School of Business, University of Michigan, Ann Arbor, MI, 48109, USA c San Diego State University, San Diego, CA, 92182, USA

Received 1 August 2007; received in revised form 1 October 2007; accepted 1 November 2007

Abstract Email marketing is a legitimate, lucrative, and widely used business tool that is in danger of being overrun by unwanted commercial email (also known as spam). Conventional approaches to maintaining the robustness of legitimate email attack pieces of the problem. In contrast, this article asserts that the email marketing infrastructure is a complex system requiring holistic analysis. In order to understand the underlying dynamics of the spam industry and to examine alternative mitigation strategies, the article develops a system dynamics model. The modeling process reveals that the system conforms to the limits-to-growth generic structure. Simulations suggest that filtering may have the unintended consequence of increasing the global amount of spam. The unexpected increase comes about because better filters can actually assist spammers by abating an information deficit. © 2007 Elsevier Inc. All rights reserved. Keywords: Email; Marketing; Spam; System dynamics

1. Toward a sustainable email marketing infrastructure The Internet offers a new paradigm for marketing, engendering a shift from product to customer focus that includes micro-level customization and customer relationship management (Rust and Espinoza, 2006). During the past decade, new forms of marketing communication gained in popularity. Search-based advertising, for example, grew from virtually nothing in the early 1990s to a $14 billion industry in 2006 (Elkin, 2007). Email marketing has been growing at the annual rate of 10%; 70% of all retailers now employ email marketing (McCloskey, 2006).



The authors acknowledge the helpful comments and suggestions of participants in the 13th International Conference on Computing in Economics and Finance, Montreal, Canada, June 14-16, 2007 and 25th International Conference of the System Dynamics Society, Boston, MA, July 29–August 2, 2007. ⁎ Corresponding author. E-mail addresses: [email protected] (O.V. Pavlov), [email protected] (N. Melville), [email protected] (R.K. Plice). 0148-2963/$ - see front matter © 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.jbusres.2007.11.010

Ironically, email marketing may be its own worst enemy. The Internet drastically lowers communication costs. Email marketing provides twice the return on investment (ROI) relative to other forms of online marketing: $57.25 for each dollar spent versus $22.52 (Direct Marketing Association). In turn, low production costs spur greater production, inducing entry to the industry by legitimate and not-so-legitimate marketers, which further increases the volume of email messages sent. As a result, consumers are awash in a sea of ads and information, some useful and some not. Knowledge workers sift through hundreds of such emails per week, more than one-half of which are spam, leading to information overload — a situation when more information is not better (Schwartz, 2004; Simon, 1971). The bottom line is that useful email marketing messages are lost in the background noise with negative consequences for shortterm ROI and long-term industry health. The marketing industry recognizes the spiraling situation of email overload and its deleterious impact on ROI (Nussey, 2007). The fundamental thesis of this article is that the email marketing infrastructure is a complex adaptive system, which necessitates an examination of the system as a whole rather than

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isolated components (Kofman and Senge, 1993; Woodside, 2006). The limitations of applying reductionist thinking to social, technical, and biological systems is well documented (Senge, 1990) and is exacerbated by inherent human blind spots to the effects of dynamics and feedback (Moxnes, 1998). As explained below, such limitations have impeded attempts to stem the tide of spam and to maintain a robust email marketing infrastructure. This article analyzes email marketing using system dynamics, which is a method that embodies the logic of feedbacks and employs computational models to simulate dynamic behavior. Graphs show the simulation results, using forms such as the volume of spam sent versus time. A post-simulation analysis in terms of feedback effects leads to a better understanding of the underlying drivers of the behavior of the email system. Thus, the method is consistent with the twin objectives of raising awareness of the hidden dynamics that impact industry health and examining the effectiveness of various mitigation strategies. The system dynamics analysis in this article reveals several mechanisms that explain key phenomena associated with the email marketing infrastructure. The first mechanism is that limited human attention acts as a limit to growth of the email marketing system. The second mechanism is that filters have an unintended consequence. That is, filters lead to fewer emails in user inboxes but much greater volumes of spam in the email system as a whole. Finally, the article explains this unintended consequence of filtering in terms of the spam targeting mechanism: filters act as a proxy for an information resource that spammers lack and enable spammers to achieve the effect of message targeting. The next section includes a review of prior research examining email marketing and spam and reveals that most approaches involve a focus on one particular aspect of the email marketing system, rather than analysis of the system as a whole. The section also provides an overview of the system dynamics methodology. The subsequent section develops a system dynamics model and offers an analysis of its behavior. Concluding remarks discuss implications for marketing professionals and policy markers. 2. Approaches to analyzing email marketing 2.1. Prior research Prior research on email marketing and spam falls into two broad categories. The first includes studies that focus specifically at reducing spam from a wide range of perspectives. The second includes studies from the marketing literature that examine determinants of response rates for email marketing campaigns. Most studies of email marketing and spam reduce the problem to one or two core components, analyze those components, and make recommendations based on that analysis. A frequent topic is the development of more efficient algorithms for distinguishing regular email from spam (Fawcett, 2003; Gray and Haahr, 2004). Filtering techniques are one of the most

popular topics of the two major conferences on spam: the Conference on Email and Anti-Spam (CEAS) and the MIT Spam Conference. To enhance filtering, email providers maintain lists of computers from which they do not accept any email: the so-called black-hole lists (Goodman et al., 2005). Another strategy is to augment filters by maintaining lists of acceptable senders — email from any computer that is not on the list will be rejected on the premise that the email is spam (Goodman et al., 2005). Another vigorous area of research examines the regulatory environment and the impact of legislation on email marketing and spam (Goldman, 2006; Gratton, 2004). Here the thinking is that laws can constrain the production of email marketing and so can eliminate bad email marketing. But, the CAN-SPAM Act of 2003 in the U.S. has not been effective in stopping the flood of spam (although a number of recent legal cases may potentially send a signal to less-than-legitimate operators). Beyond filtering and legal mechanisms, other approaches include reducing email overload by aiding recipients with information processing, specifically, presorting arriving email (Croson et al., 2005). Similarly, another proposal involves innovative use of a filter as part of a dynamic pricing mechanism, where price is determined proportionally to the filter score assigned to the message by a filter (Dai and Li, 2004). Increasing the cost of sending email may alter the economics of spam toward enhanced overall efficiency (Goodman et al., 2005). In particular, email service providers may impose a reverse Turing test (to test that the sender is human) and require that computers of spammers solve difficult computations in order to increase the cost of sending spam. Researchers also employ welfare economics to examine the distribution of surplus between sender and receiver based on whether a message has value to a given receiver (Loder et al., 2006). One analysis uses a game theoretic approach to analyze the two-agent non-cooperative game between sender and receiver, finding a unique Nash equilibrium and enabling prediction of the optimal point in the tradeoff between Type I and Type II filter errors (Androutsopoulos et al., 2005). Another study demonstrates the potential of systems thinking by developing an exploratory model of email communication and suggesting that this may be a very fruitful approach (Pavlov et al., 2005). Several marketing research studies concentrate on predicting response rates, such as for catalog mailing (Basu et al., 1995). Recent studies look specifically at email communication. For example, a model of online clicking behavior attempts to predict and improve response rates for email communications (Ansari and Mela, 2003). In this study, the focus is on learning how to use individual preferences to custom-design marketing emails, including aspects of content inclusion and presentation design. The model accounts for the heterogeneity in preferences and the existence of some unobservable variables. Ansari and Mela find that customization is very desirable, but not easily achievable. Yesmail and DoubleClick, for example, are two companies that specialize in email customization for commercial clients. Overall, marketing studies tend to focus on manipulating specific, short-term behaviors with the goal of improving return on investment.

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In sum, existing research is effective at improving filters, even though their deployment does not seem to stem the flow of spam. Prior research also helps to inform regulatory mechanisms, gives rise to proposals for new methods of spam mitigation, and demonstrates the viability and usefulness of systems thinking applied to the spam problem. To complement and extend existing studies, this article models email marketing as a socio-economic system and examines how the system behaves and responds to two specific policies. 2.2. System dynamics methodology The analytical tools of system dynamics are particularly appropriate for this investigation. Developing a system dynamics model involves a series of five steps (Randers, 1980). The first step is to define the system boundary that is appropriate for the research problem, drawing on observation, prior research, and knowledge elicited from experts. Based on the accounts of the spam industry (for example, McWilliams, 2005), the present analysis sets the boundary of the model to include the following economic actors: senders of email (broadcasters), sponsors of commercial messages, recipients of email, and technology firms that provide filtering products. The second step is to define the variables of the system. In this analysis the variables are: the volumes of spam and regular email sent by the respective types of broadcasters; the stock of messages in the backlog; the attention endowment (which measures the processing capacity of the recipients); the revenue paid to sponsors of commercial messages; and filter quality in terms of error rates (such as false-positives and false-negatives). The third step is to identify the reference modes of the system; that is, how individuals and organizations think and react within

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the system over time. For example, what actions do recipients take when their daily attention endowment (measured in terms of time) is exhausted? The fourth step is to set the relationships among variables into a causal loop diagram. Finally, the researcher builds and validates a computer model. Simulations of the model then lead to policy recommendations. 3. Causal mechanisms in email marketing system The model development steps outlined above lead to the construction of a system dynamics model of email marketing. This section explains the key causal mechanisms of the email system and the baseline dynamic behaviors they generate. Two last subsections describe an unintended consequence of filtering and compare the filtering outcome to message targeting. 3.1. Attention as a limiting condition Conventional marketing research on email communication and spam examines individual variables while acknowledging some simple causality between the variables. The email marketing context is another advertising medium with differences in key characteristics relative to print media: it is cheaper, information intensity is higher, personalization is easier, and so forth. The causal logic is that more and better volumes of email marketing lead to desired consumer actions. This view of email marketing is overly simplistic. Email is part of a complex social system that is stimulated by economic forces and constrained by cognitive limitations of the receiving side. Fig. 1 shows a schematic view of the situation. Arrows in the diagram indicate causal relationships between variables. Positive arrows imply a positive relationship and

Fig. 1. Causal relationships in the spam system.

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negative arrows mean that the variables move in opposite directions. Thinking in terms of systems reveals two primary feedback effects: a reinforcing loop leading to a wealth of information and a balancing loop leading to a poverty of attention. The letters R (for reinforcing) and B (for balancing) mark the loops. While the reinforcing loop determines the supply of spam, the balancing loop acts to quell the growth of messages. Message broadcasters and their sponsors drive the growth process of spam volume. Suppliers of commercial email messages produce and send messages to email recipients. Examples are legitimate newsletters from a consumer’s bank, legitimate but unsolicited messages from online shoe stores, or illegitimate messages intended to defraud. Spam filters analyze arriving email and discard messages which have been identified as non-valuable. However, due to the false-negative errors by the filters (Cormack, 2006), a certain percentage of unwanted spam messages is not identified as spam and, therefore, is not discarded but added to the message backlog. A filter that commits fewer false-negative errors allows fewer unwanted spam messages through and thus improves the average proportion of valuable spam messages in the backlog. The model includes the percent of false-negatives as an exogenous policy parameter. Similarly, when the filter misidentifies a valuable message as spam, a false-positive error is committed (Cormack, 2006). False-positives have a negative effect on the average fraction of valuable spam messages in the backlog. Another exogenous policy parameter is the fraction of spam messages that are valuable. The parameter represents the targeting effort by the email marketers. Ideally, the spammers would send only messages that are of interest to recipients, thus achieving perfect targeting. In the situation of perfect targeting, the fraction of valuable spam messages is one. The fraction of valuable spam messages positively affects the average fraction of valuable spam messages in the backlog. Spam and regular messages are added to the message backlog. The message backlog is a stock variable, which is indicated by a rectangle around the variable name. Backlogged messages can be either processed or deleted. The size of the message backlog and the average fraction of valuable spam messages in the backlog determine how many valuable spam messages can potentially be processed by the recipients. Recipients spend some daily time endowment reading messages in the message backlog. Hence, the number of valuable spam messages processed daily depends on the daily time endowment, the average fraction of valuable spam messages, and the size of the message backlog. Each of these three determinants has a positive effect on the number of valuable spam messages processed (Fig. 1). The model assumes that processed valuable commercial messages generate sales (otherwise the message would not be valuable) and the sponsor receives revenue. Assuming that revenue positively relates to spam funding (which is a stock), the graph connects revenue and spam funding with a positive arrow. More spam funding means more money spent on spam production, which means more spam added to the backlog, which means a larger message backlog. This causal logic

completes the wealth-of-information feedback loop, which tends to increase the supply of spam. When the time required to complete a task is greater than one’s time endowment, information overload occurs (Simon, 1971; Schultz and Vandenbosch, 1998). As information overload increases, recipients delete more messages (Fallows, 2003). These two relationships complete a balancing feedback loop called the poverty-of-attention loop. The feedback structure in Fig. 1 is an extension of a generic structure called limits-to-growth (Senge, 1990). To understand the dynamics of a system depicted in Fig. 1, the analysis proceeds to build a corresponding computational model and then to perform numerical experiments. The appendix provides a detailed description of the model. The following sections describe the experiments. 3.2. Baseline behavior The first experiment simulates the growth of spam, and Fig. 2 presents the resulting trajectories of selected variables. The dynamics that Fig. 2 reveals can be understood in terms of the causal links of the diagram in Fig. 1. The simulation starts at low levels of spam funding (line 2 in Fig. 2) and, correspondingly, low levels of spam production (line 3). Both spam funding and spam production are set to near-zero levels. The message backlog (line 4) is also set to a relatively low level. Email recipients have enough time to process messages and hence experience relatively low levels of information load (line 5) due to email. Correspondingly, recipients delete hardly any email (line 6). Gradually, the revenue from spam encourages more spam production (see the causal logic in Fig. 1). Some of the processed messages are valuable to the recipients (line 1). As the flow of spam rises, the number of valuable spam messages processed also increases for a period of time. If the attention of recipients were not limited, the reinforcing feedback loop (marked with an R in Fig. 1) would result in an exponential growth of spam production. However, spam does not increase indefinitely. At around time 80, information overload (line 5) starts to increase rapidly due to the swelling message backlog; this leads to more email being deleted (line 6). Because the forces of the balancing loop (labeled as poverty-of-attention in Fig. 1) become significant near the end of the simulation, the growth of variables eventually stagnates. The distinctive S-shaped trajectories are the result (Fig. 2). The convergence of the system to a steady state may seem unreasonable in light of the global growth of spam volume. But Melville et al. (2006) find that the spam flow to an educational institution (which has a fixed number of email inboxes) is generally steady during an academic year. This model also assumes a fixed number of recipients, and, therefore, a steady state appears to be a reasonable outcome. The steady state values for the stocks are in the Appendix. 3.3. Unintended consequences of filtering Existing research on email marketing and spam focuses mainly on the development of ever-more effective spam filters.

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Fig. 2. Transitory and steady state behavior of an email marketing system.

In theory, such mechanisms work well at mitigating information overload by accurately detecting a message containing text that indicates that the message is likely to be unwanted. Thus, it seems rational to deploy filters as a solution and to expect that better filters will lead to less spam. However, despite an apparent improvement in filtering techniques, the global volume of spam still appears to be growing (Garretson, 2007). As the analysis described in this section demonstrates, a view of email as a system suggests that improvements to filtering software may perversely contribute to the growth of the total flow of spam.

To simulate an improvement of the filtering technology, the percent of false-negatives and the percent of false-positives are gradually reduced beginning at time 30. The simulation avoids transitory dynamics by starting in the steady state. Fig. 3 displays trajectories from the simulation. Fig. 1 is helpful in understanding the causal logic of the simulation. Line 1 in Fig. 3 gives the percent of false-negatives. Note that the graph omits the false-positives trajectory because both trajectories (falsepositives and false-negatives) are similar. After day 30 in the simulation, the filter becomes better at identifying unwanted spam messages (line 1 drops), and,

Fig. 3. A simulation of an improved filter.

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Fig. 4. A simulation of improved targeting.

therefore, the average fraction of valuable spam messages (line 2) improves. This improvement leads to the processing of more valuable spam messages (see Fig. 1), more sponsor revenue (line 3), more spam funding (see Fig. 1), and more spam production (line 4 in Fig. 3). The simulation keeps track of the measure called spam as a fraction of all email traffic (see Fig. 1 and Appendix for the exact definition). Given that volume of regular messages is constant, as spam production increases spam as the fraction of all email traffic also increases (line 6). The growth of the spam production ensures that the spam added to backlog (line 5) returns to a steady state level. In summary, spam production is higher in the presence of better filtering. This outcome may be characterized as an unintended consequence of filtering. 3.4. The targeting effect of filters The finding that filtering contributes to the growth of spam may be puzzling at first. But, the result becomes more transparent when one realizes that filtering mitigates the problem of asymmetric information. An information asymmetry occurs when one party participating in an exchange knows something that the other party does not (Varian, 1992). A classical example of a situation with information asymmetries is a used car market (Akerlof, 1970; Jensen 2007). In the case of email, the information asymmetry is due to the fact that spammers do not know the preferences of recipients. Targeting improves the response rates of a marketing campaign (Chittenden and Rettie, 2003; Ansari and Mela, 2003). Message targeting involves choosing a message’s content, format, and timing to match the particular needs and preferences of its recipient. Spammers tend not to use targeting, not only because targeting is costly but also because spammers have less

ability than legitimate email marketers to obtain the information needed to customize messages to the preferences of each recipient. Instead, spammers rely on untargeted mass mailings. Increasing the exogenous variable representing the fraction of valuable spam messages (Fig. 1) simulates an improvement in targeting. After the fraction of valuable spam messages is raised on day 30, the average fraction of valuable spam messages in the backlog also rises (line 1 in Fig. 4). Correspondingly, valuable spam messages processed (line 2), sponsor revenue (line 3), and spam production (line 4) all grow. The experiments confirm that filtering and targeting have very similar effects on spam production. In both cases, spam production increases. By deploying filters, system administrators inadvertently enable the same outcome that would be obtained if the asymmetry of information were reduced and spammers were able to target their messages. 4. Summary and recommendations Despite the lucrative nature of email marketing, consumers are overloaded with information, both wanted and unwanted. However, the result of mitigation strategies that address only the individual dimensions of the problem is “record growth, and record irritation,” with spam accounting for 88% of all e-mail traffic in August, 2007 (Garretson, 2007). The main implication of this research is that the email marketing infrastructure is complex, requiring an analysis that takes account of the whole system. A system dynamics model that captures the key causal relationships in the system can identify the underlying dynamics and reveal unexpected consequences. Thus far, the primary industry response to excessive levels of spam has been to deploy filters. As the model system dynamics model reveals, this has given spammers the equivalent of the

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information they would need to target their messages. Consequently, filters are likely to encourage, not diminish, spam production. The literature contains a number of other approaches to mitigating information overload, including variants of email postage, attention bonds, and reverse Turing tests. Before industry and regulators choose any of these approaches for general implementation, system dynamics may be used for an analysis of the likely outcomes. Unlike filtering, some of these proposals would change the nature of email as a free, anonymous communications medium. The experience with filtering suggests that before taking such drastic measures to stem the flow of spam, policy makers and system managers need to evaluate the resulting system to confirm that the proposed changes do not lead to undesired behavioral and informational consequences. Such an analysis must take into account the dynamic feedback and causal-loop mechanisms that govern the system. The model presented and analyzed in this paper exemplifies the approach, and demonstrates the benefits of system dynamics modeling to analyze the email-marketing industry.

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Table 1 Model Recipients Parameters R Number of recipients aR Average volume of regular communication TR Time a typical recipient spends on email γ Normal response delay τ Message processing time ρ Fraction of valuable spam messages d¯ Average sensitivity to overload

100 recipients 10 messages/day/ recipient 20 min/day/recipient 4 days 1 min/message 0.01 dimensionless 3 dimensionless

Variables Message backlog Volume of regular messages Messages that are identified as valuable are added to the backlog Spam added to backlog Regular email added to backlog Daily time endowment The daily time required to process messages Information overload Processed messages Deletion Valuable messages in the backlog Valuable messages added to the backlog Valuable messages that are either processed or deleted Average fraction of valuable messages of all types (spam and regular email) in the backlog Valuable spam messages in the backlog Valuable spam messages added to the backlog Valuable spam messages that are either processed or deleted Average fraction of valuable spam messages in the backlog Spam messages in the backlog Removal of spam messages from the backlog either through processing or deletion Average fraction of spam messages (valuable and non-valuable) in the backlog Spam as fraction of all email traffic

Appendix A. System dynamics model This section contains a mathematical formulation of the model, which enables complete reproduction and simulation of the model. The model includes two types of broadcasters. One broadcaster sends only regular email; each regular message is valuable. The other broadcaster sends spam, which is financed by sponsors. Only a fraction of spam is valuable. The model has a coflow formulation (for definition, see Sterman, 2000) in the Recipients sector, which allows keep track of the message backlog, the number of valuable messages (both regular email and spam) in the backlog, the number of valuable spam messages in the backlog, and the number of spam messages (valuable and non-valuable) in the backlog.

(d/dt)M = mi − m0 − md a = aRR mi = bi + ai bi = (1 − η1)ρb + η2(1 − ρ)b ai = (1 − η1)a T = RTR T⁎ = (M / γ)τ λ = T⁎ / T m0 = min(T / τ, M / γ) mdAB= eod·d¯·(M / γ) dV AB  mAB dt ¼ mi 0 νAB = (1 − η i 1)(a + ρb) νAB ¯ 0 = (m0 + md)β P

AB

b ¼ VM

dV B B B dt ¼ m i  m o νBi = (1 − η1)ρb

νB0 = (m0 + md)ρ¯ B

qP ¼ VM

dB dt ¼ bi  b0

b0 = (m0 + md)θ¯ P

B h ¼M

b/(a + b)

Sponsors Parameters τS Spam budget duration ξ Fraction of surplus allocated to spam funding r Marginal revenue per spam message

10 day 0.1 dimensionless 2000 $/message

Variables

Fig. 5. Misspecification rate, Ф, and its relationship to false-positive errors, η1, and false-negative errors, η2.

Spam funding Expenditure on spam by sponsors Valuable spam messages processed Sponsor revenue Sponsor cost Sponsor surplus Spam budget allocation

(d/dt)S = i − e e = S / τS bp = moρ¯ RS = rbp CS = e π = RS − C S i = max(ξπ,0) (continued on next page)

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Table 1 (continued )

Table 2 Steady state values for variables

Broadcasters Recipients Parameter Price of sending a spam message Pb

1 $/message

Variable Spam production

B = e / pb

M V AB VB B S Ф

Message backlog Valuable messages in backlog Valuable spam messages in backlog Spam messages in backlog Communication funding Aggregate misspecification rate

8830 messages 2920 messages 492 messages 6402 messages 202,796 $ 0.1 dimensionless

Technology firm Parameters Initial percent of false-positives η˜1 η˜2 Initial percent of false-negatives Ф⁎ Tolerable misspecification rate Ф˜ Original misspecification rate λϕ Filter improvement delay τϕ Filter shock delay ε Negative shock to filter

0.01 dimensionless 0.12 dimensionless 0.1 dimensionless 0.1 dimensionless 10 day 1 day 0 dimensionless

Variables Misspecification rate Filter degradation Filter improvement Percent of false-positives Percent of false-negatives

(d/dt)Ф = ϕi − ϕ0 ϕi = ε / τ ϕ ϕ0 = (Ф − Ф⁎) / λϕ pffiffiffi g1 ¼ a g˜ 1 ; a ¼ U= U˜ pffiffiffi g2 ¼ a g˜ 2

The technology firm supplies a filter. The filter may block a valuable message, which is referred to as a false-positive error. The filter may allow a non-valuable spam message through — a false-negative error. The Receiver Operating Characteristic (ROC) curve (Cormack, 2006) summarizes the tradeoff between the two errors (Fig. 5). The area above the ROC curve is the aggregate misspecification rate, which this model denotes as Ф. If the tradeoff between false-positives and false-negatives remains constant, then, given some initial values, changes in the aggregate misspecification rate determine the new values for false-positives and false-negatives. The best filter corresponds to the upper left corner of the graph. The worst filter is the lower right corner of the graph. The lower left corner of the graph presents a no-filter situation. The model has been implemented and simulated in Vensim DSS. Table 1 has parameters and variables organized according to the four sectors of the model: recipients, sponsors, broad-

Fig. 6. Lookup function for effect of overload on deletion, eod.

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