Taking comfort in decisions: Implications in a pandemic

1.Introduction

Knowledge management involves collecting, storing, disseminating and using information to manage knowledge and help make decisions [1, 2]. Often the terms “data”, “information”, and “knowledge” are viewed hierarchically, where data consists of the building blocks of facts, information being how those facts are assigned, integrated, and contextualized into meaning, and knowledge the result of using those meanings to better understand the world and to make decisions.

Regardless of what field one examines, data is ubiquitous. Data is generated and used by government agencies, business organizations, cities and states, and even via devices like smart watches and fitness trackers, by individuals. Data not only is associated with historically “measurable” attributes, but also new attributes whose measurement is enabled by new technologies [3]. For example, consider marketing and advertising. Years ago, publishers and advertisers might have been able to quantify the number of newspaper and magazine readers and even understand their demographic mix, but today, websites can monitor how long viewers spend on a page, where the viewer came from, where he or she goes next, and what items on the page catch the viewer’s fancy. More data is collected in much more granular fashion that ever before.

Technology enabled capabilities create new challenges that address the three questions involving how knowledge is managed: How is data collected, stored and disseminated? How does data achieve meaning as it is integrated into information? How is information used to create knowledge, used to navigate the world, and used make decisions?

A key domain where knowledge management has changed the landscape of how practitioners do their job is health care and public health [4, 5]. Starting with the base unit of the patient, many ongoing measurements can be collected, all in service of answering the question, “How healthy is he or she?” Collecting data on attributes like blood pressure and pulse rates has been done for years [6], but advances in medical technology have enabled measuring building on the old measured attributes and measuring new attributes with a precision unthinkable even the recent past [7]. While collecting, processing, storing, and disseminating data and information for one person is challenging, doing this for large populations is even more so. Knowledge management systems are needed to make all phases of this endeavor happen.

The scope of academic research and publications in the area of knowledge management in health care decision modelling is enormous. Two macro categories may be defined as concerning Medical Issues and Management Practices. Medical Issues decision-making concerns topics such as conducting clinical trials [8, 9], modeling the transmission of infectious disease [10, 11, 12] and developing predictive simulation models used to predict the outcomes on patient intervention strategies [13, 14]. These papers illustrate medical decision modelling and concern strategies that directly affect individuals in societal or hospital settings.

The second macro area involves modelling Management Practices, which includes decision models used in government level programs such as the Medicaid system in the United States [15] or home health services [16]; large health systems such as managing conglomerates of hospitals formed in health care mergers and resource allocation between hospitals [17, 18, 19]; sundry management issues arising in hospitals, and day-to-day decision modeling at a micro level such as scheduling personnel [20, 21], managing intensive care units [22, 23] disaster preparedness [24] and allocating resources in the Covid-19 pandemic [25, 26]. At the intersection of these two categories is the issue of modeling technologies which can be medically oriented or management oriented [27] and decision modeling methodologies.

Clearly the application of knowledge management and decision-making technologies is broad, both as measured by the domains where the decision-making technologies and methodologies are applied, and also by the technologies and the methodologies themselves. The effectiveness of a specific technology or decision methodology often is situational, depending on the facts concerning the environment in question. Appropriateness depends the availability of technological and other resources, information availability, and the proclivities on the decision makers for among other things, a propensity to accepting and managing risk. Regarding risk, a decision maker might be a pessimist and somewhat risk averse, which might mean that one set of decision evaluative alternatives would be appropriate. Another decision maker might be an optimist which would mean that she might use another set of evaluative alternatives. The Comfort Criteria which we will discuss below, would be appropriate for this second optimistic decision maker.

The recent Covid-19 global pandemic has illustrated the benefits and challenges facing knowledge management and the process of making evidence-based decisions. Populations are aggregates of individuals and pandemics affect the health of populations as the contagion spreads from one person to many. As such, a pandemic’s effects range from the micro to the macro, from one person’s evolving state of health, to states of health in local communities, the nation, and the world.

Pandemics also are multidimensional because the contagion affects people and communities in many ways. While the core involves how the contagion affects a person’s health and then, the health of those around him, there also are effects along other dimensions. Examples include the economic, educational, political, and social dimensions. These dimensional effects also are interrelated, e.g., a contagion’s political effect involves closing schools, or its economic effect impacts the emotional well-being of displaced workers. We live in a multi-dimensional universe and effects along one dimension affect many others.

Because of these interrelationships, knowledge management and decision making in a pandemic not only involves looking along one dimension, or in one domain, but many others as well. A decision never is just a medical or public health decision, but depending on its nature also becomes, in effect, and economic, social, or even psychological decision too. It is natural that individuals associated with each domain, public health related and otherwise, and often with the best of intensions, think of their domain’s needs first while placing the needs of others in the background. Physicians first think about health. Business owners first think about their business. Parents first think about the health and education of their children.

Because a pandemic affects many domains, for decisions to be effective and equitable, we posit that they in some manner must be acceptable or satisfactory to multiple constituencies or stakeholders. Using advanced methods and decision tools can help. These methods and tools involve collecting, verifying, framing, and presenting information that is accessible to, and understood by, all parties. In addition, these methods and tools also must help integrate information across disciplinary domains. Doing this will result in better or at least more informed decisions to enable decision makers at all levels of the process, from an individual citizen to a head of state, make better decisions.

2.Specific issues related to pandemics

In this section we review five issues that are related to knowledge management and decision making in pandemic environments. While each issue also affects non-pandemic environments, the pandemic environment itself, and the ongoing crises and often chaos associated with it, exacerbates the immediacy of each issue and impacts how knowledge management systems function [28]. Five issues are:

4) For each governmental level and each constituency, many decision makers exist, with the decisions of one affecting the decision environment of another

Each level of government has many disciplinary constituencies. For example, in the United States federal, state, and local governmental units exist, and within each are advocates in the areas of medicine, public health, economics, commerce, social institutions, education, and politics. While countries with more top-down control can enunciate and more easily implement policies, countries with more governmental, disciplinary, and individual discretion may encounter “disharmony.” By this we mean, the recommendations by one jurisdiction may not be followed by another below it in the governmental hierarchy, or ultimately, even by individual citizens. This dissonance increases as the pandemic persists and people become perturbed at making ongoing sacrifices. The recommendations of one disciplinary unit in a jurisdiction may not be followed by other units, even in the same jurisdiction. For example, a state governor may require mask wearing and a city mayor may ignore the recommendation – of vice versa.

Figure 1 illustrates this dynamic for a given level of government, with the Medical/Public Health constituency at the center and other main constituencies surrounding it. While the public health constituency communicates policies from its perspective, the other constituencies receive these messages and, based on individual and governmental behavior and regulations, may amend the recommendations and act differently. This, in turn, may affect the progression of the contagion itself and change recommendations which creates a temporally evolving situation. Figure 1 represents one of four ‘slices’ or levels: The national, state, local, and individual. For each slice, Figure 1’s relationships are relevant, albeit achieving different levels of importance.

Figure 1.

Constituencies engaged in the decision process.

Individuals comprise the lowest hierarchical level, yet their behavior taken in aggregate drives all of the others. In some cases, individuals have little discretion – e.g., if restaurants are closed, people cannot dine indoors. But regardless of how higher-level decisions affect them, people (and lower levels of government) can choose to follow or ignore public health guidelines. Their decisions affect the overall health of the larger community: A business owner may choose to open her business circumventing local regulations; a locality may define regulations that conflict with its state’s; a state may ignore directions enunciated by the federal government.

Nothing is illegal here, given the decision rights of political entities at each level. However legal it is, when many entities make decisions with conflicting outcomes, the resulting disharmony creates a confusion and suboptimal environment for all concerned. Examples include rules for mask wearing, gym and beauty salon openings, attending sporting events, and attending social gatherings. Beyond confusion, legally conflicting decisions causes resentment and leads to circumventing the regulatory and governmental chain of command, creating a “wild west” environment where anything goes.

5) Constituencies often are pitted against each other in “zero-sum” type conflicts

A fundamental conflict underlying many decisions made in a pandemic concerns the tension between public health and other constituencies such as businesses (where public health decisions impact economic activity and jobs), education (where public health decisions affect a child’s educations and social development), and social institutions (where public health-based restrictions may affect religious organizations and family gatherings). While the conflicts need not be zero sum, often they are perceived to be so. Compounding the conflict is the ongoing nature of pandemics, where sacrifices – made by one constituency for another – rather than having a defined end, go on and on and become open-ended. A restaurant may be willing to close for a few weeks or even a month, but when one month extends to six and twelve months with no end in sight, the owner reconsiders and decisions change. The same is true for schools where students, especially those in elementary grades, may encounter negative effects regarding not only their education in online environment, but also impediments to their social and emotional growth. These repercussions often are more serious than the repercussions of a young child contracting the contagion with minimal adverse effects.

In perceived zero-sum environments each constituency often seeks to optimize its own returns, while downplaying others. Taken to the extreme, public health measures are recommended that discount economic impacts or educational impacts on children. While public health decision makers may point to the long run, and provide evidence where short term sacrifices will result in better long-term performance, information as disseminated and interpreted may belie these assertions. Or conversely, businesses may open and ignore the longer-term impact on the health of others who might catch the contagion – from the business owners perspective other’s suffering is unrelated to his customers or his business. Figure 2 seeks to capture this decision environment.

Figure 2.

Domains and the decision environment.

The inside circle contains four levels, from the national to the individual. The actions of each affect the others in a cyclical manner, and eventually individual decisions in aggregate affect amended government policies. While arguably each level contains all domains (or constituencies) portrayed, public health measures often are articulated and disseminated from the national level on down, often through recommendations of government agencies. These may or may not be followed by other levels but they are received and acted on. States also have public health agencies, but being closer to economic activity in the state, they may be more concerned with businesses and commerce. Localities are concerned with this as well, but here education often is paramount as schools (in the United States) are a local responsibility and parent interactions with government occurs at the local level. Finally, individuals are most aligned with social interactions with friends, family, and other institutions like schools, churches, and voluntary organizations.

The ultimate objective is to foster a harmonious decision-making environment where, while each constituency might not obtain its optimal outcome, the outcomes are aligned and, in some measure, good enough and satisfactory overall.

3.Implications informing decision modeling

The above discussion suggests that selecting a decision alternative in a pandemic environment is complicated because a pandemic environment by definition is unique and provides the decision maker with little information. Herbert Simon [31, 32] posits a theory of bounded rationality, where he discusses decision making when decision makers cannot always make mathematically optimal decisions, but rather must choose among decision alternatives while bounded by the restrictions of their own cognitive limits, and also limits imposed on them by their decision environment. One outcome of this is Simon’s idea of satisficing, i.e., making decisions that while not optimal, are good enough.

The decision problem as we frame it is not one of satisficing, but rather decision making under uncertainty. Here, the decision maker is still rational and seeks to make the best decision, in an environment where the probabilities governing the outcomes of the various possible states of nature are unknown. Because of this uncertainty and the unavailability of probability estimates, methods using expected returns are inappropriate. In this case the “bound” for the decision maker is the uncertainty surrounding the state of nature probabilities, i.e., the decision maker has no idea what the probability of occurrence of the various states of nature will be.

For decision making under uncertainty, various evaluation criteria exist for framing the problem and choosing the alternatives. These depend on the level of optimism and pessimism of the decisionmaker, or as we discuss here, his level of bias. For example, one commonly used method is to frame the decision using a regret criterion, where for each decision alternative, the payoffs for each state of nature are judged relative to the best possible payoff for that state of nature. This may be thought of as a glass half empty approach, because the outcomes are always found wanting when judged against the best.

While the regret criterion is appropriate for a pessimist, what about the non-pessimist, or the optimist? Here, we present an alternate method, which may be a more realistic approach, using what we call a comfort approach, where the payoffs are based on the difference between the actual payoff and the worst possible payoff for that state of nature. This may be thought of as a glass half full approach, and still falls within the broad purview of Simon’s bounded rationality concept.

For decision making in a pandemic, each constituency (or domain) makes decisions that affect itself and others. Some key issues that inform decisions and how they are made in pandemics are:

The next section discusses methodologies that can be used to make choices in this manner. Using these methods can reveal decision alternatives that meld the preferences of all constituencies to arrive at choices that better satisfy all parties’ underlying needs.

4.Decision modeling

A decision model affords analytical rigor to an unstructured problem, providing the capability to appraise alternatives which integrate the decision maker’s disposition [36]. In a decision problem, Ai is decision alternative i, for i=1,…,n; Sj is state-of-nature j, for j=1,…,q; and ai⁢j is the payoff if the decision maker selects Ai and the state-of-nature is Sj. In our discussion, we consider larger payoffs as better, without loss of generality. The quantity and quality of information regarding the states-of-nature vary in different situations, including the circumstance in which there are no dependable estimates of the probabilities of the states-of-nature. In this case, decision making under uncertainty, decision makers engage their disposition in choosing an alternative. We can use the terms disposition, attitude or bias interchangeably to represent the decision maker’s natural tendency regarding a general decision approach towards a sense of optimism or pessimism.

The decision maker uses the ai⁢j in determining the preferred decision alternative. A decision maker may summarize, or determine an aggregation of, the collection of potential payoffs for an alternative across the states-of-nature in order to efficiently compare the alternatives. Effective payoff is defined as Pi=𝐴𝑔𝑔j⁢[ai⁢j], and is a summary measure, or aggregation, of the payoffs across the states-of-nature for a particular alternative Ai. The effective payoff summarizes the decision maker’s evaluation of all payoffs that may be realized given that a particular alternative is selected and before knowing which state-of-nature occurs. One approach is to calculate: Pi=𝐴𝑔𝑔j⁢[ai⁢j]=Maxj⁢[ai⁢j]. This summary measure would be an optimistic view in anticipating the payoff. The decision maker could then select the alternative associated with the maximum effective payoff. This is the so-called maximax criteria. Another approach is to calculate: Pi=𝐴𝑔𝑔j⁢[ai⁢j]=Minj⁢[ai⁢j]. This summary measure would be a pessimistic view in anticipating the payoff. The decision maker could then select the alternative associated with the maximum effective payoff. This is the so-called maximin criteria. Below we will generalize the approach to include a decision maker’s bias which could be anywhere from pure optimism to pure pessimism. The decision criterion is to choose the alternative with the optimal effective payoff. Using the decision criterion of maximum effective payoff, we calculate Pi=𝐴𝑔𝑔j⁢[ai⁢j], for each alternative, Ai, and then select the alternative Ai⁣* such that Pi⁣*=Maxi⁢[Pi].

A decision maker may also use the criterion of regret, where regret is the difference between the payoff obtained given a chosen alternative and the best payoff that could have been obtained for that state of nature. We let Vj=Maxi⁢[ai⁢j], that is, the maximal payoff across the alternatives, given that state-of-nature Sj ensues. The regret associated with selecting alternative Ai, if the state-of-nature is Sj, is ri⁢j=Vj-ai⁢j. The regret is the difference between the payoff obtained by selecting alternative Ai, given that state-of-nature Sj occurs, and the most that could have been obtained, given that the best decision alternative for that state-of-nature had been selected. Effective regret is notated as Ri=𝐴𝑔𝑔j⁢[ri⁢j], and is a summary measure, or aggregation, of the regrets across the states-of-nature for an alternative [37]. The effective regret summarizes the decision maker’s evaluation of all regrets that may be realized given that a particular alternative is selected and before knowing which state-of-nature occurs. One approach is to calculate: Ri=𝐴𝑔𝑔j⁢[ri⁢j]=Maxj⁢[ci⁢j]. This summary measure would be a pessimistic view in anticipating the regret. The decision maker could then select the alternative associated with the minimal effective regret. This is the so-called minimax regret criteria. Below we will generalize the approach to include a decision maker’s bias which could be anywhere from pure pessimism to pure optimism. Using the decision criterion of minimal effective regret, we calculate Ri=𝐴𝑔𝑔j⁢[ri⁢j], for each alternative, Ai, and then select the alternative Ai⁣* such that Ri⁣*=Mini⁢[Ri].

Using the regret criterion in decision making implies a sense of reflecting on what is foregone by not having made the optimal decision. This is a glass half-empty mind-set, or a measure of opportunity loss for not having received the best payoff. A complementary approach, the Comfort Decision Model [38], is based on not on what is absent relative to the best case, but on what is achieved relative to the worst case. This approach implies a glass half-full outlook. Comfort reflects a sense of gratitude, while regret that of a sense of entitlement.

Comfort is defined as the difference between the payoff received by selecting alternative Ai and the worst payoff that could have been received under that state-of-nature. In comfort decision modeling, the decision maker determines how beneficial the payoff is contrasted to the worst case. In a sense, we determine the level of comfort the situation yields. Under this comfort perspective, we define Wj=Mini⁢[ai⁢j], that is, the minimal payoff if state of nature Sj occurs. The definition of the comfort associated with selecting alternative Ai, if the state of nature is Sj, is ci⁢j=ai⁢j-Wj. In comfort decision making, our criterion is to maximize the comfort associated with our decision, while in regret decision making our criterion is to minimize the regret associated with our choice of decision. The effective comfort is a measure that summarizes the decision maker’s evaluation of the possible comforts that may be realized given that a particular alternative is selected. We define the effective comfort as Ci=𝐴𝑔𝑔j⁢[ci⁢j]. The effective comfort of an alternative, Ci, is dependent on the aggregation rule used for combining an alternative’s individual comforts across the states-of-nature. One approach is to calculate: Ci=𝐴𝑔𝑔j⁢[ci⁢j]=Minj⁢[ci⁢j]. This summary measure would be a pessimistic or guarded view in anticipating the comfort. Below we generalize the approach to include a decision maker’s bias which could be anywhere from pure pessimism to pure optimism. The decision maker could then select the alternative associated with the maximal effective comfort for a given level of bias. The criteria here is the maximin comfort criteria. The procedure facilitates sensitivity analysis of the preferred alternative to the level of bias. In this case, the preferred alternative, Ai⁣*, is the alternative with the maximum minimum comfort: Ci⁣*=Maxi⁢Minj⁢[ci⁢j].

In a more general case, the aggregation can take on different forms rather than only the minimum, Minj⁢[ci⁢j]. Using the decision criterion of maximal effective comfort, we obtain Ci=𝐴𝑔𝑔j⁢[ci⁢j] for each alternative, and then select the alternative Ai⁣* such that Ci⁣*=Maxi⁢[Ci].

In decision making under uncertainty, information regarding the probabilities of the states-of-nature is not available. The aggregation, or summary measure, of the payoffs, regrets, or comforts for a decision alternative across the states-of-nature is based on the disposition of the decision maker. The summarization, or aggregation, can be completed by means of the ordered weighted aggregation (OWA) operator [39]:

An OWA operator of dimension q has a related group of weights wk∈ [0, 1], for k=1,…,q, such that ∑k=1qwk=1. These weights are utilized to specify a weighted average of the numeric values yj, for j=1,…,q, where ρ is an index function so that ρ⁢(k) is the index of the kth largest of yj. Consequently, yρ⁢(k) is the kth biggest of the yj.

The OWA operator supplies a summary measure of its arguments and provides a unifying approach to the choice of an alternative under uncertainty [40]. We define the OWA weighting vector as W=[w1,…,wq].

Within context of comfort decision-making, we calculate the effective comfort for alternative Ai as:

We define ρi⁢(k) as the index of the kth largest comfort for alternative Ai. Thus, ci⁢ρi⁢(k) is the kth largest comfort for alternative Ai. We note that if wk=1/q, for all k, then Ci=1q⁢∑jci⁢j. Also, if wq=1 and wk=0 for all k≠q, then Ci=Minj⁢[ci⁢j]. Using the expression, Ci=∑k=1qwk⁢ci⁢ρi⁢(k), provides the weighted average of comforts for alternative Ai.

Using the OWA operator, we aggregate the comfort values across the states-of-nature in determining the preferred alternative. Sensitivity analysis of the preferred alternative to the disposition, or bias, of the decision maker is a key feature of the Comfort Decision Model. The OWA weights can be obtained using a function f: [0, 1] → [0, 1] such that: f⁢(0)= 0; f⁢(1)= 1; and, f is monotonic, i.e. f⁢(a)⩾f⁢(b), if a>b [41]. In particular, using this function we can obtain the OWA weights wk for k= 1 to q using:

Decision makers combine analysis and intuition, filtering events through their own judgment [42]. Within decision making under uncertainty, with the absence of probabilistic estimates, decision makers rely on their own disposition (i.e. attitude or bias). The Bias of a weight generating function f is defined as:

We note that Bias⁢(f)∈ [0, 1]. Another observation is that if f1⁢(x)<f2⁢(x) then Bias⁢(f1⁢(x))⩾Bias⁢(f2⁢(x)). Bias is a surrogate measure of the degree of optimism, and reflects the disposition of the decision maker. The decision-maker’s attitude plays an important role is determining a preferred decision policy for dynamic decision situations [43]. If the arguments of the OWA operator are placed in descending order, then weight generating functions with lower values of Bias apply more weight to larger arguments in the aggregation. Also, weight generating functions with higher values of Bias apply more weight to smaller values in the aggregation. If Bias= 0.5, the weights are equal and the aggregation is equivalent to the mean.

A useful type of weight generating function is f⁢(x)=xr, for r> 0. For r< 1, more weight is assigned to the larger argument values, whereas for r> 1, more weight is assigned to the smaller argument values. We note that as r→∞, wq= 1, resulting in Ci=Minj⁢[ci⁢j]. Additionally, as r→ 0, w1= 1, resulting in Ci=Maxj⁢[ci⁢j]. Finally, when r= 1, f⁢(x)=x, which results in the classic mean. Specifically, when r= 1, wk=1/q for all k, resulting in Ci=1q⁢∑jci⁢j.

It can easily be shown that for weight generating function, f⁢(x)=xr, the Bias⁢(f)=r/(r+1). Solving for r yields: r=Bias⁢(f)/(1-Bias⁢(f)). Consequently, for a specified Bias, the parameter r can be determined for weight generating function f⁢(x)=xr.

A decision maker may wish to consider the original payoff values, ai⁢j, as a measure of satisfaction in evaluating the alternatives. The methodology described above relative to the Comfort Decision Model can be used to model decisions using the original payoffs, ai⁢j. This is done by replacing payoff for comfort in the above discussion. In the framework of decision-making using payoffs directly, we can calculate the effective payoff for alternative Ai as:

Because larger payoffs are better, payoff values are placed in descending order in the OWA aggregation to keep a smaller value for Bias representing a more optimistic attitude. Here ρi⁢(k) is the index of the kth largest payoff for alternative Ai. Therefore ai⁢ρi⁢(k) is the kth largest payoff for alternative Ai. Note that the index function ρi is specifically defined for each alternative Ai. The form of the summary measure of comfort is determined by the choice of weighting vector. The OWA operator can provide a multitude of ways to calculate Pi. Using Pi=∑k=1qwk⁢ai⁢ρi⁢(k), yields the effective payoff, a summary measure of payoffs for alternative Ai.

A decision maker may wish to consider regret as a measure of satisfaction in evaluating the alternatives. The methodology enumerated in the Comfort Decision Model can be used to accomplish this by replacing regret for comfort. Here since smaller regret is better, regret values are placed in ascending order in the OWA aggregation to keep a smaller value for Bias representing a more optimistic attitude. In the framework of regret decision-making we can calculate the effective regret for alternative Ai as:

Here ρi⁢(k) is the index of the kth smallest regret for alternative Ai. Therefore ri⁢ρi⁢(k) is the kth smallest regret for alternative Ai. Note that the index function ρi is specifically defined for each alternative Ai. The form of the summary measure of regret is determined by the choice of weighting vector. The OWA operator can provide a multitude of ways to calculate Ri. Using Ri=∑k=1qwk⁢ri⁢ρi⁢(k), yields the effective regret, a summary measure of regrets for alternative Ai.

5.Example

For the following example, to illustrate and relate the general mathematical methodology that we present to pandemic-specific decisions, we can think of the alternatives as vaccination strategies and the states of nature as variants of a virus. The payoff table consists of returns (in this case, fictitious values for the sake of illustrating the methodology) if a specific vaccination strategy is chosen and a specific state of nature occurs. For example, four decision alternatives and five possible states of nature could be as follows:

Table 1 summarizes a decision problem containing alternatives, Ai, states-of-nature, Sj and payoffs ai⁢j resulting from selecting alternative Ai, with state-of-nature, Sj, occurring.

We find, Wj=Mini⁢[ai⁢j]: W1= 40, W2= 30, W3= 10, W4=-40, W5= 20.

Using ci⁢j=ai⁢j-Wj, we determine the corresponding Comfort Table, Table 2, containing the ci⁢j.

Here, we demonstrate the application of the Comfort Decision Model with a sampling of illustrative calculations. In determining the effective comforts, Ci, for the alternatives, Ai, for i=1,…,n, for a pessimist, we use the OWA weights: wq= 1 and wk= 0 for k≠q. In this case, Ci=Minj⁢[ci⁢j]. Using these weights we find the minimal comfort for each alternative across the states-of-nature:

In this aggregation, A1 is the alternative would be preferred by a pessimist, with the maximal minimal comfort, C1= 45. As we continue gleaning insight from the data in the Comfort Table, we use the weight generating function, f⁢(x)=xr. For this weight generating function the Bias⁢(f)=r/(r+1) and solving for r, we find: r=Bias⁢(f)/(1-Bias⁢(f)). The Bias ranges from a low of 0.0, for the optimist, to a high of 1.0, for the pessimist. An unbiased decision maker would have a Bias = 0.5.

Figure 3.

Effective comfort vs Bias.

We show the calculations here for Bias = 0.6, which represents a slightly pessimistic attitude for the decision maker. In this case, r=0.6/(1-0.6)=1.5. Therefore the weight generating function is f⁢(x)=x1.5. With 5 states-of-nature, we calculate f⁢(k/5), for k= 0, 1, 2, 3, 4, 5, and find:

We calculate the OWA weights using:

wk=f⁢(k/5)-f⁢((k-1)/5), and find:

For alternative A1, the comfort values from the Comfort Table are:

We find ρ1⁢(k), for k= 0, 1, 2, 3, 4, 5, the index of the state with the kth largest comfort under A1:

Therefore, the Comfort values in descending order are:

Finally, the effective comfort for A1 is determined using:

We calculate the effective comfort Ci=∑k=1qwk⁢ci⁢ρ⁢(k) for each alternative, Ai, for i=1,…,4, across the entire range of Bias from 0.0 to 1.0. These results are displayed in Table 3.

Figure 3 graphically displays the effective comfort as a function of Bias for each alternative. A3 is the preferred alternative for Bias ⩽ 0.51; A1 is preferred for Bias ⩾ 0.51.

In a situation such as the current pandemic, authorities may implement decisions that are not necessarily the preferred decisions of all constituents or stakeholders. As a measure of satisfaction to a stakeholder regarding an imposed decision, we can calculate the Comfort Attainment Percentage. We define the Comfort Attainment Percentage as ci⁢j/Maxi⁢[ci⁢j]. The Comfort Attainment Percentage values represent the percent that an implemented decision’s comfort is relative to a stakeholder’s optimal comfort, given a level of Bias. For example, if the government implements A3 and the stakeholder has Bias = 0.8, then utilizing the values from Table 3, the stakeholder’s Comfort Attainment Percentage is 30%, (i.e. 14.2/47.9). However, a slightly less pessimistic Bias = 0.6 would yield an increase in Comfort Attainment Percentage to 81%, (i.e. 44.5/54.8), while at Bias = 0.5, the stakeholder would prefer A3 and would be in lockstep with the implemented decision alternative, yielding a Comfort Attainment of 100%. Comfort Attainment Percentage values are displayed in Table 4.

Applying the methodology of the Comfort Decision Model described above, using Payoffs, ai⁢j, and Regret, ri⁢j, in place of Comfort, ci⁢j, we determine the decision preferences displayed in Table 5.

Using various criteria, the preferred alternatives depend on the Bias level of the stakeholder and the criteria being considered.

Attainment of satisfaction, relative to an imposed decision, can also be determined using the criteria of payoff and regret, just as illustrated for comfort in Table 4. This is easily accomplished using the suggested method, and would be provide additional insight to support the decision process.

6.Conclusion

The recent pandemic has illustrated the benefits and challenges facing knowledge management and the process of making evidence-based decisions. We present issues that are related to knowledge management and decision making in pandemic and non-pandemic environments. The pandemic environment intensifies the urgency of each issue and impacts how knowledge management systems function. Decision methodologies, properly utilized, can reveal alternatives that better satisfy various constituencies’ essential needs. Comfort is a particularly useful criteria in the current environment and is defined as the difference between the payoff received by an implemented strategy and the worst payoff that could have been received. The Comfort Decision Model determines aggregation values utilizing attitudinal measures that provide insight to how satisfactory outcomes are aligned to constituents.