Communication of Uncertainty: The Concept of Probability in Government Press-Conferences during the Early Covid-19 Crisis in Denmark

1 The Dual Nature of Probability and the Problem of Inference

Most processes in life and in nature over the long run generally seem to occur with relative stable frequencies, which lead us to expect that some outcomes are more likely to occur than others. Historically within the life sciences the unstable and irregular, yet relatively predictable, character of living organisms and processes has been debated and captured by the concept of the norm and the normal (Canguilhem 1943[1966/1998]). In probability theory, processes are considered random if they have an unpredictable outcome. It raises the question whether and how it is possible to make reliable predictions about the future, in this case concerning impacts of a virus. Depending on how the concept of probability is understood, there are two answers to this question, which have to do with ‘the dual nature of probability’, i.e. aleatory (‘stochastic laws of chance processes’) and epistemic probability (‘assessment of reasonable degrees of belief’), respectively (Hacking 2006[1975], 12; Radner 2000).

2 Probability Concepts in Political Communication

3 Framing the Uncertainty of the Situation

In Denmark on March 11, the prime minister, the head of the Danish Health Authority, and the head of the state police went on National TV to address the situation concerning the spread of the Covid-19 virus, and to announce a lockdown of all unnecessary activity across all public institutions for a period of initially 2 weeks (beginning on March 13). Public employees, who did not maintain critical functions, were sent home with pay and instructed to work from home to the extent that it was possible. Private companies were strongly advised to follow their example. The political communication reflected a strong appeal to the moral sentiment of the Danes, thereby referring to social (intersubjective) norms when arguing for a specific decision during the press conferences, for example by changing the traditional strategy of crisis management: ‘We usually seek community with each other as Danes by being close. Now we must stand together by keeping apart’. (Prime minister, March 11, 2020). The prime minister emphasised the seriousness and the uncertainty of the situation, applying a ‘precautionary principle’ (Prime minister, 11 March, 2020), by which she meant that since the government did not yet have reliable data on which to base decisions, it is better to be safe than sorry. ‘As prime minister, I’d rather have the authorities take one step too far within a specific area, than not far enough. Then we must evaluate later’. (Prime minister, March 6, 2020). Applying the principle of precaution in this situation is problematic, since it was uncertain whether the consequences of a policy would be more harmful than refraining from introducing the policy (Martin et al. 2020; Mormina 2022). The lockdown included day care centres, primary schools, upper-secondary education and other educational institutions. All public employees, who did not maintain critical functions, were sent home with pay and instructed to work from home to the extent that it was possible. Private companies were strongly advised to follow this example. Schools and day care institutions remained open for the children of the employees who performed emergency functions in society or who could not find an alternative solution. The prime minister also emphasised the novelty of the situation and the corresponding lack of knowledge and took a political and personal responsibility:

I will also say this to the whole Danish population: That we stand on untrodden lands in this situation. We have never tried it before. Will we be making mistakes? Yes, we will. Will I be making mistakes as prime minister? Yes, I will. (Prime minister, 11 March, 2020)

With the expression ‘untrodden lands’, the prime minister unmistakably says that there is (yet) no reliable evidence (frequency calculations or knowledge of propensities) on which to base decisions, which therefore precludes the possibility for decisions based on expertise (calculation and prediction models), and rather warrants a climate for political decision-making (assessment and judgement) for which she takes responsibility. She thereby applied an aleatory, specifically a frequentist, perspective: Nobody knows anything about probabilities unless they have calculations of frequencies of infections relative to a sufficiently large data set. However, a week before, on March 6, when the first few cases of Covid-19 had been detected in Denmark, she explained that ‘the authorities plan for different scenarios’ (Prime minister, March 6) implying an epistemic (or logical) perspective, since politicians must make decisions about possible future scenarios and their probabilities (possible worlds, relative to the available information), i.e. assessments of which scenario is most likely to occur. Thereby, and addressing the whole population, the prime minister implicitly switched between various notions of risk, uncertainty and ignorance, i.e. such as for example the technical inexactness implied by error bars (risks assessment and planning) and the methodological problem of modelling, which concerns confidence levels (and thereby uncertainty and reliability). Yet, the phrase ‘untrodden lands’ implies a knowledge gap and, therefore, ignorance (Funtowicz and Ravetz 1990, pp. 23, 1993), or perhaps even that the pandemic is indeterminate (Wynne 1992), i.e. that there is no way of knowing how the pandemic will develop, since it might be inherently unstable or random.

The underlying question was whether the development of the infections and the spread of the virus were rationally calculable or whether the event was uncertain and unforeseeable and, therefore, required deliberation and assessment of the scarce reports that were available. As mentioned above, the prime minister emphasised the uncertainty of the situation due to delay of the incubation period of the virus rather than the calculable risk of the situation: ‘There is a delay from the time of infection to hospitalisation. Likewise, the way we behave now won’t appear in the data until in three to four weeks’. (Prime minister, 11 March, 2020). In other words, the sound empirical basis for the determination of the frequency of hospitalisations does not appear in time to serve as a basis for decision-making. The prime minister later referred to the virus as an ‘insidious disease’ (Prime minister, April 6), which emphasised the indeterminacy and, therefore, the political nature of the situation and the need for swift government action.

Five days prior to the announcement of the lockdown, on March 6, and after the prime ministers’ introduction to the situation, the Head of the National Health Authorities downplayed the unpredictability of the existing knowledge of the Covid-19 virus. On the one hand, it is a completely new variant of the virus, but on the other hand, the health authorities possess the relevant and general knowledge of how to prevent the spread of viruses: ‘We know how this virus infects [people]. We shouldn’t cough into each other’s faces. Hygiene, handshakes, handwash, etc.’ (Head of the National Health Authorities, March 6, 2020). In the above quote, the head of the health authorities claims to know how ‘this’ new virus infects people, although he implicitly refers to the infection rates etc. of previous or similar variants of the type of coronavirus (frequency calculations, or the general propensities of viruses). Moreover, he refers to knowledge of how already familiar coronaviruses generally spread (thereby applying a logical or conditional view of probability). Furthermore, he claimed to be able to speak of the probabilities of various forms of population behaviours, communicating these premises in everyday language. In other words, knowledge of the general propensity of how viruses spread is sufficient for assessing the probabilities of various scenarios relative to each other. Therefore, the experts can speak meaningfully about the probability of these scenarios, even if we do not yet possess solid data and frequency calculations of the new Covid-19 type. On the one hand, this is a ‘propensity’ view of probability (referring to the nature of viruses) or a frequency view (referring to initial frequency calculations from other countries). On the other hand, it is a ‘logical’ concept of probability where information of previous examples serves the role of evidence that the outcome of one scenario is more probable than another (although not yet calculable). The expert probably felt the need to assure the citizens, who were watching the press conference and felt uncertain about the whole situation, that the health authorities possess the relevant expertise to manage the situation, even if it is a new variant of the virus.

After the briefing, a journalist asked about the limit of 1.000 people at social events and required justification for the decision. The head of the national health authorities responded:

Well, I thought I might say something, first, about the health scientific documentation [for our recommendations] regarding large events. We’re standing on good documentation, but at the same time it is a new disease that we have only known for a few months. [However], we have experience with widespread outbreaks of flu, also with historical cases and previous preventive initiatives like these. (Head of the National Health Authorities, March 6, 2020)

In the above quote, historical cases are mentioned as relevant information. The health authorities have seen something that – possibly – resembles the new virus and, therefore, it would be safe to base decisions concerning mitigation strategies on such experiences. Even if there is previous ‘scientific documentation’ (in the sense of statistical calculations of frequencies of hospitalisations or of risk groups in large data sets and for many kinds of known viruses), still no, or only very limited frequencies have yet been calculated empirically for the new Covid-19 virus.

We have experience from previous outbreaks of pervasive epidemics. It seems that 10–30 % of the population can be affected in the first wave of an epidemic – because we don’t have immunity. We know that from historical cases. (Head of the National Health Authorities, March 10, 2020)

In other words, the head of the health authorities must appeal to both an aleatory conception of probability (the natural propensity to affect 10–30 % of the population) and to an epistemic conception (using historical examples of outbreaks of pervasive epidemics) as relevant information for making (conditional) inferences about plausible, future outcomes in the absence of systematic, experimental tests.

4 The Gradual Reopening: Learning as We Go

After the initial 2 weeks, the lockdown was prolonged for another 3 weeks (5 weeks in total). After the Easter break on April 20, schools and other institutions were gradually reopened. During the lockdown, the authorities had emphasised the experiential character of the situation:

At the same time, we’re using the situation as a chance to know more about the virus. And learning from experience we can now say that on average people are hospitalised for about three weeks now. I must be honest and declare that it is much longer than we first thought. (Minister of health, April 6, 2020)

The minister openly communicated the uncertainty of the health expertise that strongly influences the procedures, strategies and management of health care. It was a balance, because on the one hand, a large proportion of the population was worried that the country might open too soon, risking a further spread of the virus. On the other hand, shop owners and others were desperate to get their businesses going again and questioned the need for the precautions. It seemed to be a ‘wicked problem’ (Rittel and Webber 1973), introducing a post-normal framework of decision-making (Funtowicz and Ravetz 1993; Rainey et al. 2021), which entails coping with complexity, ambiguity and mutually excluding perspectives in decision-making and risk governance (Renn, Klinke and Asselt 2011). The government had to emphasise that the existing knowledge so far was highly uncertain, based still on a very small, or at best belated, calculation of the frequencies of the regularities in the patterns of the observations, thereby maintaining a characterisation of the situation as political (in the above-mentioned sense). However, the minister of health also had to refer to some kind of certainty to justify the decisions made:

We know one thing for certain, which is that the positive development depends entirely on the behaviour of the Danes. Therefore, we must continue to sneeze into our sleeves, keeping a distance to each other, and not getting together too many people etc. (Minister of health, April 6, 2020)

This statement transfers responsibility to civil society, i.e. that people must be capable of following the recommendations concerning the general spread of viruses (Nord and Gardell 2023).

However, members of the press kept driving at the uncertainty of the situation, implying that the policies are arbitrarily decided. After a while, the suspicion was too much for the Head of the Serum Institute who consequently felt the need to articulate a more solid form of knowledge:

The decision that the government has made is grounded in a mathematical model, so this is not guesswork! It is based on investigations demonstrating that the regulated, careful and gradual reopening is responsible, so we can go through with it without the health care system breaking down. (Head of the Serum Institute, April 6, 2020)

According to the head of the Serum Institute, the model is not arbitrary since it is based on the – at the time – available and seemingly relevant data. However, as previously mentioned, stating that it is better to base decisions on available data rather than no data at all is not a valid claim, since data can be misleading. There could be dark figures, i.e. undetected presence of virus in the population, which would make the initial beliefs (Bayesian prior) about the extent of the infection not only inaccurate but directly misleading. In the beginning of the pandemic, taking a test was often a strong indicator of the pre-test probability of infection (Piltch-Loeb et al. 2021). The head of the Serum Institute does not state it directly, but it is implied that the predictions of the mathematical model are gradually calibrated and thereby improved as more data flows in, and the Serum Institute will continue to monitor the effects of the reopening. The emphasis that ‘It is not guesswork!’ implies that even if the prior assumptions, on which the model is based, were chosen arbitrarily (for example, based on misleading data from previous epidemics), the experts will gradually optimise the model’s capacity to make more precise predictions. And herein lies the rationality of the Bayesian principle of learning.

As the examples above demonstrate, it was a difficult task for the administrative authorities to communicate directly with the public. On the one hand, they tried to express a confident attitude and downplay the appearance that the decisions were arbitrary (basing decisions about the new virus on data regarding previous viruses). On the other hand, they also wanted to communicate the uncertainty of the calculations and predictions (that they are on uncharted lands, upholding a watchful alertness and scepticism, and disclaim responsibility). In the following quote, the head of the Serum Institute first makes a prediction with certainty but quickly corrects himself and stresses that the conjecture is an expectation:

However, we will see an increase – we expect to see an increase – in the number of sick, and in the number of hospitalisations. (Head of the Serum Institute, April 6, 2020)

Probability thereby concerns expectations about future outcomes. The question is to what extent the uncertainty is calculable and manageable, and how and to what extent the uncertainty should be communicated. The meaning of the concept of probability continually slips back and forth between various kinds of aleatory (frequentist, propensity) and epistemic (logical-inductive, subjective and Bayesian) conceptions. On the one hand, it seems important to maintain an awareness of the unpredictability of the situation, but on the other hand, there is also a possibility to learn and to justify decisions about the future course of events even if the observed cases are limited. From the beginning of the lockdown, the head of the health authorities had emphasised the contingent nature of the situation:

At some point, the containment strategy [tracking the contamination chains, keeping the possibly infected quarantined] won’t hold anymore. I can’t say exactly when. It is an hour-to-hour, a day-to-day assessment of the situation. (Head of the Health Authorities, March 10, 2020)

It is a reminder that probability theory is based on the need to interpret the signs (of nature, of things) and to assess the degree to which these signs could work as evidence for a conclusion (Hacking 2006[1975], p. 44). The improved reliability of the statistical calculations and thereby the predictions based on a larger ‘n’ do not eliminate the need for interpretation (see also Piltch-Loeb et al. 2021). As the head of the Health Authorities states:

We have some experience regarding this disease – especially from China and Northern Italy – so we know the burden of disease, the distribution of the disease, that is, how many people will only be lightly affected, and how many will have to go to the hospital. We must translate the Chinese and Italian data to Denmark. There is a different age distribution in Denmark compared to Northern Italy. Northern Italy has a larger group of seniors so perhaps that is why they have an increased rate of sickness and a heavier strain on the capacity for intensive care. (Head of the Health Authorities, March 10, 2020)

As the communication above demonstrates, the public was invited to co-reflect on the uncertainty of scientific research during the early Covid-19 press-conferences. They were an occasion for a large part of the population to witness these continual deliberations, which is an important part of research practices.

5 Justifying Decisions in the Face of Uncertainty: When and How to Reopen the Schools?

One of the interesting questions during the lockdown was when and how to reopen the schools. Children were very early on identified as those who were neither infected, nor infected others, very easily. That was already announced by the Head of the Health Authorities on the first press conference:

This disease does not seem to infect children at any high rate. And unlike the epidemic that we had in 2009 children do not seem to spread the virus very much. Whereas [in contrast to children] the chronically ill and the elderly comprise a risk group. (Head of the Health Authorities, March 6, 2020)

Speaking of ‘infection rates’ testifies to the frequentist (aleatory) use of the concept of probability, since the probability value has been calculated statistically. Notice the careful use of the word ‘seem’ in the above, expressing due uncertainty, about the preliminary calculations. But it also signifies a willingness to learn from previous experiences, i.e. to make informed guesses (‘in contrast to the epidemic in 2009’), which indicates an epistemic concept of probability.

The difficulty for the health authorities in the very early days of the outbreak was to identify and define the risk groups with the purpose of targeting and differentiating the recommendations, and without having to do it through trial-and-error. Was it more dangerous to send the kids back to school if they could spread the virus unknowingly because of very mild infections – for example to their grandparents who would presumably in many cases pick them up from school or daycare? The problem here is not so much whether the various scientific analyses are accurate (statistical frequency calculations), but rather a question of which scientific result to use as evidence and give the appropriate weight (inductive, logical probability), and how to make decisions under such uncertain conditions and irreconcilable disagreements (Ongaro 2021; Qvortrup and Lykkegaard 2023). The calculations themselves do not answer these questions, but the various probability theories provide a framework for analysing the justifications for the decisions.

After the first 5 weeks of lockdown, and as the weeks progressed, the epidemiologists observed a favourable trend in the infection rates. Less people than expected had been hospitalised, so after the Easter break, the youngest children (0–5) and pupils (6–11) were sent back to daycare and school by April 20, 2020, which was sooner than expected. On April 14, when society was about to reopen, the prime minister held another press conference and announced the change of plans.

We have commenced what we call ‘phase one’ in the reopening of Denmark. It is a difficult task. The municipalities are reopening the daycare centres and schools for the small children. And the number of hospitalisations we see now mean that we can do more during phase one than we had first imagined. (…) We must continue to have the virus under control. And things are going quite well with the joint venture. Therefore, the idea right now is to open slightly more. (Prime minister, April 14, 2020)

By using the phrase ‘the idea right now’, the prime minister emphasised the provisional character of the situation.

Perhaps therefore, the prime minister emphasised that the professionals in daycare centres, schools, libraries, etc. will handle the changes much more efficiently if decisions are made locally. ‘You [the Danes] can do a lot when common sense is allowed to rule instead of asking permission 10 levels up’ (Prime minister, April 14). According to the prime minister, the most efficient way to administer and temporarily re-organise society will, therefore, be to encourage each professional and citizen at the local levels to make their own (subjective or group-level) evaluations of what makes sense in a particular context. In that sense, the subjective and intersubjective assessments work as betting quotients, which will allow personal as well as common sense to rule (like an invisible hand). However, this is also where we saw the most conflicts during the Covid-19 crisis, when individual and group-based probability assessments conflicted with each other. Professional and commercial interests sometimes clash, and so does personal judgement.

The press soon picked up these disagreements and became a vehicle for the diversification of opinion and shifted its attitude from pure mediation to scepticism towards administrative and government expertise. After the briefing, one of the journalists asked the representative from the health authorities about the intensification of the reopening:

My second question goes to the Head of the Serum Institute: Seven days ago, you presented a model demonstrating that even with the most probable course of events there would be 200 patients hospitalised in intensive care by now. The actual number is 93. Now you say that you can open society a bit more than planned without the spread getting out of hand. But why should we believe [these estimates] when the previous models have been totally off the mark? (Journalist, April 14, 2020)

It is unclear from the context whether the journalist finds the statistical uncertainty intolerable (the margin of error), or whether he (also) thereby implicitly applies an exact understanding of knowledge: Either the models make precise predictions, or they cannot be trusted at all. Journalists during the press conferences generally seemed to ignore the question of probability, presumably because it is easier in that way – rhetorically – to hold authorities accountable (see Blom et al. 2021). Therefore, the head of the Serum Institute began to explain how the calculation of probability becomes more credible as data increase:

I won’t say that the models have been totally off the mark. But more data has been added. So, the more data points that are added to the model the more accurate the projected curve will be. So, it is simply a question of more data making the model more accurate. And that also means that there is this opportunity to expand the reopening [of society] slightly more without the health care system breaking down if we continue to keep a distance to each other. (Head of the Serum Institute, April 14, 2020)

The head of The Serum Institute holds on to the Bayesian rational model of decision-making and explains how decisions are based on continual calibration of long run calculations and analyses of frequencies. The purpose of the continual calibration is to gradually minimise the uncertainty of the projected curve (Bayesian learning) and yet at the same time retaining the small chance that an apparent connection between a hypothesis and a conclusion may be a coincidence (frequentist).

The purpose of the calculations made by epidemiologists and virologists is to minimise the risk through calculation and analyses of frequencies that the observed regularities are coincidental (statistical uncertainty). Rather than proving something to be the case, they try, through the continuous collection of data, to improve or calibrate the model for decision-making, Thereby, they try to provide a basis for decision-making by interpreting how the partial data could meaningfully count as evidence for preliminary conclusions.

The prime minister also recognised the preliminary character of the knowledge that was developed, but at the same time emphasised the need to make swift decisions (see also Radner 2000 for a discussion of cost-effectiveness and rationality in decision-making):

If we were to wait for the calculations until we are certain then we would have to wait forever. They [the scientists] constantly make new calculations. Because… because it is a new situation. It has no prehistory. (Prime minister, 29 May, 2020)

She, therefore, continued to emphasise the uncertainty of the situation (applying a frequency perspective), and thereby opened a space for political decision-making based on assessments of the available information (logical inferences).

6 Conclusions

The above analyses have demonstrated how various government authorities communicated the coincidental character of the Covid-19 crisis and thereby how various conceptions of probability in political communication justify different policy decisions. Perhaps not surprisingly, political decision-makers on the one hand try to emphasise that the situation is uncertain, that no relevant knowledge of the situation exists, and that immediate action is required (see also Zhou, Liu and Yang 2024). They do that first by appealing to a frequentist concept of probability, i.e. that it is not possible to objectively determine the situation, since the variant of the virus is new, and no solid data yet exists. Then, by appealing to single-event experiences, they argue for the probability of a full-blown epidemic (experiences from Italy and China with outbreaks and pressure on the health services) and, thereby, emphasise the necessity for a swift assessment of the situation (logically, inductively) and prompt action. The strategic (or selective) use of different concepts of probability in communication at the press meetings enabled politicians to sidetrack the administrative expertise and conquer a space for political decision-making. This is most evident in the case of the prime minister’s communication, since the ministers of Health, Foreign affairs, and Justice – besides being politicians – (in Denmark) also play an administrative role as heads of the ministries and their adjacent public institutions. These ministers’ communication is balanced between on the one hand respect for the public institutions that they represent and, on the other hand, being members of the government. They oscillate between different uses of the concept of probability, but most often apply logical-hypothetical constructions such as ‘If the spread of infections increases, then…’. Thereby, the decisions are conditioned on the plausibility of the inferences. They try, subtly, to emphasise the expert knowledge when available and strategically opportune, yet at the same time downplay the plausibility of the available knowledge to open a space for political decision-making.

Something similar is the case for the heads of the public research institutions, such as the health authorities, who – sometimes in the same sentence – apply two different concepts of probability. Even if data concerning the new variant is limited, these authorities give the impression that they still possess the relevant expertise to handle the situation based on historical cases of epidemics. The Serum Institute that calculates the frequencies and constructs models of the probabilities of various scenarios on the one hand expresses confidence in the general knowledge already available (of past experiences, logical-inductively) but also emphasises the uncertainty of the available knowledge of the new virus (thereby applying a frequentist perspective). Moreover, the statistical insight that there is always a small chance that the calculated correlation between current behaviours and future outcomes is a coincidence is sometimes downplayed and replaced by a propensity perspective (i.e. believing to know the very nature of past as well as future epidemics, i.e. that they come in waves with certain distributions etc.). As more data flow in, the applied probability concept shifts to a Bayesian view in the sense that these models will continually improve as more data are added. Rationality, from a Bayesian perspective, does not mean ‘determinable beyond doubt’ but rather ‘gradually more precise’, which emphasises the developmental, evolving character of knowledge.

As indicated in the analyses above, the various uses of the concept of probability thereby either extend or limit a space for justification and decision-making concerning risks. By adhering to a frequentist perspective, decision-makers can side-track the influence of experts in decision-making (since no relevant risk assessments are available), thereby opening a space for political decision-making (emphasising specific stakeholders’ perspectives, values, hopes or fears). At other times, the application of a logical concept of probability (using historical examples or references to natural propensity) serves the role of relevant evidence for making inferences about the credibility of a suggested policy, which thereby enables decision-makers to limit the relevant options and to render some of those options more important than others. The application of different aspects of the concept of probability in communication thereby enables authorities to frame the uncertainty of a situation, and to justify different approaches to risk management. Therefore, it is important for citizens and journalists to be aware of the implicit shifts in the communication, and generally to recognise that the dual nature of probability plays an important role in the framing and justification of knowledge in support of decision-making.