17 Probabilities
X.J. Lin
Description
In everyday life, we frequently encounter beliefs, knowledge claims and assessments of probabilities. We may not always be aware of them, but they are used as tools for either supporting an argument or opposing one. It turns out that, when looked at from a philosophical perspective, it is not always evident how we can be certain about a belief. Certainty covers epistemological questions about the limits of knowledge and what it means to have knowledge. As not all philosophers would agree with the possibility of being certain about a belief, the next step would be the use of probabilities, which is the philosophical tool we will be discussing in this chapter.
First of all, it is worthwhile to establish what probabilities are. If being certain means holding a belief without doubt, then probabilities are subject to degrees of belief. A general explanation is that probability expresses how likely an event is to happen or a proposition is to be true. While this seems to be a trivial description, probabilities also find their way into philosophy. The term appears among others in philosophy of science, about how they confirm scientific theories, or in philosophy of metaphysics in questions about causation. More foundational, the interpretation of probabilities are up for philosophical discussion until this day (Galavotti, 2005). Probabilities can for instance be understood as degrees of belief (Bayesian interpretation) or from previous experiences by means of relative frequencies (Frequentist interpretation). The way probabilities behave do not change among the different interpretations, but how they translate to our real world is understood differently.
As a tool, it can be interesting to distinguish objective probabilities from subjective probabilities. They are not interpretations of probabilities, but a different way of categorisation. Subjective probabilities can be attributed to an individual’s judgement about the likelihood of an outcome, so they can simply be made up by one person. The probabilities differ from individual to individual because they do not have complete information about the event, resulting in a subjective probabilistic assessment. Think of a friend who claims that the probability of rain tomorrow is 50% and another who claims that there is 70% chance of rain tomorrow. Objective probability, on the contrary, refers to situations where the likelihood of an outcome is indeterminate. This may be the probability of winning the lottery when you know the number of tickets sold.
Because there is much debate surrounding the nature of probabilities, it becomes clear that the concept is not as straightforward as initially may appear. Probabilities are associated with statistics and uncertainty, which may be hard to comprehend for the untrained reader. This chapter considers how a more critical way of reasoning about probabilities can be helpful in the migration debate. Given the distinction between subjective and objective probabilities, we can learn how we can place the migration debate into a more complete perspective. Together with the help of Kahneman and Tversky’s prospect theory, which will be elaborated on in the chapter, the tool teaches us how to avoid reasoning errors about probabilities and uncertainty.
This is important, because it sometimes seems attractive to accept statistics about migration without scepticism, as percentages and frequencies can feel ‘scary’ (further reading: Ionica Smeets, 2023) for some. While at the same time, thoughtful discussion and reasoning about probabilities and uncertainty do not seem an easy exercise. Partially due to the complex mathematical foundation behind probabilities, but mainly through human biases, we must be aware of. In this light, prospect theory emerges as a guide that can help us point out potential biases. It thereby teaches us how we can equip ourselves with critical thinking tools for reasoning about probabilities and uncertainties in the migration debate. We will discuss a few examples of how prospect theory helps us with reasoning about uncertainties as we progress through this chapter.
Prospect Theory
Moreover, Kahneman and Tversky (1979) have provided interesting insights into our perception of uncertainty and how we incline to react to it. This research has given insight to different biases and the Nobel Prize winning prospect theory (Nobel, 2002). While their work is primarily concerned with behavioural sciences and economics, the results also have philosophical relevance when it comes to reasoning about uncertainty. Prospect theory describes how individuals make decisions on the basis of risk-aversion. This theory challenges the longer-existing expected utility theory, which argues that rational agents maximise utility. Instead, Kahneman and Tversky observed using experimental methods that people feel losses stronger than an equivalent gain.
Suppose an agent is given a choice between receiving €500 for certain or a 50% probability of receiving €1100. Contra expected utility theory, prospect theory suggests that people will pick the €500 option even though the expected utility is higher with the alternative. Similarly, when an agent must choose between certainly losing €500 or losing €1100 with 50% chance, the second option would be chosen because of the possibility that they lose nothing. So when it comes to loss, agents are risk seeking. The level of risk aversion differs for each individual and can be adjusted accordingly when the theory is transformed to a model.
Turning to the topic of migration, this theory implies that migrants or people considering migration weigh the gains and losses of migrating, whereas a heavier weight lies on the losses depending on an individual’s level of risk-aversion. The higher this level is, the less likely the person or family is willing to move abroad. Gains and losses of migrating are, however, deeply uncertain. It is often unclear in what surrounding one will end up and what familiarities such as family, friends and culture will eventually be lost. These are risks that can and will affect one§s attitude towards migrating, which has been shown in an extensive study from the National Academy of Sciences (Clark and Lisowski, 2017).
Naturally, the extent depends on the circumstances, since many subjective values and probabilities are at play in migration decisions. An expat moving abroad for work may assign different values and weights to safety, career perspectives and human rights than refugees. For an asylum seeker, the possible gains of freedom and safety are of high value, which can explain the decision to take extreme risks. Economic migrants, who are mostly in pursuit of better financial circumstances, can be motivated by loss-aversion where staying in their home country leads to a strong perceived loss. Using prospect theory is a helpful framework to think about someone’s migration motivation in perspective, because the uncertain circumstances and level of risk-aversion is different for each individual.
Reasoning about Uncertainty and Cognitive Biases
Furthermore, Kahneman and Tversky described different heuristics and cognitive biases in their 1974 article Judgement under Uncertainty, foundational for their broader framework prospect theory. According to the article, decisions we make are influenced by availability bias and anchoring, among others. Firstly, availability is described as follows:
‘there are situations in which people assess the frequency of a class or the probability of an event by the ease with which instances or occurrences can be brought to mind’ (Kahneman and Tversky, 1974).
The bias occurs when someone overestimates the probability of an event because of the prominent availability in their memory.
In addition, availability is influenced by recentness and impact of an event. For instance, the photo of the dead newborn in Lampedusa (Sky news, 2023) tend to be more impactful than an image of full migrant boats on the sea. This signifies the influence of media in the perception of migrants. The easier it is for someone to recall an event, the easier it seems to overestimate the probability of an event. Media can put a strong emphasis on the tragic side of irregular (also referred to as ‘illegal’) refugee migration, leading to the readily available perception that for example refugees are not treated properly according to basic human rights. In another way, the emphasis could be placed on crime or poor integration, which may cause people to overestimate these risks of migration.
Closely related is another bias described by Kahneman and Tversky: anchoring bias. This concerns the first piece of information that is received when making a decision. As Kahneman and Tversky (1974) explain:
‘in many situations people make estimates by starting from an initial value that is adjusted to yield the final answer … different stating points yield different estimates, which are biased towards the initial values’.
What follows is a higher weight given to the initial information, resulting in the anchor shaping the direction of the discussion or perception. For instance, one prevalent example is the Dutch politician Geert Wilders stating that the country is full (PVV, 2013), steering the discussion to whether a country is full or not. Thereby the living conditions of migrants or the genuine reasons behind migrating are framed as beyond the point of discussion. Simultaneously, more weight is given to the anchor’s statement, while many more nuances can be made (NRC, 2013). As a result, different news outlets focus on this statement, investigating the claim and again giving attention to the politician, making it easier to recall the statement and in turn also contribute to the availability heuristic.
Moreover, the effect of framing is also identified as a cognitive bias by Kahneman and Tversky, leading to different judgements and choices made by the agent. This effect is widely used by politicians and applied to numbers about migration. It is effective for underlining their statements or claims without having to twist the facts. For example, former Dutch Minister of Social Affairs used the statistic that ‘400,000 people immigrated to the Netherlands’ in 2022 is unacceptable, thereby indicating that this is more people than the number of inhabitants in Utrecht (Nieuwsuur, 2023). Or consider former U.S. Vice President Mike Pence’s claim about having ‘reduced illegal immigration and asylum abuse by 90%’ with his ‘remain in Mexico’ campaign (Twitter, 2023). What both statements have in common is that they use statistics to frame their claims, thereby referring to, what seems to be at first sight, hard facts of the situation. The numbers are used in such way that one can difficulty deny the succeeding claim. However, there is space for uncertainty if no context about the numbers is provided, because it is unclear what the numbers precisely mean.
Given that framing is a powerful tool used by politicians and public speakers, it also provides space for uncertainty if no context about the numbers is supplied. It is often not immediately visible what context is being avoided. In our first example, the former Minister did not mention the fact that the war in Ukraine started that year and many Ukrainian refugees migrated to the Netherlands (CBS, 2023). Additionally, the number only concerns the number of migrants entering the Netherlands (gross immigration), while omitting the fact that almost 180,000 people left the country in the same year (CBS, z.d.). Our second example illustrates framing in a different manner, namely by cherry-picking data which are favourable for the speaker. Besides that numbers about illegal immigrates are always estimates (TNH, 2017), it turned out that the 90%-claim resulted from comparing data from the month with the highest arrests to the month with the lowest number. Also notice the use of the notion ‘illegal immigrants’, which posses the frame of migrant as criminals. Surely, both examples indicate that the politicians were not lying or announcing falsehoods. However, the statement would not be as powerful when this context is added.
In summary, we have seen that looking at migration through the lens of prospect theory offers interesting insights about the decision-making under uncertainties. There are many different factors that play a role in the complex decision about migrating to another country. On the other hand, we have also seen that it is not always easy to reason about uncertainties, because the context of facts is unclear or because a tragic impactful image keeps pressing on your mind. Being aware of the cognitive biases behind decision-making is one step forward towards better critical reasoning about uncertainties. One method to overcome these biases is to not only be informed by the same media outlets as you are used to. For instance, the latter example about the numbers provided by Mike Pence was also thoroughly investigated by fact checkers (CNN, 2023). Being open to other newspapers, journalists or blogs may shine a different light on the situation, allowing you to pick up different perspectives and context. At the same time, by acknowledging the complexities behind decision making, the migration debate can be continued with more nuance and empathy. This leaves the chapter with a few philosophical exercises.
Philosophical Exercises
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- We have seen in this chapter how uncertainty impacts public debate and personal decision making. Also, from prospect theory we know that each individual has different feelings about risk-aversion. When it comes to policymaking, to what extent do you think statistics and uncertainties should affect immigration policies?
- What use of statistics have you encountered in elections in your country? Intuitively, one might think of parliamentary elections, but it may also be elections of smaller scale, such as voting for the best teacher at your (previous) school.
- Reflection: Has this chapter impacted your way of looking at uncertainties and were you aware of the cognitive biases mentioned in this chapter?
References
Clark, W. A. V., and Lisowski, W. (2017). Prospect theory and the decision to move or stay. Proceedings of the National Academy of Sciences of the United States of America, 114(36). https://doi.org/10.1073/pnas.1708505114
CNN (2023). https://edition.cnn.com/politics/live-news/republican-debate-09-27-23/h_b1606aa76f39150eb1d4ea61932b2ead
Gillies, A. and Galavotti, M.C. (2005). Philosophical Introduction to Probability. Stanford: Center for the Study of Language and Information Publications. https://doi.org/10.1093/philmat/nkl022
I. Smeets (2023). https://www.volkskrant.nl/wetenschap/slecht-met-cijfers-het-helpt-al-als-u-wat-vaker-gaat-denken-dat-getallen-geweldig-zijn~b079fd4d/
Kahneman, D., and Tversky, A. (1979). Prospect Theory: an analysis of decision under risk. Econometrica, 47(2), 263. https://doi.org/10.2307/1914185
Nieuwsuur (2023). https://www.npostart.nl/nieuwsuur/07-07-2023/VPWON_1343677
Nobel (2002). https://www.nobelprize.org/prizes/economic-sciences/2002/popular-information/
NRC (2023). https://www.nrc.nl/nieuws/2023/01/05/wat-is-vol-ligt-eraan-wanneer-je-het-vraagt-a4153467
PVV (2023). https://www.pvv.nl/nieuws/geert-wilders/10532-nederland-is-vol.html
Sky News (2023). https://news.sky.com/story/lampedusa-migrant-surge-prompts-renewed-call-for-naval-blockade-from-italian-leader-meloni-12962327
Tversky, A. and Kahneman, D. (1974). Judgment under Uncertainty: Heuristics and Biases. Science, 185(4157), 1124–1131. http://www.jstor.org/stable/1738360
Twitter (2023). https://twitter.com/Mike_Pence/status/1682175740542894080
