2.1. Definition and relevance of misperceptions

Perceptions of social and political phenomena represent the subjective dimension of how people make sense of their environment. In his seminal work on public opinion formation, Walter Lippmann (Reference Lippmann1997) argued that perceptions of social reality often diverge from the real world, emphasizing that imagined representations of the world are what shape human behavior. When perceptions are inaccurate, that is, they are obviously ‘false or contradict the best available evidence’ (Flynn et al., Reference Flynn, Nyhan and Reifler2017: 128), they are typically referred to as misperceptions. As a cognitive category sui generis, misperceptions should be distinguished from both ignorance and knowledge: the former refers to the absence of a belief about a certain issue, whereas the latter is the possession of a correct belief (Kuklinski et al., Reference Kuklinski, Quirk, Jerit, Schwieder and Rich2000). Unlike ignorance, misperceptions are beliefs held firmly and with confidence, but unlike knowledge, they fail to reflect empirical reality.

In any case, they are a phenomenon of great normative and political importance. Normatively, the ideal of democracy depends on knowledgeable citizens who are capable of making well-reasoned decisions for the common good (Dahl, Reference Dahl1998). Democratic debates require a minimal level of agreement on facts and a shared sense of reality among citizens (Rekker, Reference Rekker, Strömbäck, Wikforss, Glüer, Lindholm and Oscarsson2022). Misperceptions run counter to this ideal by weakening fact-based deliberation and making it difficult for evidence-based policy-making to prevail. They can distort opinions and preferences on critical issues, ranging from vaccination choices (Nyhan and Reifler, Reference Nyhan and Reifler2015) to political violence (Lees, Reference Lees2022), and, unlike a simple lack of knowledge, are resistant to correction due to motivated reasoning (Kuklinski et al., Reference Kuklinski, Quirk, Jerit, Schwieder and Rich2000).

2.2. Studying misperceptions about immigration

Recent interest in misperceptions about immigration as a distinct form of cognition has given rise to a fragmented body of literature spanning many disciplines (for a recent overview, see Lutz and Bitschnau, Reference Lutz and Bitschnau2023). Empirically, a range of phenomena is subsumed under the term, including inaccurate images of immigration (Blinder, Reference Blinder2015), causal misattributions (Wu, Reference Wu2022), a lack of knowledge (Aalberg and Strabac, Reference Aalberg and Strabac2010), or, more specifically, mistaken perceptions of immigrant flows (e.g., Citrin and Sides, Reference Citrin and Sides2008; Herda, Reference Herda2010). Regardless of the conceptualization, most studies rely on population surveys as their preferred tool for measuring public perceptions. They ask respondents to give estimates on immigration-related issues—exemplified by an item from the European Social Survey (ESS): ‘Out of every 100 people living in [country], how many do you think were born outside [country]?’ The accuracy of these estimates is then assessed by comparing them to official figures and classifying the degree of deviation on a discrete scale as correct, overestimation, or underestimation (Herda, Reference Herda2013; Gorodzeisky and Semyonov, Reference Gorodzeisky and Semyonov2020). Alternatively, the extent of inaccuracy can be quantified on a continuous scale, either in absolute (i.e., percentage points) or relative (i.e., percentages) terms (Herda, Reference Herda2010).

Based on this, immigration appears not only especially prone to misperceptions but also consequential (Lutz and Bitschnau, Reference Lutz and Bitschnau2023), with such misperceptions found across countries and demographic groups (Alesina et al., Reference Alesina, Miano and Stantcheva2023). Yet, at the same time, some authors contend that their frequency may be markedly overestimated (e.g., Graham, Reference Graham2023; Deutschmann, Reference Deutschmann2025). What is more, perceptions about immigration are often not only inaccurate but also characterized by a clear negativity bias. This means that immigrants are, on average, perceived as more violent, uneducated, or culturally distant than empirical evidence suggests (Lutz and Bitschnau, Reference Lutz and Bitschnau2023). The bias entrenched here is widely believed to stem from politically motivated reasoning (Taber and Lodge, Reference Taber and Lodge2006; Kahan, Reference Kahan, Scott and Kosslyn2016; Klintman, Reference Klintman2019), which itself is largely driven by ideological predispositions and preexisting sentiments. This is also why many misperceptions seem hardwired—people refuse to accept the real figure because doing so would trigger cognitive dissonance (Rolfe et al., Reference Rolfe, Ahlstrom-Vij, Hudson-Sharp and Runge2018; Hopkins et al., Reference Hopkins, Sides and Citrin2019; Jørgensen and Osmundsen, Reference Jørgensen and Osmundsen2022). This applies to individuals from different political camps (Washburn and Skitka, Reference Washburn and Skitka2018; Lind et al., Reference Lind, Erlandsson, Västfjäll and Tinghög2022), although information treatments may still influence people’s attitudes and preferences (e.g., Grigorieff et al., Reference Grigorieff, Roth and Ubfal2020; Haaland and Roth, Reference Haaland and Roth2020; Carnahan et al., Reference Carnahan, Bergan and Lee2021). Making sense of these inconclusive findings on the frequency and nature of misperceptions requires an adequate conceptual understanding and valid empirical measurement. But despite notable advances, the field remains in statu nascendi, and its progress is hampered by conceptual and methodological shortcomings. In the following, we elaborate on two of these shortcomings that we deem to be of particular relevance.

2.3. The dominance of population innumeracy

The first shortcoming concerns the fact that, though a wide and growing range of misperceptions about immigration has been documented, most empirical research focuses on population innumeracy, which can be defined as the tendency to overestimate the share of immigrants within a population (e.g., Sides and Citrin, Reference Sides and Citrin2007; Citrin and Sides, Reference Citrin and Sides2008; Herda, Reference Herda2010; Strabac, Reference Strabac2011; Gorodzeisky and Semyonov, Reference Gorodzeisky and Semyonov2020). For several reasons, this focus is hardly surprising. First, the concept of innumeracy is well-established in the study of perceptions of minorities (Nadeau et al., Reference Nadeau, Niemi and Levine1993) and has served as a foundational entry point for research on misperceptions about immigration as well. Also, the conceptual simplicity of estimating the number of immigrants lends itself well to representation as a percentage of the resident population. Not to forget the fact that immigration population figures are easily available, allowing researchers to evaluate the accuracy of survey responses and to make comparisons across space and over time. All these features have made population innumeracy the preferred (and sometimes only relevant) metric for studying misperceptions about immigration and a mainstay in social science research.

That said, there are evident limitations both in the narrowness of this focus and in the specific type of misperception it captures. To begin with, immigration is a multifaceted phenomenon, and individuals hold a range of associations and beliefs about it. Against this backdrop, a single item cannot adequately represent the full spectrum of public perceptions. Rather, the emphasis on population innumeracy puts aside other important aspects, such as the composition of the immigrant population or the drivers and consequences of immigration—all of which have been shown to play a key role in immigration politics (e.g., Blinder, Reference Blinder2015; Herda, Reference Herda2015).

A second problem concerns methodological doubts about whether population innumeracy is simply a manifestation of a broader cognitive innumeracy bias, i.e., the difficulty many people have in accurately processing numerical information and concepts related to statistics and probability (Paulos, Reference Paulos1988). If this is indeed the case, misperceptions about immigration may primarily result from a general tendency to overestimate minority group sizes, rooted in difficulties with estimation tasks and a clear cognitive bias toward central values when judging proportions (e.g., Nadeau et al., Reference Nadeau, Niemi and Levine1993; Lawrence and Sides, Reference Lawrence and Sides2014; Landy et al., Reference Landy, Guay and Marghetis2018; Guay et al., Reference Guay, Marghetis, Wong and Landy2025). This bias tends to be stronger when the benchmark value is small. It is therefore especially relevant for immigration-related items, as the overall population share of most immigrant groups is low, and certain consequences of immigration occur rarely—a fact exemplified in a U.S. study measuring perceptions of the share of refugees (0.06%) and their likelihood of committing and being convicted of terrorism (0.00074%) (Thorson and Abdelaaty, Reference Thorson and Abdelaaty2023). A complementary issue is the underestimation of large numbers, such as when respondents are prompted to estimate the absolute number of successful asylum seekers (Guenther, Reference Guenther2024). And finally, the way items are worded may also contribute to bias: many surveys, most notably the ESS, ask respondents how many out of 100 residents in their country they believe to be immigrants. This format may itself inflate misperceptions due to the 1-in-X bias (Dickson et al., Reference Dickson, Espa, Micciolo and Savadori2024), a pattern confirmed in our analysis (see pretest report in Appendix I).

Defining which threshold qualifies an estimate as accurate (i.e., no longer a misperception) is another key challenge. An estimate that is close to the real value would be considered accurate even if the two are not identical. In previous empirical research, this notion of closeness has been operationalized either as absolute deviation, such as 1 or 5 percentage points (e.g., Herda, Reference Herda2010, Reference Herda2013; Deutschmann, Reference Deutschmann2025), or in relative terms, such as one-fifth below or above the real value (e.g., Gorodzeisky and Semyonov, Reference Gorodzeisky and Semyonov2020). Yet while this dichotomization of accuracy may facilitate empirical assessment, any threshold is necessarily arbitrary and thus leads to non-generalizable conclusions. This problem is compounded by the fact that, in some cases, larger deviations from the real value are possible than in others (e.g., when this value is 10% instead of 50%). More broadly, since people may both underestimate or overestimate the official value, these strategies reduce information and overlook the inherent directionality and gradation of misperceptions.

2.4. Misperceptions or bad guessing?

As a second shortcoming of current research, we identify a lack of measurement validity arising from the failure to distinguish between genuine misperceptions—cases in which individuals hold incorrect beliefs—and uninformedness, which refers to a state in which individuals do not know what to believe but still give an incorrect answer (Kuklinski et al., Reference Kuklinski, Quirk, Jerit, Schwieder and Rich2000). In most studies on immigration misperceptions, survey respondents are asked to give a numerical estimate but not asked how confident they are that this estimate matches reality. As a result, researchers cannot properly determine whether responses are rooted in beliefs or instead represent on-the-spot judgments that are elicited by the question posed and betray little else than simple guessing (Zaller, Reference Zaller1992; Pasek et al., Reference Pasek, Sood and Krosnick2015). This means that the most common approach conflates two fundamentally distinct phenomena. It also ignores that these phenomena carry different psychological and epistemological implications: someone who gives an inaccurate response without believing in it may be more open to correction, for instance, than someone who does (Li and Wagner, Reference Li and Wagner2020). Because of this striking mismatch between conceptualization and measurement, many studies may have prematurely treated incorrect estimates as misperceptions.

A central reason why this distinction between misperceptions and incorrect guessing has not been dealt with yet may lie in the literature’s focus on knowledge and its interpretation of wrong answers as prima facie evidence for a lack of such knowledge (Bartels, Reference Bartels1996). In addition to this, empirically distinguishing the two phenomena is a difficult undertaking and requires complex survey designs that are more costly and time-consuming to implement (Lindgren et al., Reference Lindgren, Damstra, Vliegenthart, Strömbäck, Wikforss, Glüer, Lindholm and Oscarsson2022). Consequently, most research on immigration misperceptions is unable to validly measure its outcome of interest.

3.1. Survey battery of perception items

To further advance the study of immigration misperceptions, we present a survey module designed to overcome the shortcomings discussed above. First, we address the limitations of relying on population innumeracy as the primary measure for studying misperceptions. Then, we introduce a battery of eight perception items covering four distinct dimensions of immigration. Employing multiple items is a well-established approach for measuring political knowledge (Delli Carpini and Keeter, Reference Delli Carpini and Keeter1996), and we apply the same logic here to obtain a comprehensive and reliable assessment of immigration misperceptions.

In developing the survey battery, we carefully considered three core elements: the underlying concept of each item, the benchmark value needed to assess accuracy, and the measurement scale for capturing perceptions. These elements guided the construction process of our battery to make sure that it validly and reliably captures immigration misperceptions. First, we selected aspects of immigration that are broadly comprehensible to the general public and likely to shape perceptions of the issue. This ensured that respondents were likely to have prior exposure to the subject. Without this grounding, responses would have reflected not actual beliefs but statistical artefacts arising from proxy reasoning, off-topic inferences, or on-the-spot guesses.

Second, we prioritized items that could be benchmarked against official and undisputed statistical data. At the same time, we crafted the item wordings so that they can be easily understood, are free of technical language, and accessible to respondents without any specialized knowledge—an especially important consideration in the context of immigration, where public understanding and official definitions often diverge.

Third, we chose a gradual response scale—specifically, percentage estimates ranging from 0–100—because it reflects how people typically perceive social realities: as matters of degree rather than binary facts. This scale provides more information by capturing both the magnitude and direction of perceptual inaccuracies. Such variation is key for distinguishing between systematic misperceptions and random errors. At the same time, we avoided items with extremely high or low benchmark values, as these are known to inflate measurement error due to cognitive biases and general innumeracy. By using a balanced range of official values across items, we aimed to minimize such bias and ensure that observed deviations mirror genuine misperceptions rather than scale-induced distortions.

Finally, we sought conceptual and methodological balance across the battery. It comprises eight items covering four key dimensions of immigration: demographics, culture, economy, and security. The first dimension covers perceptions of the immigrant population as a whole, while the latter three reflect three threat dimensions identified as central to the formation of immigration misperceptions (Lutz and Bitschnau, Reference Lutz and Bitschnau2023). Within each dimension, we selected two complementary items that vary in cognitive difficulty and connotation, striking a balance between positively and negatively framed content. This allowed us to capture the multidimensional nature of immigration misperceptions and reduced the risk that results were driven by the peculiarities of single items or dimensions.

Within our first dimension, we asked respondents to estimate both the population share of immigrants and the share of refugees among recently arrived immigrants. While the former is the most common question to measure immigration misperceptions, it is also the least specific and allows for comparisons with existing surveys. Several studies have indicated that the Swiss public tends to overestimate the share of their immigrant population, albeit to a lesser extent than respondents in other countries (e.g., Citrin and Sides, Reference Citrin and Sides2008; IPSOS, 2018). The second item focused on refugees as a crucial immigrant group that often dominates public attention. We thus combined a rather general question about the immigrant stock with a more specific one about recent immigrant flows.

The cultural aspect of immigration constitutes the second dimension of our survey battery. Despite its central role in immigration politics, operationalizing this dimension is challenging. We made an effort to this end by asking respondents about two immigrant groups that are frequently evaluated in terms of their cultural proximity (or perceived lack thereof) to Swiss citizens: foreigners who are Muslims—a highly migranticized and politically salient religious minority—and immigrants who hold citizenship from an EU member state. These items complement each other in that Muslims are often thought of as culturally distant, while EU immigrants are generally regarded as culturally close. In the Swiss context, both have been at the center of high-profile campaigns and referendums over the years (e.g., Dolezal et al., Reference Dolezal, Helbling and Hutter2010; Armingeon and Lutz, Reference Armingeon and Lutz2021), which increases the likelihood that people hold firm beliefs about them.

To capture the economic dimension, we asked respondents to estimate the unemployment rate among foreigners and the proportion of recent immigrant arrivals holding a tertiary degree. Both items pertain to the perceived economic impact of immigrants on their host country and address the widespread belief that most are poorly educated and reliant on welfare (e.g., Cengiz and Eklund Karlsson, Reference Cengiz and Eklund Karlsson2021; Alesina et al., Reference Alesina, Miano and Stantcheva2023). As with the cultural dimension above, the items are complementary and encompass both a negative condition (being unemployed) and a positive attribute (being educated).

Finally, we included two security-related items on immigrant crime and undocumented immigration, both of which are great public concerns (e.g., Mudde, Reference Mudde2010). Specifically, we asked for the proportion of foreigners among those convicted of a crime and that of immigrants without valid residence permits among all foreign residents.Footnote ¹ Both items reflect the perception that immigrants pose a threat to society and undermine public safety. In this case, the complementarity of the items relates to their frequency: while undocumented immigrants are a small minority, a majority of those convicted of a crime is non-Swiss. This pattern—immigrants usually entering through legal channels but being disproportionately represented in crime statistics—is consistent across many host societies (Marie and Pinotti, Reference Marie and Pinotti2024).

All items were measured as perceptions on a 0–100 percent scale, which simplified the estimation task for respondents, ensured comparability across items, and helped avoid the 1-in-X bias (Dickson et al., Reference Dickson, Espa, Micciolo and Savadori2024).Footnote ² Official benchmark values were taken from the most recent available data of the Swiss Federal Statistical Office (see Appendix I) and range from 4 percent (unemployment and undocumented immigrants) to 66 percent (EU immigrants). This avoids extreme values while maintaining a balanced distribution across the response scale, thus enabling us to assess both the accuracy of perceptions and the direction of any deviation.

3.2. Complementary confidence measures

After constructing this battery, we had to address the challenge of distinguishing between respondents who provide inaccurate responses because of misinformation and those who are simply uninformed.Footnote ³ To achieve this, we complemented the above perception items with a measure capturing the extent to which respondents are confident in their estimates.Footnote ⁴ This approach builds on prior studies that measure confidence or certainty regarding perceptions in other issue areas (e.g., Pasek et al., Reference Pasek, Sood and Krosnick2015; Carlson and Hill, Reference Carlson and Hill2022; Guay, Reference Guay2022; Graham, Reference Graham2023) to assess whether individuals genuinely hold beliefs in falsehoods or not.Footnote ⁵ Combined with inaccuracy, it enabled us to categorize survey responses into distinct cognitive outcomes (Table 1). Specifically, we distinguished between two types of inaccurate perceptions: those held with high confidence, which we refer to as misperceptions, and those with low or no confidence, which can be considered tantamount to bad guesses. Misperceptions reflect distorted perceptions that are often rooted in motivated reasoning, whereas guessing represents more random, ad hoc responses that draw little, if at all, on prior beliefs. The corresponding types of accurate perceptions are those held with high confidence, which we call knowledge, and those held with low or no confidence, which are essentially good guesses.

Table 1. Typology of cognitive outcomes for accuracy and confidence

These categories are ideal types, as many responses fall somewhere between them and should therefore be viewed as partially informed. This, in turn, implies that misperceptions are best understood as a matter of degree: the greater one’s confidence in an inaccurate response, the stronger the misperception. This conceptualization has the advantage of avoiding arbitrary cutoffs—commonly used in earlier studies employing confidence measures—to classify responses as misperceptions or guesses. Instead, it treats inaccuracy and confidence as continuous and distinct, meaning that giving an inaccurate response and expressing confidence in it are necessary and jointly sufficient conditions for holding a misperception (Goertz, Reference Goertz2006). This allows for a closer alignment between the empirical measurement of misperceptions and its theoretical foundation.

Applying this logic to our empirical data, we calculated a misperception score by multiplying the degree of inaccuracy by the level of confidence. The former is the number of percentage points by which an estimate deviates from the corresponding benchmark value, while the latter is first recorded on a scale from 0 (no confidence at all) to 10 (complete confidence), and then rescaled to 0–1. By multiplying these two variables, we ensured that the misperception label is limited to cases where both conditions—inaccuracy and confidence—are met. This yields a single metric that directly indicates the degree of misperceptions at the individual level.

In the same way, we calculated a guessing score by multiplying the degree of inaccuracy by the lack of confidence, effectively inverting the confidence scale. As an alternative, we also calculated normalized scores that account for the varying scales of our items. This was done by dividing the inaccuracy by the maximum possible error—defined as distance to 0 for underestimates and to 100 for overestimates. Both of these operationalizations entail some trade-offs: while the raw score may inflate misperceptions for items with rather large numerical ranges, the normalized score may understate differences by overcorrecting for scale variation. We decided to adopt the raw score as our main measure due to its better theoretical alignment and intuitive interpretability, while the normalized score served as a robustness check. These measures can be formalized as follows:

\begin{equation*}\begin{gathered} {\,\,\,\text{Misperceptio}}{{\text{n}}_{{\text{raw}}}}{\text{ = }}\frac{{\text{1}}}{{\text{8}}}\sum\limits_{i{\text{ = 1}}}^{\text{-}} {\left( {{\text{|Perceived}}\,{\text{Valu}}{{\text{e}}_i}\, - \,{\text{Actual}}\,{\text{Valu}}{{\text{e}}_i} | \times \,{\text{Confidenc}}{{\text{e}}_i}} \right)} \hfill \\ \quad\quad\,\,\,\,{\text{Guessin}}{{\text{g}}_{{\text{raw}}}}{\text{ = }}\frac{{\text{1}}}{{\text{8}}}\sum\limits_{i{\text{ = 1}}}^{\text{8}} {\left( {{\text{|Perceived}}\,{\text{Valu}}{{\text{e}}_i}\, - \,{\text{Actual}}\,{\text{Valu}}{{\text{e}}_i} | \times \,\left( {{\text{1 - Confidenc}}{{\text{e}}_i}} \right)} \right)} \hfill \\ \quad\quad\quad{\text{Max}}\,{\text{Erro}}{{\text{r}}_i}{\text{ = }}\left\{ \begin{gathered} {\text{Actual}}\,{\text{Valu}}{{\text{e}}_i}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{if (Perceived}}\,{\text{Valu}}{{\text{e}}_i}\, - \,{\text{Actual}}\,{\text{Valu}}{{\text{e}}_i)} \lt \, {\text{0}} \hfill \\ {\text{100}}\,\, - \,{\text{Actual}}\,{\text{Valu}}{{\text{e}}_i}{\text{,}}\,\,\,\,\,{\text{otherwise}} \hfill \\ \end{gathered} \right\} \hfill \\ {\text{Misperceptio}}{{\text{n}}_{{\text{norm}}}}{\text{ = }}\frac{{\text{1}}}{{\text{8}}}\sum\limits_{i{\text{ = 1}}}^{\text{8}} {\left( \begin{gathered} \frac{{{\text{|Perceived}}\,{\text{Valu}}{{\text{e}}_i}\, - \,{\text{Actual}}\,{\text{Valu}}{{\text{e}}_i}{\text{|}}}}{{\,\,{\text{Max}}\,{\text{Erro}}{{\text{r}}_i}\,}} \times {{Confidenc}}{{{e}}_i} \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \hfill \\ \end{gathered} \right)} \hfill \\ \quad\,\quad{\text{Guessin}}{{\text{g}}_{{\text{norm}}}}{\text{ = }}\frac{{\text{1}}}{{\text{8}}}\sum\limits_{i{\text{ = 1}}}^{\text{8}} {\left( \begin{gathered} \frac{{{\text{|Perceived}}\,{\text{Valu}}{{\text{e}}_i}\, - \,{\text{Actual}}\,{\text{Valu}}{{\text{e}}_i}{\text{|}}}}{{\,\,{\text{Max}}\,{\text{Erro}}{{\text{r}}_i}\,}} \times {\text{(1 - }}{\text{Confidenc}}{{\text{e}}_i}{\text{)}} \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \hfill \\ \end{gathered} \right)} \hfill \\ \end{gathered} \end{equation*}

Calculating scores in this way enabled validation through the analysis of response patterns across items and by benchmarking individual items against other issue-specific perceptions. Since misperceptions are primarily motivated beliefs, we expected to observe consistent patterns of inaccuracy and bias. In contrast, guessing—lacking motivational structure—should produce more random variations.