Perceptions of fundamental science: Evidence from a classroom experiment

Large-scale research infrastructures such as particle colliders, radio telescopes, the International Space Station, are often funded through general taxation and taxpayers are called to contribute to scienti ﬁ c discovery. How much are people actually willing to pay for investments in science? What does drive such a giving behaviour? This paper explores the attitudes of young science-outsiders (the taxpayers of tomorrow) by a pilot experiment involving 230 undergraduate students in economics at University of Milan. The experiment takes the form of a Contingent Valuation Referendum-like interview aimed at eliciting the willingness-to-pay (WTP) for the discovery potential of the CERN Large Hadron Collider (LHC), the most powerful particle accelerator worldwide. Our results point to the attitudes of students about fundamental science measured through their WTP. Building on this pilot experiment, we put forward recommendations for future research.


Introduction
Discovery is not a free lunch. Since 2000, total global R&D expenditures have tripled in current euros, from EUR 624 billion to EUR 1.8 trillion (Congressional Research Service, 2019). 1 The total capital and operations costs of some very large-scale research infrastructures (RIs, hereafter) such as the International Space Station, the Square Kilometers Array Radiotelescope (SKA), the Human Genome Project, are in the region of billions of euro. For instance, the present value to 2025 of the Large Hadron Collider (LHC) total costs has been estimated around EUR 13.5 billion 2 , while the cost of the Human Genome Project is estimated at around EUR 2.5 billion. 3 Even minor RIs, only supported by national governments, such as the CNAO research centre for hadron therapy in Pavia (Italy), the ALBA synchrotron supported by the Spanish government 4 or other public research institutes in developing countries require investments in the region of hundreds million euro (Battistoni et al., 2016;Biscari, 2012;Caliari et al., 2019;Sanz-Men endez et al., 2013).
All these scientific projects are funded either by international and national agencies through government funding, hence ultimately by taxpayers. So, the questions to be addressed are: does society perceive (big-) science as a valuable investment? Are citizens outside the scientific community willing to pay for basic research with their own money? And what factors drive this willingness-to-pay (WTP, hereafter)? These questions are interesting for both academic research and science policy (Baneke, 2019;Florio, 2019). From the academic research perspective, the questions are particularly intriguing when basic research is considered, since its definition acknowledges 'any particular immediate application or use in view' (OECD, 2002). In his timeless essay, 'The Usefulness of Useless Knowledge' Abraham Flexner (Flexner, 1939) argues that the search for answers to deep scientific questions driven solely by curiosity and deflected by considerations of immediacy of applications often leads not only to technological breakthroughs but also contributes to human welfare. In short, the cultivation of scientific curiosity would generate equally important satisfaction as the intellectual and the spiritual life do. Similarly, Flexner and Dijkgraaf (2017) says that society can tackle societal challenges, achieve deeper understanding, and pursue progress only by really valuing and funding the curiosity-driven "pursuit of useless knowledge" in both the sciences and the humanities. So, scientific curiosity would be the source of an increase in the people's utility, which feeds the willingness to contribute for investment in knowledge production. This paper wants to shed light on this public's preference for science. Interest in our questions goes even beyond utilitarian considerations. Since 2008, budget austerity has been forcing governments around the world to weigh carefully the economic and social benefits of all their investments, so from the science-policy perspective, there is great concern related to the allocation of resources for the conduct of science towards the goal of best serving the public interest and how the general public perceives this effort (Bauer, 2009;European Commission, 2016;Muñoz et al., 2012). Indeed, the main benefits generated by research infrastructures such as the creation of knowledge outputs, technological externalities, human capital accumulation, the cultural impact of the outreach, and service provision may only capture the use-value of these assets. To estimate their total economic value, the benefits related to the non-use value should also be considered (Johansson, 2016;Rousseau et al., 2021). As stated by Johansson and Kristr€ om (2015, p. 24): "If the project being evaluated affects non-use values, this should be reflected in the cost-benefit analysis". For these reasons, it is a timely need to examine the WTP for scientific discovery, even when, as in the case of the Higgs boson or the gravitational waves, there are no particular applications or use in view.
This paper investigates on the WTP for particle physics research at LHC by a pilot experimental setting, drawing from the empirical literature on the valuation of non-use benefits of environmental or cultural goods (Carson, 2011;Snowball, 2008). A sample of 230 undergraduates at University of Milan was involved in a Contingent Valuation referendum-like (CV-SBDC) 5 survey, where some questions were designed to elicit the respondents' WTP and other to control for individual variability of some socioeconomic and psychological characteristics. Given the relatively small sample size and low heterogeneity of participants, our study should be intended as a "laboratory" experiment; namely, an attempt to learn how to estimate the WTP for basic research by examining the preferences of young students (Andrews, 2001;Ricciardelli et al., 2020;Vossler & McKee, 2006) not involved in science.
Lab experiments are widely applied in economic research to respond economic questions, including how various personal traits and context influence the behaviour of economic actors on certain issues (see, for instance, Kessler & Vesterlund, 2015). However, a recently handful of papers by Levitt and List (2007a, 2007b, 2009) has heavily critised the (external) validity of laboratory studies because, according to the authors, there are many reasons to suspect that lab findings fail when generalized to naturally-occurring settings (Levitt and List, 2008). A response to this critique has been moved, among others, by Camerer (2011), who argue that generalizability of lab results is an exaggerated concern among non-experimenters and "a typical experiment has no specific target for external validity; the target is the general theory linking economic factors to behaviour" (Camerer (2011, p. 46). Accordingly, what does really matter is whether the qualitative results are externally valid, and to a lesser extent to which the quantitative results are. There is no disagreement on the debate on the contribution of lab experiments to economics on this point (Kessler & Vesterlund, 2015). In line with this argument, the contribution of this paper to the literature of welfare economics of big-science is two-fold: firstly, to explore variable of interest (awareness, attitude, personal characteristics) that influence the WTP for global research projects; secondly, put forward recommendations for follow-up research wishing to investigate on this field more deeply. The impact of big-science on society is an important issue to be investigated and deserves much more attention than is current the case.
To achieve this stated purpose, we use both parametric and nonparametric estimators to explore the drivers the respondents' WTP. Our results suggest that a non-zero positive WTP for the LHC discoveries exists and it is influenced by income, the offered bid, previous awareness of CERN and its experiments, and interest in science.
The paper is structured as follows. Section 2 briefly describes the analytical framework. Section 3 presents our results. Lessons learned for future research are discussed in Section 4. Section 5 concludes.

Analytical framework
Conceptually, the WTP for discovery can be interpreted as the individual preference for acquiring new (scientific) knowledge, which, as suggested by Stiglitz (1999) is a "global public good". Once produced, its consumption is typically not bounded in one specific locality, but its benefits widespread worldwide. Therefore, when taxpayers fund science in one country, they actually generate an externality to other citizens elsewhere. Similarly to the value people attach to safeguarding global ecosystems and heritage public goods (Strand et al., 2018), we argue that the production of new knowledge per se (i.e. even without predictable use of it) gives people a sense of pleasure and fulfilment, meaning and identity, which are source of increasing utility, and wellbeing.
Moreover, as for many years, there will be no market for (most) knowledge generated by a discovery in basic science, and no prices to convey signals to investors; therefore governments must rely on taxes. The theory of taxation for public goods suggests that citizens' preferences, elicited by some detection mechanisms, should be considered as pseudo-prices (Hindriks & Myles, 2013) and that the optimal provision of a pure public good requires that the sum of the individual WTP equals the production cost. While some large scale RIs involve a unique design, i.e. "take it or leave it" investments, more often there is a range of variants that engineers and scientists need to negotiate with funders. 6 Whatever the case is, costs are observable variables or can be predicted when designing an RI; in contrast, the individual WTP is private information, and different elicitation methods have been suggested and implemented in applied welfare economic literature (Johansson & Kristr€ om, 2015).
To estimate the WTP for scientific discoveries, we discuss both the use of parametric and distribution-free nonparametric estimators. Over the last decades, researchers have started to argue that parametric estimation relies on quite strict a priori assumptions about the underlying distribution of WTP in the target population that are effectively not testable at operational samples sizes (Borzykowski et al., 2018). In response to this argument, nonparametric and semiparametric methods started to receive more attention (Cooper, 2002;Huang et al., 2008;Kristrom, 1990;5 The referendum-like approach is also known as single-bounded dichotomous choice (SBDC) approach. 6 For example, in the case of particle colliders, synchrotron light sources or hadrontherapy with proton accelerators, the energy of the accelerated beams is function of the radius of the circular trajectory of particles, the power of certain devices, and the generators of magnetic fields. All these elements (and others) may imply different project designs that are conditioned by available funds. Other examples are radiotelescopes where the number of antennas is a function of available funds, genomic platforms where the number of sequencing machines depends upon funds as well. More in general, the operating cycle of certain RIs is not always determined by the scientific needs, but it can be longer or shorter according to available funds. If time and operating costs enter in the overall project cost, the majority of RIs have a potential element of budget flexibility. Watanabe & Asano, 2009). The non-parametric approach can be applied either using Ayer et al.'s (1955) pooling adjacent violators algorithm or Turnbull's (1976) distribution-free estimator; the latter originally applied in contingent valuation by Carson et al. (2003) and Haab and McConnell (1997). For contingent valuation (hereafter, CV) with discrete responses, the Turnbull is similar to applications by Kristrom (1990) and McFadden (1994) of the pool adjacent violator algorithm. The nonparametric estimators provide welfare measure estimates unconditional on psycho, socio-economic and demographic characteristics of the respondents or characteristics of the good to be valued, however, they provide a benchmark which is robust to potential parametric specifications errors (Borzykowski et al., 2018).
As a consequence, both parametric and non-parametric estimators are worth considering in our context since little is known about the "size" of individual preferences on basic research and what drives them. As regards drivers, we consider financial variables (e.g. the availability of personal or family income), personal interest in scientific research and awareness of the research carried out at CERN LHC (see Florio at al., 2020 for a theoretical discussion on such drivers).
The reference model we employ to parametrically estimate the willingness to pay for the research activity at CERN is the utility difference model developed by Hanneman (1984), while the non-parametric elicitation procedure is mainly based on Kristrom (1990). Details and formulas are provided in Appendix A in the online supplementary material. The experiment design, implementation, and WTP estimation follow, as far as possible, the CV guidelines by the NOAA blue ribbon panel (Arrow et al., 1993) 7 and also take on board some insights from their more recent version by Johnston et al. (2017), largely used worldwide to elicit the intrinsic value of environmental and cultural goods. We apply this framework to ask uinversity students to directly report their perceptions, opinions and WTP about the research at the CERN LHC.

Implementation and design
Our experiment was conducted at University of Milan in two rounds and it involved 230 undergraduate students in economics. In June 2016, 120 students were surveyed; the remaining 110 were interviewed after one year in June 2017. Data were treated confidentially and anonymity was guaranteed to all the participants in the experiment, who agreed to volunteer for the purpose of research. Students were not financially compensating for participating in the research (see below for details). 8 The experiment proceeded as follows. Several days prior to the experiment session, students were informed about the opportunity to take part in an upcoming research project and they were made aware that the participation in the experiment was on a voluntary basis. On the day of the experiment, upon arrival in the classroom, two expert interviewers gave participants a randomly-drawn, anonymized CV-like questionnaire containing an ID number. Different pre-printed bid (see below) were randomly assigned by groups, each containing around 40 students. Afterwards, students were partitioned to ensure that they could not communicate during the session, nor observe others in the room. To ensure anonymity and reduce the risk of social desirability bias, interviewers announced that information would be linked only to participants' ID-numbers and not to individual names; yet data would be elaborated in aggregate format only. Only participants and the interviewers were present in the experimental session.
Once all participants were seated and ready to fill in the questionnaire, interviewers began the session by reading a short introductory script. Participants were informed that they would be asked to complete a number of tasks (which interviewers would gradually describe to them) and make a number of choices. Importantly, prior to beginning the experimental tasks, and mainly in the first part of the experiment, participants were given no information about the aims of the research project, nor about what the experiment sought to elicit. This experimental design was implemented to correctly measure and analyse opinions and interests in scientific issues and the respondent prior awareness of the RIs before revealing the exact purpose of the study (Carson et al., 2003, p. 264).
The questionnaire was designed to be consistent, as far as possible, with the NOAA panel guidelines by Arrow et al. (1993), while some modifications were applied to take into account the peculiarities of the public good under evaluation.
The questionnaire (online Supplementary Material) consisted of three parts. The first part described information and perception of a respondent about issues related to research infrastructures in general as well as the respondent's interest in scientific discoveries. As showed by Heberlein et al. (2005), attitudes, interests, knowledge of the (public) good under evaluation can lead to different evaluations (and thus WTPs) by respondents; therefore attitudinal and behavioural scope sensitivity tests can be performed to validate and support results (see also Muñoz et al., 2012).
The second part contained questions aiming at eliciting the WTP for scientific discoveries.
First of all, a description of the LHC was provided to interviewees in the form of a shortened version of the Wikipedia entry "Large Hadron Collider", including five photos showing the particle accelerator in its 27km tunnel and the particle detectors ATLAS, CMS, ALICE and LHCb placed at four locations around the accelerator. In this way, respondents were given common information set about the functioning of the LHC, its research activity, and the answers that scientists expect from this research facility. Students were explained that collisions are examined to find answers to issues left unsolved by the Standard Model of particles and forces 9 such as the origin of particles' mass, a comprehensive explanation of the interactions between the fundamental forces of the universe and the phenomena responsible for dark matter (Giudice, 2010). The description was previously and repeatedly revised to refine the information it presented and to improve its clarity by means of focus groups and pilot tests carried out at University of Milan in 2015, before the experiment took place.
Just before asking the WTP questions, the questionnaire disclosed that the projects carried out by CERN, including the realisation of the LHC, are funded by the CERN Member States 10 through taxation, according to a share calculated on the respective national GDP, meaning that citizens indirectly support such projects and public contributions enable the CERN to continue its research activity. No information was however given about the actual amount of the Italian government contribution to the CERN budget.
The NOAA guidelines suggest to use a referendum-like approach 7 The (CV) method is the most commonly applied of all the methods available for valuing preferences for nonmarket goods with thousands of applications conducted worldwide. The concern on how to correctly eilicit the WTP quantifying a-prior poorly formed or even non-existent preferences for public goods was deeply debated in the occasion of the CV estimation of damages arising from the Exxon Valdes oil spill (Carson et al, 1994a(Carson et al, , 2003Diamond & Hausman, 1993). Much of the dabate was mainly addressed through the influential U.S National Oceanic and Atmospheric Administration (NOAA) panel report on CV (Arrow et al., 1993) which, since then, has provided guidelines for future applications. A key recommendation of this report concerned the elicitation method through which the WTP responses should be elicited. The NOAA panel recommended the use of a 'one-shot' or referendum style question. 8 The experimental protocol was in compliance with the regulations ratified by the ethics committee of the University of Milan Dean decree 19 July 2011. 9 To further details on the main goals of the LHC and on a non-physicists according to which, people should be asked to state only 'yes' or 'no' to the proposed bid; in contrast, Hanemann et al. (1991) have stressed the importance of followÀup questions addressed to estimate the maximum WTP value. The bid level offered in the followÀup question should be greater than that offered in the initial payment offer if the answer to the initial payment question is 'yes', otherwise the follow-up procedure is stopped. Although this approach is statistically more efficient than referendum approach, Alberini et al. (1997) found that the average WTP estimated after the followÀup approach can be lower than that implied by the responses to the initial payment question. A possible explanation is that some respondents may treat the suggested bid as a signal for the quality of the good and/or might erroneously believe that the program to be valued in the followÀup is different from the initial one. Furthermore, in favour of the referendum approach there is the argument that it mimics behaviour in regular markets, where people usually purchase, or decline to purchase, a good at the posted price. It also closely resembles people's experience with political markets and propositions on a ballot (Mitchell & Carson, 1989). On the other side, single referendum elicitation format is highly vulnerable to anchoring effects (Green et al., 1998). Although the debate is still open, in this exploratory attempt to elicit the WTP for basic science, we adopted a referendum-like approach, which seems the most accepted one in the current literature. Respondents were asked to vote 'yes' or 'no' to fund for the research activity at the LHC given the amount of income reduction (e.g. the offer price). The exact wording of the WTP question was: "Would you willing to pay EUR _ every year to fund the research activity at LHC turning down other personal expenses? With one of the following pre-printed bids: EUR 1, EUR 2, EUR 5, EUR 10, EUR 15, EUR 30. The minimum and the maximum price offered to respondents was based on previous focus groups and surveys aimed at calibrating the experiment. For those who voted 'yes', to get additional information, an open-ended question was asked to explain why they chose to vote for the program. For those who vote 'no', the follow-up question was asked to identify protest bid respondents. Moreover, in order to collect further evidence about respondents' WTP, an open-ended question of the maximum WTP was added as well: "What is the maximum amount you would pay each year to fund the research activity of the LHC (Please insert the amount in EUR)?" (Johansson & Kristr€ om, 2020). 11 In line with the CV procedures (Johnston et al., 2017, p.357) students were not financially compensated for participating in the experiment; however, the hypothetical giving to the LHC project was explicit set against decreasing consumption on other items to take into account the budget constraint underlying the utility-theoretic foundation of preferences (Carson et al., 2003; Appendix A in the online supplementary materials).
Finally, this questionnaire-based experiment were conducted by experienced researchers in order to minimize interview bias and strategic behaviour. 12 The third part of the questionnaire included questions on the individuals' demographic and socio-economic characteristics such as age, sex, gross income (both personal income and family one) and household size.

Results
Data were analysed using both descriptive and econometric procedures (Appendix A, online supplementary material). studies. The open-ended format is known to not be incentive compatible (see for instance Carson & Groves, 2007;Carson et al., 2014). Carson and Groves (2007) argue that an open-ended format may induce the respondent to act strategically to influence the outcome of the experiment. The optimal strategy would be to report either a small or a very large WTP response (Carson & Groves, 2007, p. 202). Johansson & Kristr€ om, 2020 recognise the lack of incentive compatibility of an open-ended format, but they show that such a format can cope with pure altruism, including any non-use values. In contrast, closed-ended formats could be incentive compatible but cannot cope with pure altruism as that one we are looking for with this research (see below). Their suggestion is therefore to use a procedure involving both the types of elicitation format. 12 Students were asked to fill-in the questionnaire on their own and no face-toface interviews were carried out. Interview bias arises when the interviewer accidentally leads respondent in a particular direction when answering the questionnaire, while strategic behaviour occurs when a systematic error is introduced into the sampling, when respondents select one answer over others in order to not to reveal their true opinion/position. A well-known case is that of perceived government-supported surveys leading people to skip highly-sensible information like income. descriptive statistics related to demographic and socio-economic characteristics of the respondents. Our sample of students is aged, on average, 22; while, 57% of the sample, i.e. 131 respondents is male. The distribution of respondents based on their monthly family income is: 91 (42.3%) belong to a family with a monthly income between EUR 1,000 and 3,000; 81 (37.7%) between EUR 3,000 and 5,000; 35 (16.3%) more than EUR 5,000 and 8 (3.7%) respondents belong to a family earning less than EUR 1,000.
The gross income distribution of the respondents' families is comparable with the available data on income distribution in the North-West of Italy, where the University of Milan is located. The average family income in our data is about EUR 38,200 per annum (EUR 3,187 per month) with respect to a mean in Northwestern Italy of about EUR 33,000 (the national mean is about EUR 29,500). 14 While we did not design the experiment seeking for statistical representativeness of the (Northwestern) Italian population which was not our objective, the family background of the respondents does not suggest a sample biased towards relatively high income levels (but certainly the educational background is higher than for the Italian average).
Results of the investigation about awareness and perception of RIs and interest in science of respondents are shown in Table 1 (Panel B), and Table 2.
The majority of respondents (81.1%) ( Table 1, Panel B) declare that they were aware of what an RI is. Multiple options were possible in identifying a RI. The option related to a particle accelerator was chosen by 159 (70%) students (Table 2, Panel A); 200 (83.3%) respondents said that they were interested in scientific discoveries; online news was selected by 170 students (74%) as source of information (Table 2, Panel B).
Respondents were initially asked about their view about the importance of funding RIs on a qualitative scale. Table 1 (Panel B) shows that 186 (81%) interviewed think that funding RIs is important or very important, 38 (16.5%) think that is fairly important, and 6 (2.6%) chose the options "Useless or Insignificant".
About 49% of the sample (112 respondents) had heard about LHC, 74.8% (172 respondents) about the Higgs boson; in contrast only 13 respondents (5.7%) visited CERN. The latter information is important, being the CERN at a travel distance of around 4 h from Milan by train and often targeted for visits by high schools. Thus, we have indirect evidence that this sample is not particularly exposed to previous direct information on the LHC, hence all the information students have was based on exposure to the media or on the summary information distributed during the experiment. Table 3 (Panel A) reports statistics related to WTP when asked according to the referendum-like approach. The percentage of 'yes' and 'no' is presented for each offered bid to respondents. We expect that the higher the bid, the lower the percentage of 'yes' is. Table 3 shows that no respondents rejected the first bid (EUR 1), 5% rejected the second bid (EUR 2), 18% rejected the third bid (EUR 5) and 21% rejected the forth bid (EUR 10). At the bid EUR 15 the percentage of 'no' reduced rather than increasing; in contrast and as expected, at bid EUR 30 it increased again. Although this distribution is not perfectly smooth (that is the reason why we adopt the pooling adjacent violators algorithm) overall, in our experiment the percentage of WTP 'yes' is a fairly well behaved distribution.
On the question that includes WTP motivation, respondents stated different reasons, which are shown in Table 3 (Panel B) based on their importance. Inspection of the answers suggest quite generic altruistic motivations for giving, without a preference for one statement against Note: multiple-answer questions. another one. Differently, among respondents who rejected the offered bid, the most quoted options were "I can't afford to pay anything at this time", "The activities at LHC are not worth anything to me", "The LHC is a machine that affects only physicists' and scientists' world, so it unfair to expect me (or my family) to pay for the LHC", and finally "I do not think the LHC would achieve its objectives"; (Table 3, Panel C). They are all valid reasons to reject the bid offered, so no protest bids were identified. Table 4 presents the results of the logit model as defined by Equation A.1. Model 1 includes the bid, the family income and demographic characteristics. Model 2 is extended by including variables expressing interest in scientific research. Model 3 leaves out the variables expressing interest in research and plugs in variables related to the awareness and knowledge about research activity at LHC. The full model is presented in Column 4. The estimated coefficient of the bid was found statistically significant in each specification at 1% level with the expected negative sign. This is in line with the basic axioms of utility choice indicating that the probability of WTP 'yes' decreases (increases) as the price of offer increases (decreases) (Johnston et al., 2017, p. 357). The estimated coefficient of income variable was found statistically significant at both 5% and 1% level at the highest categories with respect to the lowest category (<EUR 1,000) and the sign was positive as expected. The finding suggests that the probability of WTP 'yes' increases as the income increases. Age is not statistically significant. Conditional to our sample, this is not a surprising results since 91% our respondents are aged between 20 and 25. The variable "Male" shows no statistical significance as well, with negative sign in contrast with the existing literature on WTP for science and technology (European Commission, 2014). The coefficients on "A4 Interest in Research" and "A6 Importance of funding an RI" are significant at the 10% and 1% level respectively, with the expected positive sign (Model 2 and 4) meaning that judging funding RIs important increases the probability of WTP 'yes'. The coefficient on "A2 Particle accelerator" is statistically significant at 1% level (Model 3) and 5% level (Model 4) and the sign is positive. Therefore, recognising a particle accelerator as an RI, increases the probability of being willing to pay for its research activity. In line with the scope tests suggested by Heberlein et al. (2005), these results support the idea that behavioural intentions, as the willingness to pay for science, are influenced by attitudinal and cognitive dimensions towards this pubic good (Sanz-Men endez et al., 2013).
The alternation of negative and positive signs (e.g. in the case of the variable "A1 Knowing what an RI is" between Model 3 and 4) and/or absence of statistically significance on the remaining variables related to having heard about LHC or visited CERN are caused by the strong collinearity among them. For instance, the odds ratio between the variable "B5 Having visited CERN" and the variables "B1 Having heard about LHC"and "B3 Having heard about Higgs boson" is higher than 1 in both cases and statistically significant at 5% level. Similarly, the odds ratio between the variable "A1 Knowing what an RI is" and the variables "A4 Interest in Research" and "A6 Importance of funding an RI" is still above 1 and statistically significant at 1% level in both cases as well.
The Count R 2 at the bottom of Table 4 reveals that about 87% of respondents were correctly allocated to predicted WTP either 'yes' or 'not' in the models, indicating a relatively good fit to the data. 15 We test the same specifications (unreported regressions) by using the personal income rather than the family income. The availability of personal income shows positive sign but never results statistically significant in explaining the probability of a WTP 'yes'. This was likely due to the lack of sufficient variability in this variables since only a low share of students in our sample (20%) earned an own income. We also test a further specification including a dummy variable discriminating the year in which the experiment was carried out. We found this dummy never statistically significant suggesting that no differences in WTP responses exist between students surveyed in 2016 and those surveyed in 2017. This points to robustness of the results across different cohorts of students.
The expected value of mean WTP, which represents the "non-use value" of basic research at LHC was calculated by numerical integration, ranging from 0 to maximum bid (Equation A.2) after parameters from logit models were estimated. The coefficients estimated in Model 4 were used to determine the mean WTP, leading to a value of EUR 29 per person annually according to the following formula 16 Table 4 Results of the logit model: determinants of the WTP for discovery potential at the LHC. Robust standard errors in parenthesis. ***,**,* denote significance at the 1%, 5% 10% level respectively. The oods ratio between the variable "B Having heard about Higgs boson" and "B1 Having heard about LHC" is about 3 significant at 1% level suggesting high correlation between the variables; so the former variable was not used in Model 2 and Model 4. 15 The Count R-Square is a pseudo R-Square and measures the goodness of fit of a model in a different way with respect to the R-squared as explained variability in the OLS approach. It transforms the predicted probabilities by the logit model into a binary variable on the same scale as the dependent variable (0-1). Then it considers the observations with a predicted probability of 0.5 or higher as having a predicted outcome of 1; in contrast, it assigns the value of 0 to any observation with a predicted probability lower than 0.5. At this point, the Count R-Square compares the actual 1s (0s) with the predicted 1s (0s). The resulting number is the ratio between the number of correct predictions (observations) out of their total number. For more details see https://stats.idre.ucla.edu/other/ mult-pkg/faq/general/faq-what-are-pseudo-r-squareds/Last access on 15.09.2020. 16 One can question the assumptions behind the chosen distribution from zero to the maximum bid. Therefore, for the sake of transparency, by integrating Eq, A.2 from zero to the maximum bid returns a mean WTP of EUR 71.24. Actually, as discussed in Appendix A (online supplementary materials) an infinite upper bound on willingness to pay is inconsistent with budget constraints and also requires a projection well beyond the range of the data. We thanks an anonymous referee for this comment. EðWTPÞ ¼ Z 30 0 ½1 þ expðÀð4:7 À 0:0661AÞÞ À1 δA ¼ €29 As shown in Appendix A, the non-parametric estimations require only minor theoretical restrictions such as weak monotonicity. Pool adjacent violator algorithm estimate for the mean (WTP), Equation A.5, is: This figure can be compared with the parametric estimate. Both figures should be interpreted as a life-time commitment and consistent with many studies in the CV literature (see among others Hutchinson et al., 2001;Haab & McConnell, 1997;Carson, Hanernann, et al., 1994), we found the non-parametric estimate more conservative than the parametric one.

Lessons learned for future research
Lessons learned from this pilot experiment, which is novel in the literature, are now reported.
An obvious issue is that one should be able to design the experiment for a representative sample of citizens (taxpayers). This, per se, is not impossible, as social attitudes (including the ones towards science) are regularly performed with statistically representative samples of the population (see for instance European Commission, 2014). The main difficulty however, is that while research on social attitudes often tends to ask generic questions, here it is of essence to elicit a WTP for a specific project, as it is needed in a cost-benefit analysis setting. This poses challenges as the previous knowledge of the discovery potential related to a specific research infrastructure, or its mere existence, is an information which is usually unavailable to the public, or unevenly available through exposure to the media. Moreover, the nature of information is unavoidably superficial for the average citizen, who certainly cannot grasp the scientific importance of, e.g., knowing that the Higgs boson actually exists. In principle, one should take on board the previous exposure of respondents to outreach of science news in the media to be sure that the sample of respondents is not affected by sample bias over a key dimension of individual preferences. This is clearly revealed by our experiment which shows that previous knowledge about what is a research infrastructures, is strongly correlated to the elicited WTP. The challenge is diluited in environmental cost-benefit analysis, as surveyed respondents can be assumed to fully understand, for example, the implications for biodiversity in a given area of a specific project. Given the importance of this issue, it would be advisable to add to the usual demographics of the sampling strategy, a set of variables capturing attitudinal and cognitive information related to the project under evaluation as well as add questions about the reasons, designed such that the non-use value of science as compared to the use-value can be identified.
The second important point raised by our approach is in terms of the way to elicit the WTP in terms of opportunity cost. In our experiment and in line with the majority of CV literature, it was clearly stated that virtual giving to the LHC project was to be set against decreasing consumption on other items to consider budget constraints. While this was important, however, we investigated on the WTP without requiring the participants to actually pay anything. Some studies shows that individuals tend to overstate their WTP if not properly incentivised (List & Gallet, 2001;Murply et al., 2005), while behavioural economics often relies on the involvement of actual money to close the gap between the hypothetical and actual choices (Chaudhuri, 2008). Therefore, the main point for future research is to understand the extent to which our results reflect mere cheap talk rather than real intentions considering that we targeted students who are more likely sympathetic towards the pursuit of scientific research. Our WTP response data show consistency with basic axioms of choice, i.e. the proportion of students who would pay the amount should not increases as the bid amount increases and the relevance of the budget constraints (as revealed by the positive impact on income on the stated WTP) (Johnston et al., 2017). In addition, the survey results reveal a positive WTP, with the mean ranging from EUR 23 to 29 per person annually obtained by using both parametric and non-parametric estimators. This is of comparable size with the results of a recent study in the same field which involve a sample of 1,000 people representative of the French population . That study estimates a WTP for future particle accelerators at CERN (not the LHC) ranging from EUR 4 to EUR 17 per person per year and it is likely to be even higher for more educated people suggesting a positive association between lab experiments and field behaviour. By considering other global pubic goods, our findings can be also compared with Graham et al. (2019) investigating on the WTP for policies to reduce health damages from climate change. The authors shows that there is public support for policies to address future health impacts of climate change and the level of support varies with people's awareness of the seriousness of these impacts, their financial circumstances, and the level of education, being people with a degree or above more prepared to contribute to such policies (Graham et al., 2019, p. 114; Table 4). Our results are also in line with previous findings about the "non-use" values of some cultural and environmental goods. To mention a few, the average annual WTP for the performances at Royal Theatre in Copenhagen "as public good" was found to be EUR 27 per person by Hansen (1997); while Thompson et al. (2002) found an average annual WTP for Arts ranging from EUR 4 to 19 per households. 17 In the field of environmental economics the paper by Amirnejad et al. (2006) estimated an average annual WTP for the north forests of Iran of about EUR 30 per households and Carson et al. (2003) found that for preventing damages from another Exxon Valdez type oil spill people were willing to pay a median lump-sum WPT amounting to about EUR 20. 18 Our suggestion is hence to primarily stick to the CV approach when estimating non-use values of big-science. Recurring to an experimental setting where giving of real and possibly earned income is involved is obviously attractive, but a trade-off arises. The experimental economics literature is typically based on small-scale laboratory experiments with students (as in our case) but it does not aim then to expand to a population of taxpayers the empirical analysis, as it usually would be too costly and would pose a number of additional design problems. This unfortunately means that laboratory experiments with actual money have very limited implications for (science) policy. However, future research may try to replicate our experiment in a laboratory setting involving actual, possibly earned money, in order to highlight some qualitative issues arising in this area.
Finally, it would be interesting to check the robustness of results when alternatives are given. This would lead to the complication of adding bids for competing scientific or non-science projects, adding information in terms of consumer choice but also introducing some risks of distorting elicited preferences just because of the specific set of suggested alternatives (e.g. comparing fundamental physics to medical science projects).

Conclusions
This paper reports a "laboratory experiment" on the drivers of individual preferences expressed in monetary form for basic science. We involved a sample of 230 undergraduates in a non-science related curriculum in a classroom environment. Our findings reveal a positive WTP mainly driven by the offered bid, previous awareness of CERN and its experiments, and interest in science, and income. The interest of such an experimental approach lies in the fact that scientific knowledge is often a pure public good, funded by governments who need to guess how much they should spend to support its production. Ultimately, all citizens fund the research through taxation. Indeed, big-science projects are mostly funded by governments or international organisations such as CERN, which in turn is entirely funded by transfers by its Member States.
With all these reservations and caveats underlying a classroom experiment, it seems worth exploring ways to empirically estimate the "useless" value of fundamental research. Our contribution is to suggest that this study may offer valuable information that can be useful from science policy and academic research. In order to be funded, curiositydriven science has to continuously justify its existence. Eliciting the willingness to pay for large scale research infrastructures may suggest to governments to what extent people (at least the most educated segment of the population) have preferences for public funding of science even if there is no-use in view of the potential new knowledge. For policy makers, this evidence would represent a step forward in relation to the longstanding political disputes in research funding on how to get more economic and social value for investments in research and innovation ( Giffoni & Vignetti, 2019;OECD, 2019;European Commission, 2018). In fact, the non-use value generated by research infrastructures adds to their use value (Rousseau et al., 2021) and may play in favour of economic benefits when costs and benefits of such infrastrutures are put at stake, and would avoid a bias in favour of the research promising more direct economic returns.
In terms of academic research, the paper contributes to the literature on public goods by putting forwards some recommendations on how to assess the non-use value of the discovery potential of a large research infrastructures, whose awareness by public is somewhat blurred as compared to experienced goods such as environmental ecosystems and cultural amenities. As far as we know, this is an entirely new field in cost-benefit analysis and would greatly enlarge the perspective of environmental and cultural economics (Del Bo et al., 2016;Florio, 2019;Johansson, 2016). Additional work may investigate other fields as well, beyond high-energy physics.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
where b α * is the estimated adjusted intercept which was added by the socio-economic characteristics and other independent variables entering into the model to the original constant b α.

Non-parametric Estimation
The Turnbull's (1976) estimator is based on the estimation of a survivor function in presence of interval-censored data. 19 Following Bateman et al. (2002), the survivor function is defined as: where A j is the offered bid and n j =N j is the percentage of 'yes' responses in the sub-sample of respondents that received the bid A j . In cases wherein the survivor function is not a non-strictly decreasing function, it will not generate a valid survivor function. To correct such a problem, the Ayer et al.'s (1955) pooling adjacent violator algorithm can be employed (Bateman et al., 2002;Kristrom, 1990). The technique includes pooling data for two adjacent bid levels if the estimate of the survivor function for the higher bid level is greater than that for the lower bid; that is: Once the survivor function is estimated, the mean WTP is given by: where the mean WTP is the sum of the probabilities of the respondent voting behaviour times the difference between two adjacent bid levels.