Probabilistic and Randomized Methods for Design under Uncertainty

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Since the game was to be launched and run in the UK summer it was decided to make the theme appropriate to that time of year, as well as engaging to the widest demographic possible. Accordingly, the choice was made to base the game around running an ice-cream-van business. It is not possible to definitively address all questions in a single piece of work Morss et al.

By keeping the decisions specific to a theoretical situation e.

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As addressed in Morss et al. In laboratory studies participants can receive real monetary incentives related to their decisions see Roulston and Kaplan, ; Roulston et al. Our solution was to make the game as competitive as possible while being able to identify and eliminate results from participants who played repeatedly to maximize their score.

We also provided the incentive of the potential of a small prize to those that played all the way to the end of the game. Games have been used across the geosciences, for example to support drought decision-making Hill et al. Surveys are advantageous in that they can employ targeted sampling to have participants that are representative of the general population, something that might be difficult or cost-prohibitive on a large scale for laboratory studies. By using an online game format, we hoped to achieve a wide enough participation to enable us to segment the population by demographics.

We thought that this would be perceived as more fun than a survey and that therefore more people would be inclined to play, as well as enabling us to use social media to promote the game and target particular demographic groups where necessary. The drawback of an online game might be that it is still more difficult to achieve the desired number of people, in particular socio-demographic groups, than if using a targeted survey.

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The information in this section provides a brief guide to the structure of the game; screenshots of the actual game can be found in the Supplement. As a Met Office-led project there was no formal ethics approval process, but the ethics of the game were a consideration and its design was approved by individuals within the Met Office alongside data protection considerations. It was decided that although basic demographic questions were required to be able to understand the sample of the population participating in the game, no questions would be asked which could identify an individual.

Participants could enter their email address so that they could be contacted if they won a prize participants under 16 were required to check a box to confirm they had permission from a parent or guardian before sharing their email address ; however, these emails were kept separate from the game database that was provided to the research team.

The start of the game asked some basic demographic questions of the participants: age, gender, location first half of postcode only , and educational attainment see Supplement , as well as two questions designed to identify those familiar with environmental modelling concepts or aware that they regularly make decisions based on risk.

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Have you ever been taught or learnt about how scientists use computers to model the environment? Yes, No, I'm not sure. Do you often make decisions or judgements based on risk, chance or probability? The number of demographic questions was kept to a minimum to maximize the number of participants that wanted to play the game. Following these preliminary questions the participant was directed immediately to the first round of game questions. The order that specific questions were provided to participants in each round was randomized to eliminate learning effects from the analysis.

The first half of each question was designed to assess a participant's ability to decide whether one location temperature questions or time period rainfall questions had a higher probability than another, and the second half asked them to decide on how sure they were that the event would occur.

This format is similar to the slider on a continuous scale used by Tak et al.

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Check box under chosen location. How sure are you that it will not rain in each of these shifts? So if the participants state a probability of 0. This scoring method was chosen as we wanted participants to experience being unlucky, i. This meant that they would not necessarily receive a score that matched their decision-making ability, although if they were to play through enough rounds, then on average those that chose the correct probability would achieve the best score.

It was decided to give players traffic light coloured feedback corresponding to whether they had been correct green , correct but unlucky amber , incorrect but lucky amber , or incorrect red. The exact wording of these feedback messages was the subject of much debate. Using the data collected from the game, it is possible to assess whether participants made the correct decision for the first part of each question and how close they come to specifying the correct confidence for the second part of each question.

The participant was asked for the confidence for the choice that they made in the first half of the question, so not all participants would have been tasked with interpreting the same probability. The demographic of these participants was broadly typical of the Met Office website, with a slightly older audience, with higher educational attainment, than the wider Internet might attract see Fig. Full description of educational attainment in the Supplement professional includes professional with degree.

Before plotting the outcomes we removed repeat players, leaving participants in total.

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For the first part of the temperature and rainfall questions the percentage of participants who make the correct decision location choice or shift choice is calculated. In Figs. The boxplots in Figs. There was little difference between the presentation formats, though more participants presented with the line format made the correct choice than for the table format, despite them both having the same information content. Participants with all presentation formats had the same median probability error if they correctly chose Stonemouth.

Small sample sizes for Rockford fewer people answered the first question incorrectly limit comparison for those results, as shown by the large notch sizes. The results show that most participants correctly chose Rockford regardless of the presentation format. In this case the line format led to poorer decisions than the table format on average, despite participants being provided with the same information content. Accordingly the results for the shift choice show that there is no difference in terms of presentation format.

The results Fig. This suggests an interpretation based on a developed understanding of weather; the forecasted situation looks like a transition from dryer to wetter weather. The results also show that participants provided with the probability rating do not perform considerably differently from those with the symbol alone, perhaps suggesting that the weather symbol alone is enough to get a rough idea of the likelihood of rain. The similarity in the proportion of people getting the answer correct for each presentation format in this question Figs.

Given the small sample size when using subgroups of subgroups, we cannot conclude with any confidence whether age and educational attainment are significant influences on potential confusion. Previous work has shown that the public infer uncertainty when a deterministic forecast is provided Joslyn and Savelli, ; Morss et al. This shows that a third of people place their own perception of uncertainty around the deterministic forecast. Arguably this is a positive result, since it indicates that participants take into account the additional information and are not just informed by the weather symbol.

However, it also highlights the potential problem of being vague when forecasters are able to provide more precision. The ability of participants to make the correct rainfall decision using different ways of presenting the PoP forecast is shown in Fig. The best format would be one with a median value close to zero and a small range. Obviously we would not expect participants who were presented with a symbol or only the probability rating to be able to provide precise estimates of the actual probability, but the results for these formats can be used as a benchmark to determine whether those presented with additional information content are able to utilize it.

For the first part of the rainfall question the best presentation formats are those where the percentage is provided explicitly. The error bars overlap for these three formats, so there is no definitive best format identified from this analysis. This suggests that provision of the PoP as a percentage figure is vital for optimizing decision-making.

Note that participants who were not presented with a bar or percentage would not have been able to answer all four questions correctly without guessing. For the second part of the rainfall question Fig. This result suggests that providing a good visual representation of the probability is more helpful than the probability itself, though equally the bar may just have been more intuitive within this game format for choosing the correct satellite button. An interesting result, although not pertinent for presenting uncertainty, is that the median for those participants who are only provided with deterministic information is significantly more than 0, and therefore they are, on average, overestimating the chance of rain given the information.

This replicates the finding of Sivle et al. Further research could address how perceptions of uncertainty are influenced by the weather symbol, and if this perception is well-informed e. The results for the different temperature presentation formats in each separate question Fig. It is expected that participants would find it more difficult to infer the correct probability within the temperature questions; this is because they have to interpret the probability rather than be provided with it, as in the rainfall questions.

This would also be the conclusion for Fig. Like Tak et al. However, the average of all the questions does not necessarily provide a helpful indicator of the best presentation format because only four scenarios were tested, so the results in Fig.

The differences between the two different ways of presenting the deterministic information table and line , shown in Fig. Calafiore, Giuseppe, Dabbene, Fabrizio, PSZ JB. Summary Probabilistic and Randomized Methods for Design under Uncertainty is a collection of contributions from the world's leading experts in a fast-emerging branch of control engineering and operations research. List of Contributors p. Spall and Stacy D. Hill and David R. Stark 4 Optimization of Risk Measures p.

Tadic and Sean P. Hokayem and Silvia Mastellone and Chaouki T.

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