But perhaps the brain does not represent probabilities explicitly, but approximates probabilistic calculations through a process of sampling, as used in computational probabilistic models in statistics. Naïve probability estimates can be obtained by calculating the relative frequency of an event within a sample, but these estimates tend to be extreme when the sample size is small. We propose instead that people use a generic prior to improve the accuracy of their probability estimates based on samples, and we call this model the Bayesian sampler. The Bayesian sampler trades off the coherence of probabilistic judgments for improved accuracy, and provides a single framework for explaining phenomena associated with diverse biases and heuristics such as conservatism and the conjunction fallacy. The approach turns out to provide a rational reinterpretation of “noise” in an important recent model of probability judgment, the se model , making  Human probability judgments appear to be systematically biased, apparently suggesting that human probabilistic reasoning is not based on normative Bayesian principles, but instead on heuristic approximations of various kinds e.g., . The larYet this research tradition appears to stand in sharp contrast with the prevalence and usefulness of Bayesian models across the cognitive and brain sciences, ranging over perception , languagThus, we are faced with an apparent paradox: How can Bayesian models of cognition, and indeed reasoning, be so fruitful, when what we might view as the “basic element” of such models, human probability judgment, appears to be systematically biased?In this article, we confront this apparent paradox head-on: We develop a Bayesian model of probability judgment, which operates not through the explicit symbolic calculation of probabilities, but instead approximates probabilistic inference by drawing samples from probability distributions. One of the major discoveries of computational statistics in the last half century is that such sampling models can often efficiently approximate complex probabilistic distributions , where sWe start from the perspective that people, quite possibly implicitly, have an internal Bayesian model of the tasks they engage in. The appeal of such a model is that it carries over some of the normative justification from work on Bayesian models, which have been successful in cognitive domains as varied as perception, language processing, categorization, intuitive physics, motor control, and reasoning .sampling from the relevant posterior probability distributions, rather than being computed directly. We have argued elsewhere that this may be the most appropriate interpretation of many Bayesian psychological models: The brain is a Bayesian sampler, but does not represent, or calculate with, probabilities  appear computationally daunting. We approach this challenge by borrowing standard methods from computational Bayesian statistics mentioned above: The Bayesian calculations can be approximated by bilities .How then do people estimate the probability of an event? Aside from restricted domains with specially designed devices such as coins, dice, and roulette wheels, analytic calculation is typically impossible. We can, though, rely on the recall of past cases, or our ability to imagine hypothetical cases through a process of mental simulation. Suppose, for example, we attend an English village fair and wonder how likely we are to knock a coconut off of a stick in a coconut shy game with a single throw. We can recall past attempts at the coconut shy, by ourselves and perhaps others; and/or we can attempt mentally to simulate the process of knocking down the coconut, perhaps using some kind of intuitive physical model . Any givThese two sources of data, memory, and simulation, generate a set of specific instances (whether observed or imagined); and among these instances, the cognitive system can compare the number of instances in which the event of interest occurs (a coconut is successfully knocked down) and the number of instances in which it does not (the coconuts remain in place). As long as these specific instances are generated according to the probability of the internal Bayesian model, then sampling provides an approximation to these often intractable calculations.k is higher than that a word has k as its third letter, because it is easier to retrieve words by their initial letter, rather than its third letter. This perspective translates naturally into a sampling framework: Any factors that impact our ability to draw mental samples will influence probability judgments.Before we develop a specific account in more detail, note that the sampling-based viewpoint gains credibility from links to existing theoretical accounts and empirical phenomena. For example, n _ or fit the pattern _ _ _ _ i n g. Participants both estimated the number of _ _ _ _ i n g words to be higher and found them easier to generate. That is, items which are more easily mentally sampled are rated as more probable; and the richer cue provides a better starting point for sampling. While arising naturally from a sampling viewpoint, these results are, of course, in contradiction to the laws of probability: all words that fit the _ _ _ _ i n g pattern also fit the _ _ _ _ _ n _ pattern, and hence cannot be more frequent or probable.Differences in the ease of sampling is also one source of conjunction fallacies (though we focus on another source below). being a tax, corporate, patent, or other type of lawyer as different from an equivalent, being a lawyer. The explicitly mentioned “unpacked” elements may provide a helpful cue to sampling and hence raising probability estimates. By contrast, if the unpacked elements are low frequency, then the sampling process may be biased toward searching for difficult-to-find items, thus lowering probability estimates. Thus, by biasing the starting point of the sampling process, probability judgments with unpacked description can be enhanced or reduced, by comparison with the normal descriptions , and identify these as the probabilities. Taken as a psychological proposal concerning how people form probability judgments, we call this the We first assume that if people are sampling, then they are  generating a new set of random examples each time they answer a question, which corresponds with the common observation that human behavior is stochastic, in psychology, economic, neuroscience, and other fields . Let’s tP^RF(hit)), a judgment of the conjunction of the coconut being hit and being knocked off ), and a judgment of the conjunction of the coconut being hit but not being knocked off ), Based on this sample, a person could make any of a variety of judgments using the relative frequencies. For example, they might judge the probability of the simple event of the coconut being hit =P^RF(hit∩knockedoff)+P^RF(hit∩¬knockedoff)as required by probability theory in One rationale for the relative frequency approach is that, assuming judgments are based on the same set of samples, relative frequencies produces coherent judgments  are different from those drawn to judge P^RF(hit∩¬knockedoff), then very often the sum of these judgments will not equal P^RF(hit)). While coherence is important for the normative underpinning of probability theory, it is less important for evaluating how a sampling agent converts samples into probability estimates, as coherence is not generally achievable for such an agent.However, for a sampling agent who draws a more realistic number of samples, these strengths of relative frequency disappear. First, because it is unrealistic to assume that people remember or simulate the same set of examples each time they make a judgment, judgments made via relative frequency will very likely be incoherent . According to the relative frequency approach, we judge this probability to be 1: that the coconut will always be hit and will always be knocked off of the stick. Additionally, according to this viewpoint, if we rely on our memories alone, it is difficult to avoid the prediction that anything that has never happened before will be judged to have a probability of zero. For example, if I play the lottery with the same number each week, it is overwhelmingly likely that I will encounter an unbroken succession of losses; but I do not conclude that therefore I cannot possibly win.Considering a more psychologically plausible number of samples may in fact lead to uncomfortably extreme judgments if relative frequency is used. Suppose, for example, we return to the estimate which is based only on one sample, From a Bayesian standpoint, which we develop below, what is missing in a relative frequency model is any way of integrating the observed frequencies with prior assumptions about the behavior of colliding objects or lotteries .How, then, might we develop a purely Bayesian approach to making estimates from samples? First, we suppose that people begin with a prior concerning the possible probabilities of knocking down coconuts, winning lotteries, or other real-world events. Following the standard Bayesian statistical practice, the natural prior distribution for this unknown probability is so-called conjugate prior of the probabilistic process of interest—here, for a pairwise judgment, this is the Beta distribution.p = p1 as more likely than the case p = p2 for all possible values of p ∈ . A uniform probability density function (PDF) is consistent with the no-preference principle on p. However, this no-preference principle does not generalize to natural monotonic transformations of p, and the desire for invariance to transformation led to the development of Jeffreys’ prior, which in this case is the Beta distribution. Finally, on the extreme end, Haldane’s prior, approaching Beta, represents the belief that it is equally likely that the underlying probability is zero or one, and that it is not in-between (What makes the most appropriate generic prior Beta distribution is a contentious topic. A common desideratum is that the prior reflect “ignorance” or “lack of information”. As shown in -between .http://www.natcorp.ox.ac.uk). These BNC frequencies were next adjusted so that they reflected the number of times each phrase was used to describe a probability. Finally, Though Bayes’, Jeffreys’, and Haldane’s prior each has their own theoretical justifications, we can also empirically explore what would be a good prior for probability estimates by looking at how often different probabilities occur in natural language. To do so, we used the data reported in For our analysis, we assume that, for simplicity, the prior is the symmetric Beta distribution, Beta. This distribution has a single free parameter, β, and assumes that there is no a priori reason to expect a bias toward one or the other outcome of a pairwise event. This prior is then continuously updated in the light of samples, whether retrieved from memory or generated by simulation. So, for example, as the number of missed throws at the coconut shy increases, the more we suspect that we have poor aim: the posterior probability distribution of hitting the coconut shifts in favor of lower probabilities of hitting the coconut. How do we then convert this posterior distribution over these pairs of events into a single judgment ? The natural approach is to take the expected value of this distribution: roughly, the average of all of the possible coconut-hitting accuracies, each weighted by its posterior probability.Nhit = Nhit and knocked off = Nthrown = 1 and Nhit and not knocked off = 0 ≠P^BS(hit∩knockedoff)+P^BS(hit∩¬knockedoff)), as it is for relative frequency. However, as discussed above coherence is inherently unlikely for a sampling agent: Different judgments will be made from different set of samples. For the Bayesian reasoner, this decrement in coherence leads to an improvement in a quantity we believe to be more important to a sampling agent: accuracy. Indeed, the Bayesian reasoner is defined in such a way that it will of course be more accurate if the assumed value of β is correct. And, intuitively, it seems useful to hedge estimates in just this way: having only seen one example of a coconut being hit, it is more reasonable to estimate that probability to be two thirds rather than one.This set of judgments from the Bayesian reasoner is not coherent . Relative frequency is in fact a special case of the Bayesian sampler, assuming Haldane’s prior . This means that relative frequency is in fact a rather extreme assumption about what the probabilities are: specifically the prior belief that the underlying probability is either one or zero. If the true state of the world is closer to the value of β assumed by the Bayesian sampler than to zero, the Bayesian sampler will produce more accurate estimates , is to 0, the more likely it is that the estimated probability, P^(A), is greater than P(A), whereas the closer P(A) is to 1, the more likely it is that P^(A) is less than P(A).Perhaps the most fundamental and important systematic bias in probability judgment, which has been observed repeatedly, is conservatism: People on average tend to avoid the extremes  in their probability estimates . Conservadhering to the laws of probability when using the same generic prior for each judgment. After all, if the underlying subjective probability to be estimated is zero, a rational updating model should overestimate this probability from any finite sample—a rational Bayesian model cannot rule out the possibility that the event has a positive possibility, but simply has yet to occur by chance. So, from the present Bayesian standpoint, some degree of conservatism is normatively required and hence is not necessarily properly labeled as a bias at all.Interesting, though, the systematic “bias” of conservatism follows directly from the Bayesian model we have outlined. As described above, the Beta distribution prior over probabilities will moderate extreme relative frequencies, for any prior with β > 0, as can be seen from How conservative should people be? In our generic Bayesian model, this depends on their prior distribution, characterized by the value of the β parameter in the symmetrical Beta distribution. Another potentially relevant factor, though, is the degree of correlation between samples. While identical independent draws are suggested by drawing from an urn with replacement, natural sources of data typically have interdependencies at many scales . And indTo sum up, instead of conservatism being the result of noise , we propose that it is a rational adjustment for small sample sizes. While we assume that the samples will generally reflect the underlying probabilities accurately, a second stage corrects for the intrinsic uncertainty in the probabilities as a result of having a limited number of samples. This correction produces a “biased” estimate that is, on average, more accurate than the uncorrected, unbiased estimate, but it produces judgments that are incoherent on average as a byproduct.Our approach falls into the class of rational process models, that explain biases as the result of the algorithm used to perform inference . RecentlA, and its complements not-A, would be assigned a probability that is pulled toward .5 (varying depending on the particular sample drawn). That is, a mix of veridical and noisy memories will “regress” observed relative frequencies toward .5, in proportion to the level of noise.There is, though, an alternative, and arguably simpler, model of the mapping from frequencies to probability judgments to consider—that probability regression does not arise from Bayesian calculations, but simply from noise in the process of storing and retrieving memories of past events. This “probability theory plus noise” (PT+N) approach has been pursued by Costello and Watts in an important recent series of papers . The PT+P^PT+N(A)+P^PT+N(¬A)=1 still applies on average in the PT+N model: If A is a low probability event, then there will be more switches from not-A to A than the reverse. But each event is, nonetheless, either A or not-A, so that the sum of the relative frequencies still equals 1, and indeed this generally holds in human data  mental sample, should therefore obey the laws of probability in some cases. Using this line of reasoning, man data . In addieriments .The PT+N model, at first glance, looks like a rival to a Bayesian sampling account because it departs from rationality in the light of putative mechanistic factors, concerning the noisiness of memory. As we shall see, though, it turns out that a natural Bayesian sampling model generates predictions for a wide range of judgments that are, in expectation, identical to those of the PT+N model. However, the two approaches diverge regarding conditional probability judgments, and as a result, for the probabilistic identities that involve conditional probability judgments. In the next section, we consider how the PT+N model and the Bayesian sampler capture key empirically observed probabilistic identities. We then test the contrasting predictions of the two models in two new experiments.A and B. Participants in these experiments could be asked about of either single events ), conjunctions of the events ), disjunctions of the events ), or one event conditioned on the other ). A key feature of these empirical identities is that, according to probability theory, they should all equal zero. This key feature holds for relative frequency judgments as well—even if people are drawing a new sample for each judgment and making their judgment according to relative frequency, on average, all of the identities should equal zero.Costello, Watts, and colleagues  developeIndeed, when measuring human probability judgments, some of the identities shown in  have beeZ^1 was found to deviate predictably from zero  drawing a set of samples from memory, (b) counting the number of As, and (c) dividing by the sample size. The critical mechanism proposed by the PT+N model is that recalling samples from memory is perturbed by random noise, so that each flag is misread with a probability of d (d that an event A will be incorrectly counted as event ¬A(or vice versa). Because the noise is applied to samples at random, the probability of reading out event A will be:A and not corrupted by the noise and (b) the probability of a sample originally marked as ¬A but corrupted by the noise. Average estimates will thus have mean value ofPT+N is able to capture all of these results, at least when they are addressed individually. As noted above, this model assumes that people estimate the probability of some event ity of d , 2016a. E[P^PT+N(A)] predicted by the PT+N model is a linear transformation of the underlying subjective probability P(A).As seen in A ∩ B) or disjunctive  events, can explain above-chance rates of conjunction fallacies. The rate of random error is enhanced from d (for single events) to d + Δd (for conjunctions and disjunctions). This assumption is justified on the basis that combined variables  will be noisier than individual variables  divide by the sample size . For conditional probabilities, both events A and B are independently subject to noise d  draw a set of samples from memory, (b) count the number of  noise d , so the Z^9, multiplying the two expectations E[P^PT+N(A|B)]E[P^PT+N(B)] cancels the denominator of the conditional probability, as does E[P^PT+N(B|A)]E[P^PT+N(A)]. Because the numerators of E[P^PT+N(A|B)] and E[P^PT+N(B|A)] are the same, PT+N thus predicts that Z^9, on average, will be always equal to 0, in line with probability theory. Similar reasoning means that PT+N predicts that identities from Z^10to Z^13will always agree with probability theory. However, other identities that involve conditional probabilities from Z^14to Z^18do not have this form so that, for these, PT+N can deviate from probability theory. A summary of where PT+N matches and deviates from probability theory is given in Despite the apparent complexity of As we noted above, while a pure relative frequency model will produce the correct probabilities from relative frequencies in the limit, it can produce extreme conclusions where the number of samples is small. Recall that drawing a single sample from the posterior of the event can only lead to relative frequencies of either zero or one. But, of course, it seems unreasonable to report that an event has a probability of zero or one based on a single sample. The Bayesian sampler moderates such extreme conclusions, leading to conservatism.For simplicity, and paralleling model predictions with PT+N, we use a symmetric Beta distribution, Beta, as the generic prior on all probability estimates. The Beta distribution is a conjugate prior probability distribution for the Bernoulli and binomial distributions. It is defined on the interval , which is, of course, also the interval for probability estimates. This prior reflects the degree of belief placed on every possible probability estimate, ranging from 0 to 1.P(A). Given N samples collected, the Beta prior distribution should be updated in light of these new samples according to Bayes’ rule. Formally, let S(A) denote the number of samples of event A and F(A) denote the number of samples not marked as event A. According to the Bayesian sampler account, people will have a posterior probability for probability estimates that is distributed according to Beta(β + S(A), β + F(A)). We assume that people then report the mean of their posterior distribution as their probability estimate. For any x ∼ Beta, we have the mean of x:E[x]=aa+b. Therefore, the probability estimate is a simple linear transformation of the number of success,We now consider how people would respond to the incoming samples from the underlying subjective probability Interestingly, comparing N are not individually identifiable from the mean estimates, the mean predictions of the Bayesian sampler can be rewritten in terms of d, and are identical to those of PT+N. This bridge condition generalizes the relationship between a Beta prior and d shown by N trade off to produce various values of d.In fact, because the two parameters β and N′ for conjunctions and disjunctions, where N′ < N,Likewise, for conjunctive and disjunctive estimates, the Bayesian sampler uses the same prior distribution. However, because people have to evaluate two statements from every sample to determine if a conjunction or disjunction is true, which seems computationally more demanding, we allow for the possibility that a fixed amount of sampling time results in fewer samples N′ < N also allows the Bayesian sampler to explain the empirical observation that estimates of conjunctions and disjunctions are more variable than estimates of simple probabilities , both the event B that is conditioned on and the event A under consideration are sampled, a noisy process is applied to reading both variables, then the ratio is taken of those read as both A and B over those read as B , which are identical. Also, if A and B are independent, then both PT+N and the Bayesian sampler also reduce to their average prediction for P(A), which are again identical . In particular, even if Δd > 0, the PT+N model predicts that the expected values of Z^9to Z^13should be strictly equal to 0 . In particular, if there is a strong positive correlation between A and B and both are low probability events, then Z^10 to Z^13should be positive. Conversely, if there is a strong positive correlation between A and B and both are high probability events, then Z^10 to Z^13 should be negative. These predictions naturally lead to an empirical test of whether PT+N or Bayesian sampler provides a better account of conditional probability judgments.As shown in Here we use a standard paradigm developed by Costello and Watts for eliciting probability judgments: estimating the chance of particular weather events on a random day. Past work in this paradigm has used a large number of pairs of weather events involving descriptors such as cloudy, icy, warm, and so forth. Instead of testing a wide range of pairs of events as in past work, here we focus on two pairs of events that satisfy our desiderata for testing the different accounts of conditional probability. For the pair of positively correlated low-probability events, we selected the weather descriptors “icy” and “frosty”. The pair of positively correlated high-probability events was more challenging to find, and we decided upon “normal” and “typical” as our weather descriptors.Fifty-nine participants  were recruited through Student Research Experience Subject Panel, University of Warwick, and completed the 30-min experiment in exchange for course credit.icy, frosty} and {normal, typical}. For each weather pair, we gave all of the 20 possible unique probability queries , the query was presented in the format of “If the weather in England is [B] on a random day, what is the probability that weather will also be [A] on that same day?”We adopted very similar questions to those from the experiments of 1 and 3A2 for all 20 unique queries involving {icy, frosty} and all 20 unique queries involving {normal, typical}, respectively.The mean probability estimates across blocks and participants are shown as bars in Figure 3AAll the combined probability identities should be zero if people’s probability judgments are fully coherent. Because, on average, judgments made of samples via relative frequency follow the laws of probability theory , relative frequency also predicts that expected values of all identities are equal to zero , and negative results when the described events are high probability .In agreement with previous work, not all of the identities were equal to zero; this indicates that people’s probability estimates are not coherent. Whether samples are corrupted by noise (as in the PT+N model) or tempered through Bayesian inference (as in the Bayesian sampler), the predicted mean values of an identity can differ from zero  = pi,f + pi,¬f and P(icy|frosty) = pi,f/. This leads to a total of six free parameters to describe the underlying subjective probability parameters of both {icy, frosty} and {normal, typical}.Because model predictions depend on the values of underlying subjective probabilities, which are unobservable, we allowed these probabilities to be free parameters for all models, using three free parameters for each pair of weather events. For example, for our task it is sufficient to know the subjective probabilities of icy and frosty, For the first type of quantitative comparison, we fit the five models  to the means of all probability queries at the individual level. We chose here to fit the models to mean judgments rather than to each raw judgments to avoid having to specify additional processes for each model, such as mechanism for how participants round their probability estimates, as empirically participants often  round their estimates to the nearest .05 or .10 .d . We also calculated the protected exceedance probability, a more sophisticated measure of whether a model is fitting a preponderance of participants, which takes into account the relative evidence for each model for each participant , the Bayesian sampler explains participants’ data better than PT+N, but the models perform very similarly when sample sizes are fairly unrestricted. Similarly, for the more restricted sample sizes, the Bayesian sampler better fit significantly more participants than the PT+N model , while the proportions of best-fitted participants for either model are nonsignificant from 50% for larger sample sizes . In There are advantages and disadvantages to fitting raw judgments in this way. Disadvantages include the inability to determine how much more likely one model is than another for an individual, that we do not have a method for correcting for differences in model complexity, and that this analysis is very computationally expensive, particularly when computing PT+N’s prediction distribution for conditional probabilities. Because of the lack of complexity penalty, we only compare the more complex Bayesian sampler and more complex PT+N models as the simpler versions will always perform less well. The advantages are, however, that we can compare the predicted distributions of the model to the data, and that the β, This method provides a complementary view of the data to the probabilistic identities and fits to the mean estimates for each individual. Both of the other methods suggest that the Bayesian sampler’s formulation of conditional probabilities is a better model of the data. The fits to the raw estimates show the Bayesian sampler performing better when sample sizes are restricted to be small, but having performance indistinguishable to that of PT+N when sample sizes were less restricted. As the fits to the raw estimates take into account the predicted response distribution in addition to the predicted mean responses, this could reflect a real advantage for the raw response distributions predicted by PT+N which compensates for the worse fit to the means. Alternatively, because a large number of samples needed to be allowed to equate the two models’ performance, PT+N’s equally good performance could also be an artifact of fitting the models to responses that were rounded by the participants. Rounding can both reduce the variability of responses and bias the means , and the two models may well differ in their ability to cope with rounded data. A large number of samples allows the Bayesian sampler to produce a consistent response, but causes its mean predictions to converge with probability theory. PT+N, however, can produce consistent responses that deviate from probability theory, and so could potentially better match the results of rounded responses.or operation could be seen as providing alternative labels of a single event in cases of synonymous labels. For example, when people state that this curve is Gaussian or bell-shaped, the bell-shaped description is actually intended to provide a further explanation of the Gaussian, rather than being the second argument to a disjunction. This kind of pragmatic inference could potentially explain the mismatch of all of the models to the disjunctions involving one negation, as shown in p = .033, and protected exceedance probability of the Bayesian sampler was .9595). Regarding the qualitative model comparisons on the key probabilistic identities, Z^10to Z^13, these do not involve any disjunction judgments  were recruited through Student Research Experience Subject Panel, University of Warwick, and completed the 30-min experiment in exchange for course credit.cold, rainy}, {windy, cloudy}, and {warm, snowy}. All of the 20 possible unique probability queries was asked . The protected exceedance probability (where closer to 1 is better) was .9911 for the Bayesian sampler. This result suggests that the event pairs {cold, rainy} and {windy, cloudy} were in fact not treated as independent by participants, as this fit measure distinguishes between the Bayesian sampler and PT+N, unlike the results for the key probabilistic identities. The mean predictions based on best-fitted models are shown in Based on the MSE fits to the mean responses of each individual, the Bayesian sampler (combined over the two variants) best explained 61.90% (52 of 84) of participants, whereas the PT+N model (combined over the two variants) best explained the remaining participants see . The prop < .001). However, the individual level result is reversed when more samples are allowed, the proportions of participants best-fitted by the PT+N model is significantly greater than 50% when N ≥ 24 . In We also evaluated model performances based on how accurately their predicted distributions of probability estimates describe distributions of raw judgments for each individual. The general relationship between the minimized Wasserstein distance and the maximum sample size allowed for the models is similar to the one in Experiment 1: The Bayesian sampler has a better fit when samples are relatively few, while this advantage diminishes with more samples allowed .We have argued that sampling can play a crucial role in forming probability judgments, and indeed is key to explaining aspects of well-known biases including some versions of the conjunction fallacy and the unpacking effect, as well as probability matching . But, asHere we provided a generic Bayesian account of how this problem can be addressed. It turns out, unexpectedly, that the approach perfectly mimics the predictions, in expectation, for many judgments from a major recent theoretical account with strong empirical corroboration: the probability theory plus noise (PT+N) model . The genThe unbiased estimates of probabilities produced by the relative frequency approach are only reasonable, from a Bayesian perspective, in the limit of large samples. But unbiased estimates are unappealing for small samples, for which they lead to unreasonably extreme estimates. More generally, minimizing bias  will often lead to a dramatic increases in variance, and thereby a poor correspondence with the underlying subjective probability parameters see . From a on average and less vulnerable to exploitation. The Bayesian sampler trades coherence for increased accuracy, and for a sampling agent small deviations from coherence may have minimal cost. The reason is that even for a reasoner making unbiased estimates via relative frequency, it is extremely unlikely that the same set of samples would come to mind every time, so that even an individual set of judgments made via relative frequencies is unlikely to be coherent. If sampling underlies judgment, this makes coherence unachievable, and perhaps helps explain why the brain sacrifices coherence on average for improved accuracy  and P(A ∩ ¬B), then they cannot consistently also have a uniform prior on the simple event P(A), as the Bayesian sampler would assume.It is tempting to take the success of the Bayesian sampler in explaining people’s probability judgments as a sign that probability judgments are indeed as rational as possible, assuming that people are basing their estimates on samples. However, we must inject a note of caution, as while we have shown that using a single generic prior to smooth the generated samples when making a probability estimate will improve that estimate overall, it is not actually the best possible prior that can be used when it is clear what is being judged. Indeed, as is critical to fit the empirical data, this generic prior produces judgments that are on average incoherent. More fundamentally, using the same Beta prior for judgments of simple events, conjunctions, disjunctions, and conditional events actually implies that across judgments people have inconsistent prior beliefs about the probabilities of events. For example, if people have uniform priors ) on the conjunctions A prior distribution that is similar to our Beta prior but results from consistent beliefs about the probabilities of simple events, conjunctions, disjunctions, and conditional events is the Dirichlet prior, a generalization of the Beta prior. We give details of this prior in the The Dirichlet prior that leads to coherent probabilistic judgments on average also does not require complex calculations to employ , but that there will still be a number of extreme estimates. The Bayesian sampler, by contrast, predicts very few extreme judgments because both the mean and individual judgments will be pushed away from the boundaries. One suggestive observation is that people tend to avoid boundaries when using Likert scales, a phenomenon that has been argued to arise because people make estimates using the mean of posterior distribution . This isThe biases observed in probability estimates are biases of self-consistency: If participants were able to make coherent estimates, even if their estimates show no correspondence to real-life probabilities, then the probabilistic identities in P(X|A ∩ B) versus P(X|A), rather than P(A ∩ B|X) versus P(A|X)  . Howevers P(A|X) . Along ss P(A|X) .configural weighted averaging, assumes that a person’s estimate of a conjunction is the weighted sum of its constituents  and demonstrated that PT+N better matched the data than the quantum probability model. Because the Bayesian sampler and PT+N models make identical predictions regarding the mean values of some of these identities , the Bayesian sampler also shares some of these empirical advantages over quantum probability. However, the Bayesian sampler as defined above does not produce order effects, which are a key focus of the quantum probability model  < P(C|e ∩ A) and P(A ∩ C|e) < P(A ∩ B|e) in accordance with confirmation, an ordering reversal which is not possible to produce using a model that simply regresses both types of judgments toward 0.5  participants almost always produced the extreme conditional probability estimates  = 1);  = 1); , and botO) = 1); . NonetheQualitative reasoning may be a time and effort-saving process, but even solely using a sampling process, there are ways to reduce the amount of sampling required. Most saliently, amortization, the process of reusing samples between similar queries in order to avoid drawing a new set of samples, can be used to reduce effort . AmortizAnother potential development of the Bayesian sampler would be to have an account of sample sizes, and in particular, how sample sizes might differ depending on question complexity, rather than merely having separate free parameters for samples for different types of questions . A direction for future work is then to specify a relationship between query complexity and sample size, and an interesting way in which to do so would be to characterize the “cost” of various cognitive operations such as generating a sample and evaluating a property of a sample. These costs could reflect the computational costs of sampling as well as the opportunity of cost of continuing to sample instead of moving on to the next task. Finally, in the Bayesian sampler and the extensions discuss above, we have made the simplifying assumption that people draw independent and identically distributed (i.i.d) samples from their posterior distribution. But, as we touched on in the introduction, this does not match the empirical data on how people generate hypotheses. Instead, people generate correlated samples in which the identity of the next sample depends on what was produced earlier. For example, in animal naming tasks, participants who were asked to freely recall animal names as they come to mind produced sequential recollections in which neighboring items tended to be semantically related . SimilarN items can only yield N + 1 outcomes). Two factors make this unlikely to be observed experimentally. First, inevitably there will be noise in the process of translating the results of sampling into  responses . Second, estimating, and taking account of, sample autocorrelation would lead participants to reweight samples appropriately,These results imply that people are instead using an algorithm that generates autocorrelated samples such as Markov Chain Monte Carlo MCMC;  or more death from natural causes, participants in the explicit unpacking task are asked to report multiple probability judgments for unpacked descriptors such as (a) death from heart attack, (b) death from cancer, and (c) death from other natural causes (e.g., death from heart attack, cancer, and other natural causes (The explanatory power of a more realistic Bayesian sampler can be best illustrated through the “unpacking” effect. There are, arguably, two types of unpacking effects: explicit and implicit. In the explicit unpacking effect, participants are asked to judge each unpacked descriptor separately, but in the implicit effect they make a single judgment about the unpacked disjunction. For a descriptor such as es e.g., . By contl causes . The expl causes , whereasl causes . These tl causes . In contl causes . AdaptinWe introduced the Bayesian sampler, which assumes probabilistic judgments are made by first generating samples from either memory or an internal probabilistic model. However, instead of naïvely estimating probabilities using the relative frequency of samples, the Bayesian sampler uses a generic prior over probabilities to improve the accuracy of these estimates. The Bayesian sampler is a departure from exact Bayesian models, because it assumes subjective probabilities are only accessible through samples, and cannot directly be introspected. Our approach thus is a better match to the phenomenology of making probability estimates, where it often feels that we can easily retrieve examples, but are uncertain about our probabilistic estimates. By assuming that people adjust for their degree of uncertainty correctly in the light of a limited sample, we explain a variety of classic empirical biases in probabilistic judgment.


Low-income urban communities, and the individuals that live within them, continue to face disproportionate interconnected social, economic, and environmental challenges related to their built, natural, and social environments. The aim of our phenomenological research study was to elevate the experiences of residents living in low-income urban neighborhoods in terms of their communities’ environmental challenges. Our objectives were to (1) identify challenges across neighborhoods, (2) identify ways individuals and communities are addressing those challenges, and (3) assess the individual and collective efficacy and engagement of communities to lead environmental improvements in neighborhoods. This study brings forward the voices that are often ignored or misunderstood in these communities and uses an ecological-social perspective. We conducted focus groups (N = 68) in four low-income urban neighborhoods across two Ohio cities in the United States. Participants described five key challenges in their communities: Pollution, abandoned buildings with associated crime, low food access and health concerns, trash and illegal dumping, and lack of trees. We assessed engagement and efficacy using two frameworks focused on individual and community readiness to engage in and lead community change. Policymakers should acknowledge the valuable contributions and leadership capacity of residents in low-income communities to implement environmental initiatives. Low-income urban communities, and the individuals that live within them, continue to face disproportionate interconnected social, economic, and environmental challenges related to their built, natural, and social environments ,2,3,4,5.The aim of our phenomenological research study was to elevate the experiences of residents living in low-income urban neighborhoods in terms of the environmental challenges their communities were facing. Our objectives were to (1) identify challenges across neighborhoods, (2) identify ways individuals and communities are addressing those challenges, and (3) assess the individual and collective efficacy and engagement of communities to lead environmental improvements in neighborhoods. Our research moves beyond previous research focused more on residents’ descriptions of their environment. This research also provides an analysis of motivations, perceptions, and characteristics of individuals and communities who have been inspired to act or have the capacity to take action.This study was conducted in four low-income neighborhoods across two cities in a Midwest state. Each neighborhood has its own unique history, with the land, the economy, and the people shifting and adapting to periods of rapid urbanization, economic recessions, downsized manufacturing industries, white flight, drug crises, red lining, flooding, disinvestment, revitalization, gentrification, and overall abandonment. We hosted four focus groups with individuals living in these spaces, as they reflected on their built, natural, and social environment. Our study brings forward the voices that are often ignored or misunderstood in these communities. We highlight the residents’ ideas and solutions for improving their neighborhoods. Policymakers should acknowledge these valuable contributions, ideas and leadership capacity of residents in low-income communities to implement environmental initiatives.The social and physical environment has been shown to be as important of a cause of mortality as human behaviors and underlying biological mechanisms of disease . Public Research related to the interactions between humans and their social, natural, and built environments exists in a diverse range of academic and practice-oriented disciplines . The complex nature of this work is best served through interdisciplinary perspectives, especially in light of increasing concerns related to natural processes impacted by human made activities ,27. The We position our research within two frameworks. First, we draw upon an ecological-social  perspective that focuses on the multidimensionality of systems that interact with one another ,31. Our The current research was part of a project focused on perceived risks and actual food safety concerns in four neighborhoods across two large urban cities in a Midwestern state with vacant lots potentially available for urban agriculture. The original research study with detailed sampling and coding methods has previously been published . Data waThese focus groups were audio recorded, transcribed and reviewed, during which open coding was used to establish emergent themes in the data, as outlined by  in her rThe first and second authors determined the questions that had not been analyzed in the previous publication and that would likely yield responses regarding the neighborhood environment. We first focused on the contextual and introductory question: “How would you describe your neighborhood to someone who does not live here?” To ensure re-immersion in the data, the first author re-read each of the transcripts, noting any responses that related to this research question as part of a theory-informed, or interpretive coding process ,58. WhilAfter re-reading the transcripts, it was apparent to the researchers that participants were expressing more about actions they were or were not taking, neighborhood processes, and sense of community. These themes were determined from the direct words of participants during each of the four conversations, reflecting a deeper conceptual interpretation about residents’ views and interactions with their natural, built, and social environments, within the context of the integrative ecological-social and environmental justice framework. The first author shared these themes with the co-authors, re-positioning the research questions to include individual and community efficacy and engagement. This interpretive approach allowed for further exploration of unique assumptions, ideologies and concepts that may help to shed light on and address distinct ecological and justice-oriented challenges participants were experiencing or witnessing  ConsensuOur sample (n = 68) came from Community 1 (C1) (n = 27), Community 2 (C2) (n = 28), Community 3 (C3) (n = 8), and Community 4 (C4) (n = 5), with 66 participants completing a demographic survey. C1 and C2 are nested in the same city, and C3 and C4 are nested in another city. Detailed descriptive results have been previously published ; Table 1The average housing vacancy rate across C1 and C2 is 16.67%, compared to 22.1% for C3 and C4. Compared to the median household income of $50,700 in Franklin County  where C1The C1 sample (n = 27) had a greater percentage of Black residents than the Census data for the ZC where the neighborhood is located (33.3% compared to 19%). Of those who reported monthly income (17/27), all reported incomes lower than the neighborhood median household income. The sample has a high school or equivalent degree rate that is almost twice that of the neighborhood (51.9% compared to 28.5%), but much less than the neighborhood rate for undergraduate degrees (7.4% compared to 19.4%). Over 32% of participants from C2 (n = 28) identified as white compared to the neighborhood (58.8%), while 57.1% of the sample identified as Black, compared to 35.1%. The sample had a greater rate of individuals with a graduate degree (21.4%) compared to the neighborhood (8.3%). Of the 18 participants who reported monthly income, all reported less than the neighborhood median household income . In C3, 87.5% of participants (n = 7) identified as Black, which is greater than the general neighborhood rate (71.1%). Twenty-five percent of the sample obtained a high school degree or equivalent, which is comparable to the neighborhood rate of 28.7%. Of those who reported household income (n = 5), all reported income less than the median household income. The racial makeup and education of the sample from C4 varies greatly from the general neighborhood, and this is due to a very small sample size (n = 4). All participants identified as Black, no one earned greater than an associate’s degree, and all who reported income (2/4) reported income less than the neighborhood median household income. When asked to describe their communities, participants from each of the four neighborhoods discussed a range of observations they had of the built and natural environment, along with associated aspects of the social environment see . From thParticipants also described diversity within neighborhoods and different experiences depending on the block or street in that neighborhood. In addition, participants often stated their concern and then followed up with a litany of perceived causes or contributing factors to these issues, reflecting participants’ worldviews, experiences, and assumptions. Some provided reasons as to how these concerns impacted individual and community well-being.You just got tired of it. You trying to relax, all you hear is gunshots, or somebody arguing, somebody out there fighting […] I be like, don’t you get tired of that?One common theme across all groups was noise and air pollution. Participants described noise pollution related to traffic, loud music, and violence. The concern about the noise, especially coming from violent situations and disrespectful people is best reflected by Arielle, a resident in C4:The carbon emissions are getting so bad that I’m cleaning off my walls constantly living right on a main street […] in front of a bus stop […] my air ducts stay dirty constantly. We’re changing the filters in my furnace constantly.Participants in C1 and C2 described sewer smells and were concerned about nearby water treatment facilities. Car traffic and associated carbon emissions and exhaust from cars and city buses were often described as a cause of air pollution. Betty (C1) shared:[This neighborhood] has historically been one of the most industrial parts of town […] and there have been issues with the EPA with them [a local steel company] and with others, so it makes you nervous […] People worry about—different times when some of these stories are in the paper and people talk about the cancer rates being high, all these things, it’s hard to tell what’s real and what isn’t, you know, but there’s some concerns there.A participant from C2 specifically stated that acid rain was an issue due to the emissions from a major utility company serving the area. Someone from C3 expressed concerns about brownfield sites that exist in their Rust Belt community, and Leon (C2) similarly shared concerns and uncertainty about high rates of asthma and cancer risks:In C2, residents also discussed the concern about the lakes and rivers where many people regularly went fishing for their food, citing concerns about contamination and safety. People outside my neighborhood are coming in these houses sleeping. The slumlords don’t care. The houses get empty. You call them squatters […] There’s three guys in the house two doors from me that comes in there and sleeps nightly.Participants in three of the groups  described the social and environmental ills associated with abandoned buildings, empty lots, abandoned housing, and rundown housing. Many residents were concerned about “squatters”, “the homeless”, and people using drugs who they observed residing in those spaces. Francesca (C2) shared:We have one property owner who will rent to anybody for cash, and we know it’s a way of him laundering his drug money, and we have problems with people living in a garage or living in a shed, and their drug paraphernalia is out in the alley where kids are cutting across to go to school or out on the street where people are walking. That’s an issue.Juliet (C2) described a situation in which she thought the property owner was using the space for money laundering, which impacted people in the community because it increased the drug problems in the area. She stated:I think the decline probably began when I was very young, but you can see that after in the past 20 years, and the past 10 years and the past five years, there’s been more buildings boarded up. Business is leaving the area and things of that nature. So, [now] […] there’s not a lot of options in terms of where you can get food from.Hudson (C3), who moved back into the community, focused on when this urban decay became apparent in the Rust Belt city, describing an additional outcome when food stores closed:Concern for children was voiced during conversations in C3 and C4. Participants described the need for more youth activities, sharing that several recreation centers had closed or reduced their hours, which is likely related to the economic and population decline of the area. Every neighborhood shared their concerns about crime, which included explicit details of robbery attempts and lengthy discussions about drug use, shootings, and overall violence.It’s just that in every poor neighborhood, you have a liquor store or you have [store owners] that’s always selling liquor. It’s kind of like the government wants to keep the poor, poor. Which don’t make sense, but it seems like they killing us off by liquor. If you go to any poor neighborhood […] you can get liquor before you get food. That is ridiculous and that’s what most people choose […] You got all these hot spots.Access to food proved challenging, with participants discussing high food prices and high cost of prescriptions that sometimes translated into decisions about whether to eat or take medication, higher rates of diabetes, and concerns about cancers. Participants in C3 were frustrated by the lack of full-service grocery stores, and the need to take public transportation to access affordable food. Many communities mentioned fast food restaurants and liquor stores. Demetrius (C3) shared his observations of liquor stores, and as a result, his distrust of the government, and what he perceived to be a form of social control and oppression:There are a lot of places you can get food, and that brings in a problem though too because the homeless will come down here and then they beg so it’s good and bad.Residents from C1 shared that, while they were pleased with the number of places where free food was provided , they simultaneously voiced a potential unintended consequence. Dan (C1) shared:This statement reflected overall sentiments towards persons experiencing homelessness, despite the fact that several focus group participants disclosed their current or past status as being homeless.[I am] scared to eat anything, because every time you look up the news, they’re saying it’s going to kill you. There’s something wrong with this, something wrong with that. Well, we’re all going to die because we won’t be able to eat nothing […]. Bread going to kill you, something’s wrong with the bread. Vegetables, the pesticides. Can you tell you tell me what I’m supposed to eat because […] I’m only eating popcorn right now. That seems to be pretty safe so far.C3 expressed fear and concern about food which they had learned from television, such as use of hormones and steroids and the impact on children’s health. Several participants stated they wish they could afford organic food because of health concerns. These messages made it harder to shop for food, especially on a limited income with few options. Adele (C3) said:Accessing food appeared to be a stressful endeavor for residents. Affordability and health concerns were made even more complex for some residents. C3 participants shared concerns about hospitals shutting down in the area, coping strategies using alcohol, and concerns about untreated mental illnesses.I get these plastic bags up on my patio […] it’s like Kroger and Aldi’s, all the little bags. I don’t know how they end up in the yard.Trash and illegal dumping were also identified as an environmental problem in each of the four communities. Residents discussed the nature of common trash and litter, which included cigarette butts, candy wrappers, food wrappers, rocks, glass, beer cans, food, and fast food waste. Participants shared how people from both within and outside the neighborhood threw garbage out of car windows. Others blamed the stores that used plastic bags. Evelyn (C1) said:There’s always trash. It’s not often that the city actually coming down the street and actually sweeping the street, or whomever does picking up trash or things like that, outside of your regular garbage day.Emilia (C4) wondered why the city was not taking care of their neighborhood:You see a lot of needles laying everywhere […] You might step on one. You can get just about anything from being stuck by a dirty needle, and people just throw them around like they’re nothing. It’s kind of crazy.Others were concerned about specific types of trash, like needles from people using drugs. Lucian (C1) explained what he saw and why it is a concern:Empty vials or things like that. That’s an issue. Because little kids around, they going to get and play with it and who knows who’s HIV positive.Gabriel (C4) shared a similar concern:Participants were also concerned about people abusing drugs and their behaviors impacting their communities . Focus group conversations included discussions about dead animals in the street, in empty lots, and in dumpsters, generally reporting who they felt were responsible. Isobel (C1) lives in a public housing complex and shared that residents whose culture includes “slaughtering animals in the house” often threw “the parts they don’t want in the trash. We find a lot of dead animals in our dumpster, goats, chickens, animal parts.” We’re intruding on their [deer] territory. All this was theirs before we came.Residents were surprised to see ground hogs, skunks, and deer, though one participant said:We’ve got a lot of rodents, raccoons, opossums, you name it. Beavers. I’ve been chased by all of them, yeah.Betty (C1) exclaimed:They come from another neighborhood and driving [sic] their truck and throw trash on our property.Many residents were especially angered by illegal dumping done by people outside of the community. One resident (C3) expressed he felt people used his neighborhood as a “dumping ground.” Sean (C2) stated:Another participant described looking out the window of public transportation while crossing major roads and seeing everything from tires to animals over the embankments, which he described as “weird dumping.”Just trash laying by the dumpster and food with maggots and bugs crawling all over it, and rats and everything.Residents expressed potential environmental health hazards related to the trash. Nancy (C1) shared her concern:I’m looking at bugs. I’m looking at gook and smell—they [people] even defecate over there. They even defecated on my stoop.Betty (C1) added:They might, by seeing the garbage, feel more depressed just by seeing it, it makes you feel depressed. So, I can only imagine just like seeing garbage all over. That would make me depressed, just seeing it.She was also concerned about how “overflowing dumpsters” might impact the soil. Bevaun (C2) shared a concern related to how trash impacts mental health:When I was a young girl, there were fruit trees everywhere, and right now I’d say you’d be lucky if you found one mulberry bush now […] We had cherry trees, apple trees, pears, grapevines, and they’re pretty much extinct now.In every focus group, trees were discussed. Many residents surmised that the lack of trees in their neighborhood was due to removal by their respective cities, though the reasoning for the removal was not discussed. Several residents connected their observations of trees to childhood memories. Rosemarie (C2) shared:I’d like to see the days when the cherry trees was out, the grape vines that everybody had growing in their yard. When you was little, you’d go back in the yard and try to get off the little cherries off their trees and they’d run you out of the garden and everything […] You don’t see no cherry trees around here no more. You don’t see any of that stuff.In C3, Gabriel shared similar sentiments:Beyond providing pollination, food, and a source of enjoyment for kids, people shared that trees were needed to improve the air quality in their communities and reduce noise from traffic.Although much of the conversation in the focus groups focused on the challenges that residents were facing in their neighborhoods, many residents identified neighborhood assets that existed in the community . These iUrban environmental concerns are multifaceted and involve numerous private and public actors, individual, and systemic contexts . The theWe considered what residents said about their role in community processes to improve the quality of life, what actions they were engaging in as actors in their communities, and ways in which leadership emerged from some of the communities. Here, we elaborate on the meanings and implications of these roles, in the context of research literature. Residents who are aware of the problems in their neighborhood, believe that the neighborhood is capable of dealing with these problems, have social ties to the neighborhood, and feel there is the capacity for strong leadership are more likely to be involved in neighborhood change efforts . PsycholThough civic engagement is linked with increased empowerment , more reYou afford what you can afford. I mean, for now you got to deal with what you can deal with. I mean, that’s the way of life. If we can afford to be anywhere else, I’m quite sure we would move. But if we can’t, we got to deal with what we can deal with.In our analysis, people who spoke during the focus groups were aware of, and often focused on, problems their communities were facing. Environmental justice frameworks acknowledge that environmental issues happen over time . Though Anything can happen. Even needles. I don’t pick up needles up on the street.Several residents expressed their own lack of actions out of fear, apathy, or exhaustion . Frederick said:They hit ’em, they leave ’em laying in the street. Don’t nobody pick ’em up, so you smell that for like two or three days before somebody decides they want to pick it up. Me personally, I don’t mess with dead animals. I’ll tell you in a minute, I’m not picking it up.In the lengthy discussion about dead animals in C2, Arielle expressed the concern and why she did not get involved:I understand you talking about people tearing down [abandoned buildings] and grow [a garden], and that’s cool […] But […] people going to do things out of spite, know what I’m saying, because I’m not saying everybody’s like that, but some people just because. That’s just like in life. If I see you doing something that I might like, and I’m like, wow, he’s doing this, and I might just hate on you. People do that. It’s the way of the world.Some participants did not seem to believe their community could change, which is similar to a study showing that individuals expressing “learned helplessness and fatalism” were less likely to feel that change could occur . DemetriI’m just saying, say you got a garden now, and maybe two or three families like, why they build that, we didn’t want no garden. They might like, okay, when everybody leaves, we gonna go over there and tear their tree down or dig it up or whatever they’re going to do to it, and then you come in you be like, ‘We just had a tree yesterday, where did it go?’Arielle (C2) shared similar ideas to Demetrius (C4). She added:If everyone just picked up pieces of trash that they saw, I don’t see it [trash in neighborhood] really being a problem.Others recognized their ability to control major community issues . Emilia I mean, I’m willing to put in the work, and I don’t like too much hard work.· I’m more intellectual than I am hands on, but I’m willing to put in the work, be it on the phone, going to the meetings, whatever, to get it done.· I just don’t know who to go to get this done, because there’s so much worried about—our city recently has been more worried about bringing the $34 million in for that stadium, and the casino, than they are about the people that live around the area that have to survive whether we’re working there or not.During the discussion about trees removal, Betty (C1) enthusiastically shared that despite the trees being gone “the soil was still there”. She further expressed a willingness to address problems, sharing her strengths, uncertainty about how to address the problem, and rallying people around issues related to income inequality and failed promises of economic development opportunities in their community. Her motivation and sense that something could be done reflect her care and sense of ownership for the neighborhood ,43, placI don’t know, it’s just real hard when you’re one of those people who gives to the whole community, and you see that stuff coming at you every day. […] It’s too stressful […] how long do you live in a place where you’re continually stressed out by the fact that you see little kids across the street that aren’t fed right so that their hands are shaking, or they’re in dumpsters at midnight when you know after school time they’re not properly fed […] there’s too many things that no matter what I and others do, it continues.One resident exemplified evidence of the impact toxic stress had on her willingness to address community issues, expressing the desire to leave the community because it was too challenging and was impacting her well-being . NarissaIt’s a lot of people out there needing help, and I know God brought me out of that situation, and I did thank God for what we did for me. And if he can do it for me, I know he can do it for other people, so that’s all I want to say.In C2, an underlying focus on faith impacted the way that people felt situations could improve, which was unique to that focus group. For example, Harrison shared:I don’t get any help.Many focus group participants identified ways they were already engaging in activities to address the identified environmental issues. Umbrosia (C2) encouraged people to buy locally, to “put the money back into the community” as a way to address economic issues in the neighborhood. Betty’s (C1) preferred method of action was calling people in positions of perceived power. She called the health department and Community Crime Patrol but didn’t “get much of a response”. Frustrated by the lack of support from her apartment manager regarding the overflowing trash at the nearby bus stop, she contacted the transit authority and attended meetings, but said:convince new residents in our building that this is part of the issue that they need to help me address, because we all live there. It’s up to us to do it.Her most recent action was to:You call them and they don’t come out ‘til they feel like it. I get real tired of that.Frederick (C3) expressed discontent with calling authorities about trash:You see the needles there. We do the neighborhood watch and then we sweep it up, but other than that —That happens quite often, like two or three times a week […] but sometimes we just be like tired and don’t bother cleaning it up.Residents often worked with neighborhood block watch groups to address many of the problems associated with drugs in their communities. This method of surveillance could prove successful, as research has shown that having networks of neighbors policing the area can prevent some crime because potential offenders have concerns about being seen committing the crime . DemetriShoot up and do stuff all night long […] trying to sell it [drugs] out on the side.Narissa (C2) described efforts that she and other neighbors on their block watch have taken, which included documenting license plate numbers and documenting where individuals would go to:You need to move before we have to come get you in a body bag, because this is crazy, and it’s just that bad.She also described harassment she endured by a neighbor and “crack dealer” in which she says a police officer that cruises the area regularly showed concern by saying:Though she continues to try and improve her neighborhood and “help them,” she said that it often results in retaliation.I boarded the houses a thousand times and these young guys go in there […] People come and throw garbage and stuff out on the street. Every morning I might pick up garbage and different bags and stuff. It’s how you going to keep it clean and keep it maintained.Frederick (C1) shared how he was trying to help out by boarding up abandoned houses, picking up people’s trash, and helping his sister mow her lawn. Despite his frustrations, he continued his efforts to try to keep his area clean:I’ll tell them, hey, you want this, you want that, here, I need my trash taken out. In the winter I need my sidewalk cleaned, my stairs cleaned off […] I’ll send them to where I know there’s resources.Betty (C1) who shared she had been homeless, recognizes that some of the people who need money or who are homeless can help her with tasks outside of her apartment and she can help them identify community resources:She also shows a willingness to take action if she has any problems with people, sharing that she calls the community police if the homeless “are becoming a problem.”While community relationships are very important, successful collective efficacy requires equitable agency when establishing formal state and community leaders while addressing economic and racial inequality . During I’ve been trying to talk some of my neighbors into, let’s see if we can get city hall to help us plant more trees.Betty (C1) energetically shared how she tried to engage neighbors to take their fight for trees as a proposed solution to carbon emissions to city leaders:I guess my opinion is, is that I’ve lived here for 12 years, and when you start to care, it’s like the neighborhood will test you, you know. I got my house cleaned up, and I had neighbors say, “Don’t fix up your house, you’re just drawing attention to yourself”. Well, I care. I live here and this is how I want to live, and, you know […] people will take from you if they think that they can. […] Until we say this is not acceptable that I live next door to this, or that you’re here and acting this way and we don’t say anything because we’re afraid—if you stand up for yourself, you are probably going to get targeted, but until we stand up for ourselves, nothing is going to change. So we have to start doing that.Oliver (C2) acknowledged that it would be easier to be apathetic and not care about the neighborhood, but he chooses to lead by example, despite concerns about unintended consequences of leadership :Just got to keep doing it [gardening]. Just because they do something to it, doesn’t mean you should stop. If you keep doing it, they’re just going to get tired. So sooner or later, they’re going to—they destroy your garden, plant it back. They’ll get discouraged when you just keep coming back. Keep coming back.Bevaun (C2) had similar beliefs, and was of the opinion that working hard will eventually wear down those who are trying to destroy that work:Though many participants mentioned their current efforts to improve their community and willingness to take action, residents also acknowledged that they needed broader support from existing systems in which decisions were being made on behalf of their neighborhoods. A community’s capacity for change is reflected in residents’ sense of community and collective efficacy, or the idea that neighbors have shared expectations, trust, and take action together ,43,76. PBetty (C1) identified city council leaders as an important group to engage for several issues that could impact relevant neighborhood issues, but also identified a longer term opportunity to influence the structure of council  so that it would be more representative of unique voices from different neighborhoods across the city.Then she [property owner with tenants abusing drugs] came begging to the neighborhood group, help [her] get rid of them.Juliet (C2) was frustrated about “slumlords”:We have awesome police down here, community crime patrol, and other folks who would spend months writing down license plates and doing all this other stuff to give that to the police so we could get rid of them.Juliet then shared how they helped the property owner:Now I’m not scared to take my dog in the backyard at midnight to do her business, so that’s good.Juliet chose to engage an individual (the “slumlord”) with whom she was angry and frustrated, accessed the existing trained officials who uphold their duty to protect people, their network of concerned and engaged neighbors, and a non-profit crime prevention group. Juliet’s efforts were successful:So even though many “don’t all live down here […] they care about the community […] If they see one of the ladies being harassed, maybe a homeless person asking for change, they’ll step out from their businesses and stop it.Betty (C1) also mentioned the importance of the Community Crime Patrol and police. She identified that business owners were interested in having residents and customers feel safe:Her sense of community reflects research that is safe and has an appropriate level of resources and services .I think the trash or whoever, [the city] supposed to— they should come by and clean that up. At least once or twice. I don’t see them never do it, which we don’t never have that come by.C4 participants expressed dissatisfaction and uncertainty about the willingness or capacity of city services to support environmental efforts with them. Demetrius explained:I called the police about abandoned houses, but they go turn the knob on the door—I watched them—turn the knob on the door and walk away, get in the car. I called them back, I say, you didn’t even go in the house […] What good is calling the police? They don’t do nothing […] They give you a reference number, it don’t mean nothing. They get to it maybe a month later when there are rats or something. It’s just pathetic.Frederick (C3) did not trust that contacting the police made a difference in his community when his observations were that the police did not take appropriate actions:I give a helping hand so you can get a leg up and get on down the roadParticipants from C1 disclosed their concerns about crime, but for the most part, felt connected to their neighbors. Betty said:We do take care of our own people.Dan (C1) said:There have been a couple incidents that they tried to harm us, you know, but we stick together.Ann (C1) said that as a senior, she feels protected:I grew up in the projects […] And what’s different as growing up—well, as a child we didn’t know about prejudice, but black people stayed by theirself [sic], and the white people stayed to theirself [sic]. And for this neighborhood, for me coming to it as an adult, even as growing up as different neighbors, I’ve learned from this neighborhood, very loving, is the diversity that we have […] No matter who you are, what you have done, we’re all people together […] if you need help, if I need help, we have each other.C2 residents similarly shared that “people look out for each other” (Narissa). Arlena (C2) discussed the diversity of the community, in comparison to where she was raised, and how neighbors help one another:On the other hand, C3 and C4 conversations tended to focus on fears residents shared about others, often describing concerns about starting gardens and people intentionally contaminating them or ruining them. Overall, these sentiments may point to low social structure and solidarity .Each community focus group discussion was unique to the circumstances in their neighborhood, but also to the number of people in the focus group and the tone and dynamics of the focus groups themselves. The conversations in C1 and C2 around assets and proposed solutions were much more involved. This was likely due to the larger number of people in those groups and the location of those focus groups. Both were held in public libraries that have rules that our focus groups had to be open to the public’s participation, unless people did not meet our IRB requirements of being younger than 18, not living in the identified zip codes, or arriving after we started our focus groups. Since we had grant funding for grocery gift card incentives, we were financially able to accommodate larger focus group sizes, though it was not feasible with time constraints of the grant to host more than four focus groups . The facOur C3 and C4 meetings were held in a central location at a college student union off of a bus line. While we coordinated with two key liaisons and their network, the attendance was much lower. We asked participants why they thought others would not come and there was generally a lack of trust of people outside the community, the weather was rainy, and the cohesiveness of the communities was much less than C1 and C2. In addition, while the location was easily accessible, we recognize that having a meeting on a college campus may not feel accessible for persons living in C3 and C4 where college education rates are very low. The C3 focus group, specifically, was heavily dominated by the problems of the community. People were less inclined to discuss what they appreciated about their community or ways to improve it. We were more limited on time for the C3 group because our C4 focus group was being held immediately afterwards and we started late to wait for people arriving from public transportation.Though the original intent of this research was not related to policy, our purpose was to elevate the lived experiences of residents living in communities that are facing innumerable challenges of poverty, crime, trash accumulation, illegal dumping, health concerns, and poor food access. Our analysis shows that these voices and their perceptions are crucial to efforts that can address environmental health issues and improve the quality of life for all residents there. These conversations were impactful for residents and have contributed to many new programs and efforts for C1 and C2. We are less aware of changes in C3 and C4, but this may be due to stronger relationships with community members in C1 and C2, the location of researchers in the city where C1 and C2 are located, and continued community-engaged research in C1 and C2. Residents were deeply concerned about litter, illegal dumping, and homelessness in C1. Since the focus groups, the chamber of commerce worked with the city to obtain funds to support several resident-driven efforts to address these issues. This includes residents who work together in teams to clean-up assigned areas throughout the year. They are given supplies and special t-shirts and compete to remove the most litter from their neighborhood block. These citizen participation efforts are impactful, as neighbors and children see people they know picking up trash, which can have a positive psychological impact on behavior. In addition, it builds camaraderie and encourages people to care for the natural and built environment. The city is also supporting an initiative to pay persons who are chronically homeless to beautify and clean up areas along the commercial corridor that is still largely vacant. The clean-up efforts and re-investment by the city are part of a larger city plan to expand this corridor and attract businesses for economic development purposes. Residents in C1 have also created online Facebook groups to track illegal dumping in their communities and encouraged the use of the city’s online service report system to bring attention to the issues and have overflowing dumpsters in alleys immediately removed.Throughout the city where C1 and C2 are located, efforts to increase citizen participation in democratic processes have occurred. Citizens can serve on area commissions and are encouraged to attend meetings to voice their concerns. Several neighborhood civic groups exist to discuss issues before bringing them to government officials or the area commission. People are invited through paper flyers in mailboxes, door-to-door canvassing, and online social media groups. A local agency hosts a neighborhood leadership academy to help residents in these low-income communities develop their leadership skills and understand democratic processes. A progressive political group has organized efforts to recruit, train, and support residents from these neighborhoods to participate in coalition-building around progressive values that are intended to improve the quality of life for their neighborhoods. This includes supporting candidates for serving as representatives on the Democratic Party Central Committee of the county.Lastly, since our focus group conversations, some of the residents from C1 and C2 have worked together to improve healthy food access. In C1, the urban farm has expanded to include perennial fruits and berries along with their annual vegetables and herbs. They have received federal funding to expand their food production space and implement a community-supported agriculture (CSA) program for residents in their neighborhood. The CSA delivers weekly produce grown on previously-vacant lots and works in coordination with programs serving low-income households. Over 140 households have participated since 2016. Residents in C1 and C2 participated in neighborhood meetings to help inform a local food action plan that was adopted by the city and county. In C2, a focus group member helped lead efforts to build an urban fruit tree forest and has led efforts to bring food-related businesses and restaurants to their neighborhood. C2 focus group members worked with a local church, community development agency, private and public sponsors, and the regional foodbank to transform a former drive-through liquor store into a free fresh produce market. A community center also hosts free weekly community meals that are highly attended and has a pay-as-you-can restaurant. Both areas have seen increased businesses. Information from our focus groups are extremely valuable to stakeholders in the community and policymakers who likely reside outside of the community. Our methodology of working with community leaders in C1 and C2, in particular, has allowed for conversations that started in those two-hour meetings to continue. Researchers involved in this study continue to conduct work in C1 and C2 and people still reference those focus groups at the libraries. Our analysis shows that resident voices and efforts are an important part of the solution. It is recommended that researchers share their analysis with policymakers and provide briefings back to communities to continue conversations and ensure involvement by residents who are most impacted by the challenges and can be important change agents.Approaching individual or collective efforts to improve the built, natural, and social environments needs a multi-pronged approach that starts with residents’ voices. They know best the issues that are most concerning in the community. This study focused on the lived experiences of residents living in low-income urban neighborhoods in their own word. They focused on five specific challenges in their community: Pollution, abandoned buildings with associated crime, low food access and health concerns, trash and illegal dumping, and lack of trees. Further analysis showed that within each community there are individuals who are engaged, potential leaders that may benefit from support and training, and others who can easily identify barriers that could be targeted for efforts by trustworthy groups. Two of the communities (C1 and C2) in our study seemed to have a greater sense of community, awareness of specific resources, opportunities for impact, and potential grassroots leadership, while C3 and C4 seemed to have little trust in political systems and civic structures. This study was not intentionally targeted for policy change. However, the focus groups served as spaces where conversations led to action. Policies have been enacted and programs have been created, in part due to leaders in the focus groups engaging with community members to address their challenges. While these results may not be overly generalizable, knowing where to start comes from listening to the people experiencing environmental injustices and recognizing that “A land ethic begins with knowing and loving the land, and committing to citizenship within it,” (summarizing Aldo Leopold) .