Rethinking Representation and Diversity in Deliberative Minipublics

Deliberative minipublics often seek to recruit participants who are representative and diverse. This raises theoretical and practical challenges, because representativeness and diversity can be interpreted in multiple ways and can conflict with one another. We address this issue by proposing a purposive design approach, according to which the appropriate conceptualisations of representativeness and diversity, and thereby recruitment strategies, depend on the deliberative mini-public’s aims. We argue that deliberative minipublics frequently have mixed aims, which can justify hybrid recruitment strategies that reflect distinct senses of representativeness or diversity.


Introduction
Deliberative minipublics assemble a group of ordinary citizens, expose them to relevant information and positions on an issue and facilitate deliberation, which then yields results that are used as input in decision-making (Fung 2003). Representativeness and diversity are frequently cited as desirable characteristics of participant groups in deliberative minipublics (Brown 2006;Caluwaerts & Ugarriza 2012;O'Doherty & Burgess 2013;Rowe & Frewer 2000). However, representativeness and diversity can be interpreted in multiple ways. Statistical representativeness -wherein the distribution of relevant characteristics in the sample resembles that in the general population -is often distinguished from cross-sectional representativeness, wherein all relevant characteristics present in the population are also found in the sample but not necessarily in the same proportions (Brown 2006;Goodin & Dryzek 2006). Moreover, diversity may refer to a wide variety of perspectives or demographic categories, or to the inclusion of members of socially marginalised or discriminatedagainst groups (Steel et al. 2018). Representativeness and diversity may also come apart. For instance, if one viewpoint is statistically predominant in the population, then maintaining cognitive diversity would seem to require a nonrepresentative sample. Consequently, a better understanding of the complex interactions between diversity and representativeness is crucial for the future design of deliberative minipublics.
In this article, we suggest a purposive design approach that emphasises articulating the aims of deliberative minipublics and linking them to concepts of representativeness and diversity, which can then guide recruitment strategies. According to this approach, deliberative minipublics may differ in their aims, and a single minipublic may have mixed or hybrid aims. The appropriate concepts of representation and diversity, therefore, should be chosen in light of this heterogeneity. Our approach contrasts with an influential position on representation in deliberative minipublics according to which political equality (understood as the equal chance of influencing political outcomes) justifies interpreting representation in a statistical sense and recruiting participants via random sampling (Fishkin 2018;Smith 2009). Whereas this approach attempts to proceed deductively from universal principles of democracy, we take the aims of deliberative minipublics to be variable and the relevant concepts of representativeness and diversity to vary accordingly.
We distinguish three goals of deliberative minipublics. First, some seek to approximate the counterfactual public will, that is, to estimate the distribution of preferences the public would have regarding a menu of policy options if the public were to be informed and were to deliberate on the subject. This is frequently the aim of deliberative polling, especially as advocated by James Fishkin (2018). Second, deliberative minipublics sometimes aim to elicit a range of perspectives, that is, to explore the views or concerns that emerge from informed deliberation among some suitably diverse sample of the population. This aim is briefly suggested by Mark Brown (2006), and is illustrated by an actual deliberative minipublic that we describe below. The third and final aim of deliberative minipublics we consider is what we call co-creating recommendations. This aim is exploratory and decision oriented: it encourages the exploration and development of novel proposals, and prompts participants to develop collective recommendations and reasons for them. It differs from the first aim in not presuming a preset menu of options, and from the second in not being satisfied to merely record a range of disparate perspectives. While these three aims are inspired by actual deliberative minipublic formats, to our knowledge they have not been explicitly formulated in previous works on public deliberation.
We advance the following claims in connection with these three aims. First, recruiting a sample of participants that is statistically representative of the relevant population should be a priority given the first aim (approximation of the counterfactual public will) but not necessarily so for the other two. This claim is consistent with the observation that, among deliberative minipublic formats, only deliberative polling strives for statistical representativeness (see Goodin & Dryzek 2006). But our proposal furthers the discussion by providing a principled explanation of why these differences should not merely be seen as defects of deliberative minipublics that do not aim to recruit statistically representative samples. Second, for all three aims, there can be good reasons to include certain groups in proportions greater than would be expected from a random sample. We argue that political equality, while sometimes cited as an argument for random sampling (Fishkin 2018), in fact provides a powerful reason to oversample minority groups when populations have been constituted in starkly inequitable ways. Our third claim is that mixed aims of deliberative minipublics can justify hybrid recruitment strategies. Our approach entails that random sampling, while having its place, should not be treated as a definitional criterion (pace Smith 2009) nor as an indicator of quality (pace Fishkin 2018) of deliberative minipublics. It also suggests that organisers of deliberative minipublics should be explicit about their aims and should recognise that these aims are often mixed, in which case, attaining them may require hybrid recruitment strategies.
The article is organised as follows. In Section 2, we review the existing literature on representation and diversity in deliberative minipublics and identify what we consider as shortcomings of existing arguments. In Section 3, we propose and defend our purposive design approach. First, Section 3.1 elaborates the three aims already alluded to earlier, and illustrates each with an example of an actual deliberative mini-public. Next, Section 3.2 develops our three claims and the consequences they entail. Finally, Section 4 concludes by reemphasising the central themes of our purposive design approach and contrasting it with alternatives.

Statistical Representativeness Versus Cross Sections
While a substantial literature exists on the concept of democratic representation, much of it focuses on electoral representation, for instance, as found in legislative assemblies (Brown 2006;Urbinati & Warren 2008). In contrast, participants in deliberative minipublics are not usually elected, and hence typically lack the legal authorisation to make decisions on behalf of broader publics 1 and usually cannot be held accountable by them. We focus, then, on nonelectoral concepts of representativeness. Within the nonelectoral category, Nadia Urbinati and Mark Warren (2008) distinguish between self-authorised and citizen representatives. In the former case, an individual or organisation takes it upon itself to publicly represent the interests of a particular constituency defined, for instance, by ethnicity, religion or profession. Citizen representatives, in contrast, do not present themselves as representatives of others and only act in this capacity within the confines of the deliberative mini-public. Citizen representatives may self-select to participate or be recruited by deliberation organisers. 2 Although self-authorised representatives are included among the participants in some types of deliberative minipublics, citizen representatives are usually the majority. And in some minipublic designs, selfauthorised representatives are excluded from participating as deliberators, although they may be invited to express their positions and arguments (Kaldec & Friedman 2007). Our focus here, then, is on the possible senses in which a group of citizen representatives can be said to represent a larger populace. For convenience, in what follows we use 'representativeness' specifically in relation to nonelectoral citizen representatives.
More than one notion of representativeness can be found within the literature on deliberative minipublics. According to an influential proposal, representativeness requires that the statistical distribution of demographic or other relevant characteristics in the minipublic matches that of the population. This is typically taken to motivate random selection of participants on the principle that a large random sample will approximate the population distribution, and that in an ideal democracy all citizens should have an equal chance of influencing the political process (Brown 2006;Dryzek & Niemeyer 2008;Caluwaerts & Ugarriza 2012;Fishkin 1995Fishkin , 2018Fung 2003;Hainz, Bossert, & Strech 2016;Landemore 2013). We call this statistical representativeness. An alternative is that representativeness only requires a ' cross-section,' wherein relevant demographic categories and perspectives are represented in the minipublic but not necessarily in the same proportions as in the population at large (Brown 2006;Goodin & Dryzek 2006;Hainz et al. 2016). We label this position cross-sectional representativeness. Cross-sectional representativeness is sometimes motivated by the aim of ensuring a diversity of perspectives in deliberation, which may be swamped in a statistically representative group if one perspective tends to dominate in the population (Brown 2006).
We begin by examining arguments given in favour of statistical representativeness and random sampling. Fishkin (2018) argues that statistical representativeness achieved via random sampling gives each citizen an equal chance of participation in the deliberative mini-public, and therefore embodies the democratic ideal of political equality: 3 'The idea is to equally count everyone's views under conditions where they can really think in order to give expression to a meaningful public will. Hence, we will draw on work that combines random sampling to help achieve political equality with conditions facilitating in-depth, thoughtful discussion' (Fishkin 2018: 7). Fishkin cites the ancient Athenian nomothetai, in which citizens were selected by lot to consider proposed changes to laws, as a precursor of his approach (Fishkin 2018: 22). However, we argue that political equality does not justify random sampling for two reasons. 4 The first is that random sampling does not correct for social inequities that may skew sampling frames and underlying populations. The second is that 'random sampling' is a somewhat misleading term to describe the process: individuals are randomly invited to participate in the deliberation, but those who accept need not be a random or representative sample. 5 Random sampling may fail to give everyone an equal chance of participating because social inequities can skew sampling frames and underlying populations from which individuals are selected. A sampling frame is a list of individuals that is taken to correspond to an underlying population. For example, suppose the aim is to recruit a sample of registered voters in the state of California. The population then consists of registered voters in California, and the sampling frame is a list of registered voters maintained by the state elections board. In this case, social inequities (i.e., voter suppression) can skew both the population and the sampling frame. Voter suppression can skew the underlying population by creating unfair obstacles to voter registration for certain groups of people (e.g., by closing government offices where people can register to vote in predominantly African American counties). In this way, social inequities may affect who is and who is not a registered voter. Moreover, voter suppression can directly distort the sampling frame, for instance, if inaccuracies in the voter registration list (e.g., a registered voter being removed from the list in error) do not occur at random but are more likely to disenfranchise minority voters. As Carol Anderson (2018) documents, suppression of minority voter registration, especially African Americans, has been a persistent phenomenon in the United States since the reconstruction era, and has experienced a revival following the 2013 Supreme Court decision in Shelby County v. Holder that weakened the Voting Rights Act of 1965. In such circumstances, a random sample drawn from a list of registered voters will not give everyone an equal chance of being invited because not everyone had an equal chance of being on the list.
Voter suppression is noted by Fishkin as one of the ills of contemporary democracy (Fishkin 2018: 4). Yet some deliberative polls discussed by Fishkin are based on samples of registered voters (Fishkin 2018: Chapter 3). So, when voter suppression is a problem, voter registration lists and random samples drawn from these lists will be skewed by that inequity. In general, social inequities are likely to distort sampling frames, such as lists of registered voters, people with stable addresses, people who respond to the census and so on (see Wojciechowska 2019). To our knowledge, Fishkin does not address the problem that sampling frames and underlying populations might be skewed by social injustices. However, Fishkin (2018) argues that in actual deliberative polls, there is no evidence of distortions resulting from more advantaged people dominating the process, or from polarisation in which deliberation drives group opinion to a more extreme version of the view the majority initially preferred. Not all research on discursive equity in deliberative polls agrees that their internal processes are as free of distortions as Fishkin suggests: participation inequality has been measured (Gerber 2015), and some strategies have been used to counteract it, such as enclave deliberations for marginalised groups (Abdullah, Karpowitz, & Raphael 2016). However, we do not pursue this issue here. Instead, we note that distortions arising in the process of deliberation, while an important concern, are separate from the impact of societal inequities on those who are deliberating in the first place. Similarly, Athenian nomothetai, due to their exclusion of women and slaves, would not have satisfied the principle of political equality, even if their members had been randomly selected from adult male citizens and their internal processes had been free of distortions.
Second, even if everyone has an equal chance of being invited, it does not thereby follow that all have an equal chance of participating (Smith 2009;Wojciechowska 2019). Such considerations can be used to motivate stratified random sampling, which several scholars have advocated (Rowe & Frewer 2000;Longstaff & Burgess 2010;O'Doherty & Burgess 2013). In this approach, proportions of participant categories (e.g., along demographic lines) might be set by a sampling frame (e.g., census data), and then populated by individuals who have accepted randomly issued invitations to participate in the deliberation. For instance, suppose that 1,000 people are randomly issued invitations, and among those, 100 accept, with a gender breakdown of 60 women and 40 men. If the desired number of participants is 50, then 25 of the men and 25 of the women among those who have accepted the invitation might be selected to participate. Thus, stratified sampling might correct for statistical nonrepresentativeness arising from bias regarding who accepts invitations, or perhaps from random variation in small samples (Smith 2009: 81). Note that as described, stratified sampling does not address the concern that social inequities may skew the sampling frame. However, it could do so, for example, by increasing the proportions of groups thought to be underrepresented due to inequities that distort the sampling frame.
The considerations in the previous paragraph further weaken the link between political equality and recruitment to deliberative minipublics by randomly issued invitations. Random sampling does not counteract inequities that may skew the sampling frame or bias who accepts invitations to participate. Thus, when there are good reasons to think that such effects are present, random sampling is not merely insufficient to achieve political equality, it is also not necessarily the best way to approximate it. If inequities and ensuing biases are known, then stratified sampling or other approaches that correct for them may be more likely to result in everyone having an equal chance to participate. For instance, consider what Fung terms an ' affirmative action' approach to recruitment, wherein organisers attempt to achieve ' demographic representativeness by publicizing the event in communities that would otherwise be underrepresented' (Fung 2003: 342). Approaches that target relevant but likely to be underrepresented groups could be combined with random sampling. For example, a group that consists of five percent of the population might receive 10 percent of the invitations if they are half as likely to accept. Difficulties can certainly arise for methods that aim to counteract biases, for instance, if efforts to increase the numbers of one underrepresented group inadvertently exclude others (Smith 2009: 81). However, such challenges fail to rescue political equality as an argument for random sampling. Even if methods to counteract inequities that bias participation in deliberative minipublics are imperfect, the may be more likely to equalise the chance of participation than random invitations.
In addition, some scholars express ambivalence about statistical representativeness, especially due to its potential effects on minority perspectives and demographic groups. For example, Gene Rowe and Lynn Frewer (2000) state that participants should be representative of the broader public, but urge that caution should be exercised about disenfranchising marginalised groups of society, and that members of all affected communities should be present. Despite these qualifications, they conclude by emphasising that representation should consider the distribution of views, and caution that in a small sample there is a risk that representing every viewpoint might diminish the influence of the majority (Rowe & Frewer 2000: 12). Similarly, some have suggested that statistical representativeness should be balanced against diversity. For example, Kieran O'Doherty and Michael Burgess write that 'random sampling with attention to maximizing the diversity of participants seems to offer the best option for constituting a deliberating minipublic' (O'Doherty & Burgess 2013: 60). These discussions suggest that diversity might be a reason to depart from statistical representativeness to some extent. However, O'Doherty and Burgess leave unclear when statistical representativeness should be sacrificed in the name of diversity, to what extent, and why.
Let us turn, then, to cross-sectional representativeness. The primary motivation for this conception of representativeness is that it may result in greater diversity, in both demographics and perspectives, than statistical representativeness would. Suppose that there are 15 relevant perspectives to represent in a deliberative minipublic that will convene 50 participants, but that two perspectives account for 80% of the general population. In this case, a sample that is statistically representative with regard to perspectives cannot include all 15 of them, assuming that each person has no more than one perspective. The two most popular perspectives take up 40 of the 50 seats, leaving only 10 seats for the remaining 13. Cross-sectional representativeness, then, is naturally associated with a concept of diversity according to which greater diversity entails a larger number of relevant characteristics among the deliberators. Thus, in the example, deliberators are more diverse if all 15 perspectives are present rather than only 12 (i.e., the 2 most popular plus 10 others). Consequently, achieving cross-sectional representativeness can require reducing the proportions of majority groups, as defined by perspectives, demographics or other characteristics judged relevant to deliberation. Arguments for crosssectional representativeness in deliberative minipublics often suggest that greater diversity is likely to improve epistemic quality or validity of deliberation (Brown 2006;Bohman 2006;Caluwaerts & Ugarriza 2012).
However, the argument for cross-sectional diversity encounters some difficulties. One is that the number of relevant perspectives may be too large for it to be practical to include all of them. Questions about which perspectives are most important to include and why they should be included seem unavoidable, yet cross-sectional representativeness provides no guidance on how such judgments should be made. The second difficulty concerns the implicit conception of diversity as simply an increasing function of the number of relevant characteristics present. Diversity might instead be thought to depend on the presence of specific characteristics, such as perspectives associated with socially marginalised groups (Steel et al. 2018). Moreover, in some cases, the epistemic advantages of diversity might be more closely linked to the presence of certain perspectives that are less commonly heard from -for instance, of those with relevant lived experiencesthan with the number of different perspectives (Harding 2015). Both of these difficulties can be elaborated in connection with intersectionality.
While its interpretation is much debated (Carastathis 2014;Crenshaw 1989Crenshaw , 1991Hancock 2016;Hill Collins & Bilge 2016), Marta Wojciechowska (2019) characterises intersectionality, in the context of deliberative minipublics, as emphasising that social categories are multiple and dynamic. They are multiple in the sense that people fall under several overlapping social categories (e.g., gender, ethnicity and sexual orientation), and dynamic in that categories need not be viewed as discrete (e.g., gender may be viewed as a continuum along which a person may move rather than as a fixed dichotomy between male and female). Intersectionality is also specifically focused on cases in which multiple socially disadvantaged attributes apply to a person (e.g., black female homosexual), and suggests that the total impact of overlapping disadvantages tends to be greater than the sum of the effects considered separately (Wojciechowska 2019). In Kimberlé Crenshaw's (1989) classic formulation, failure to appreciate intersectionality results in implicitly understanding sexism as it is experienced by white women and racism as it confronts black men, making discrimination faced by black women difficult to communicate and remedy.
A multiple and dynamic approach can be expected to increase the number of categories to be represented. For example, only three binary attributes (e.g., male versus female, black versus white, heterosexual versus nonheterosexual) produce eight intersections, each of which might be represented, while four binary attributes result in 16 intersectional categories and so on. The possibility that attribute categories might be represented as dynamic rather than discrete accentuates this situation.
At a minimum, accommodating the potentially dynamic nature of categories involves adding an additional category for those who prefer not to identify according to a commonly presumed set of discrete options. Thus, in the case of gender, a 'none of the above,' 'trans,' or 'X' category might be listed along with male and female. Such an approach would significantly increase the number of possible intersections, 6 despite being rather inadequate from the perspective of intersectionality. For instance, simply adding a catchall category for nonbinary gender foregrounds the binary categorisation as the default and does not specify an alternative dynamic mode of identification. A more thorough going intersectional approach might permit respondents to choose between discrete and dynamic modes of gender identification and provide a format for each type of response. A more adequate inclusion of dynamic modes of representation, then, would increase the number of possible intersectional categories even further.
Intersectionality, then, draws attention to the first difficulty for cross-sectional representativeness noted above: the number of categories may be too large, making it impractical to represent all of them. Intersectionality's focus on overlapping disadvantaged categories could limit the number of intersections that it is important to represent. However, such an approach appears to be at odds with the underlying rationale for cross-sectional representativeness, which does not privilege representing some categories over others, and conceives of diversity as a function of the number of categories present. A focus on groups subject to intersecting social disadvantages, then, highlights the second difficulty for cross-sectional representativeness, namely, that some categories or intersections may be more important than others as far as diversity is concerned.
In sum, at least two concepts of representativeness -statistical and cross-sectional -are discussed in the literature on deliberative minipublics, and the rationale for each leaves something to be desired. Statistical representativeness is typically linked to random sampling, which in turn is justified by its appeal to political equality as a fundamental democratic principle. Yet political equality does not justify random sampling if the relevant population is skewed by social inequities. In such cases, achieving political equality may require compensating for known inequities that are likely to be reproduced in random samples. Cross-sectional representativeness, on the other hand, faces the problem that the number of relevant categories can be expanded to such an extent that it is unfeasible to include all of them. In such circumstances, the question of which categories are most important to represent is unavoidable. In the next section, then, we develop an alternative approach to representation in deliberative minipublics.

Purposive Design Approach
Our proposal suggests a flow from the aims of a deliberative mini-public to relevant conceptions of representativeness and diversity, and from there to appropriate recruitment strategies. The links between each of these steps should be thought of as guidance rather than as a deterministic process, since factors besides those we highlight may also be relevant. Nevertheless, we claim that the guidance provided by our purposive design approach is informative from both a theoretical and practical point of view. We also claim that our proposal is a theoretical improvement over the approaches discussed above, and that it can assist practice by encouraging more justified and transparent rationales for recruitment strategies in the design of deliberative minipublics. Developing our approach requires distinguishing among several possible aims of deliberative minipublics (Section 3.1), and explaining how those aims connect to different concepts of representation and recruitment strategies (Section 3.2).

Counterfactual public will, eliciting perspectives, and co-creating recommendations
Many aims of deliberative minipublics have been suggested. These include informing the public, building community or citizen capacity, informing decisionmakers of citizens' concerns or perspectives, oversight of public officials and reasonable social choice (see Fung 2003). The three aims we examine -(1) approximation of counterfactual public will, (2) eliciting a range of perspectives, and (3) co-creation of recommendationsare not intended to be exhaustive, and we devote little attention to some possible aims, such as monitoring elected officials.
To properly understand these aims, it is helpful to distinguish four stages of a deliberative mini-public: recruitment, deliberation, results and uptake. In the first two stages, participants are recruited to participate in the minipublic via random invitations or other means, and are then presented with information and questions on which they deliberate. Results are then produced from this deliberation, for instance, before and after survey results in the case of deliberative polling or a document summarising recommendations. Note that some components of the results, such as pre-deliberation surveys, may be acquired prior to the deliberation. However, the results are not completed until deliberation has ended. Finally, these results are expected, or at least hoped, to have uptake by impacting decision-making at some level of the political process.
The three aims we examine pertain to the results stage and concern the type of information that the result of the deliberative minipublic intends to convey. In the case of approximation of the counterfactual public will, the question is: What proportions of the public would favour which policy options if they were to be informed and deliberate about them? In the case of eliciting a range of perspectives, the aim is to provide information about what issues, concerns or views the public may have regarding some matter, such as a newly proposed publicly-funded programme or project. While eliciting a range of perspectives is a feature of every minipublic at the deliberation stage, conveying a range of potentially novel views is not always what is desired from the result. Deliberative polls survey participants on a preset list of alternatives, and the third of our aims, while encouraging the exploration of novel proposals, does not simply aim to record a range of expressed views and perspectives, but prompts participants to make collective decisions.
Aside from the results, other stages of the deliberative process might also have aims of their own. For instance, it may be hoped that engaging in deliberation will increase the knowledge and civic-mindedness of participants. We regard such goals as generally compatible with the aims we focus on here. Nevertheless, we think that the aims associated with results merit special attention as the results are what prior stages build towards and are what will be adopted if uptake occurs. We chose the specific aims examined here because they are all illustrated by actual deliberations and cover a large wide range of possible objectives related to the results of deliberative minipublics. The systematic coverage of the three aims can be seen by considering two axes: exploratory and decision oriented. The results of deliberation are exploratory if they encourage the expression of novel proposals, solutions or ideas rather than merely a selection from a prespecified list of options. They are decision oriented if a recommendation of some sort is expected, rather than only an expression of a range of views or perspectives. Thus, the first aim (approximating the counterfactual public will) is nonexploratory but decision oriented, while the second (eliciting perspectives) is exploratory but not decision oriented, and the third (co-creation of recommendations) is both exploratory and decision oriented. The fourth combination (neither exploratory nor decision oriented), while theoretically possible, seems unlikely to be useful in practice. If results focus on a predetermined list of alternatives (and not, say, an exploration of concerns or issues participants have regarding them), then there is little the results can do besides record which alternatives participants prefer (and hence, be decision oriented). Finally, the three aims should be thought of as points along a continuum rather than as discrete, with the consequence that a deliberative minipublic may adopt an aim that combines elements of more than one of the three aims we highlight. This last point is examined further in Section 3.2.
Consider an example of a deliberative method that seeks to approximate the counterfactual public will, that is, to estimate which policy options would be preferred by what proportions of the population if they were to be informed and were to deliberate on the matter. A clear example of this is Fishkin's method of deliberative polling. As Fishkin (2018:1) states, 'Deliberative democracy is a practical answer to a philosophical question: What would the people think should be done if they could consider key issues under good conditions for thinking about them?' We view this claim as a rough characterisation of the aim of deliberative polling rather than as a description of deliberative democracy generally. Deliberative polling can be broken down into four basic elements: (1) randomly recruited participants who are (2) exposed to an evenhanded presentation of information and views on a topic, (3) engage in structured deliberation, and (4) respond to pre-deliberation and post-deliberation surveys assessing their preferences regarding a list of predetermined policy options (see Fishkin 2018).
A good example comes from a deliberative poll conducted in Vermont in 2007 to facilitate public input on decisions regarding the implementation of statewide electricity options (Luskin et al. 2008). This poll began with a telephone survey of Vermonters who were contacted via random digit dialling. These calls involved both a questionnaire and an invitation to partake in the deliberation event, an offer that was sweetened by a USD 150 honorarium. A total of 750 respondents were contacted and invited, of whom 152 agreed to participate in the subsequent two-day deliberation. Prior to the deliberation, participants were mailed an information packet presenting information and differing options for electricity generation in Vermont. Upon arrival, the participants completed a self-administered survey, along with one more prior to leaving, making a total of three surveys. The deliberation itself involved both facilitatorguided small group discussions and large group plenary sessions which encouraged public interaction with expert panels. The comparison of pre-deliberation and postdeliberation survey results found changes of opinion on several important topics. For example, in the postdeliberation survey, participants were more in favour of generating electricity from renewable energy sources and less in favour of oil and coal. According to the report of the deliberation, 'The post-deliberation distribution of opinion gives a picture of what Vermonters would think about these issues if they knew, thought, and talked more about them' (Luskin et al. 2008: 1; italics in original).
Let us turn, then, to the second aim we consider, namely, eliciting a range of perspectives. This aim is common in focus groups, wherein deliberators learn about a project or proposal and are invited to discuss hopes or concerns that arise for them regarding it. In such cases, there is a risk that individuals involved with the project from a government, business or academic perspective may focus on concerns that are very different from those that would be significant to members of the public. Thus, this aim is exploratory and often preemptive: to discover unexpected issues and potential problems early in the process when changes are easier to make. However, focus groups that aim to elicit a range of perspectives need not ask which policy should be adopted. The aim can simply be to discover the range of concerns, issues, or values that members of the public would deem important in relation to the topic.
To illustrate, consider a series of minipublics conducted to engage the public in the area of genomics and biotechnology in British Columbia. As genomic research is a sector supported by both private and public resources, this project sought to create a policy development process that could meet ' democratic values of representation, transparency and accountability' (Burgess 2003:1). Eleven focus groups were convened to elicit a diversity of interests in relation to genomic governance and research. Interests were understood broadly as 'things in which people perceive themselves to have a right or a share, e.g., common goods' (Burgess 2003: 4). These include their hopes for benefits as well as concerns about how things might go wrong. The key insight is that deliberations are naturally framed around an issue and that this foregrounds a particular set of interests and philosophical assumptions about how they interact, potentially precluding interests that may be important to the public (Burgess 2003). Burgess illustrates this idea as follows: 'One example is the focus on safety that characterizes much of the policy debate related to biotechnology… This sets the scope of the inquiry to exclude concerns related to the effects of biotechnological approaches on the political economy of agriculture, the further concentration of wealth and the influence of a consumer-based definition of benefits on the common good and future generations' (Burgess 2004: 8). Thus, the focus groups aimed to elicit a range of interests that members of the public regard as important in connection with genomics and biotechnology without imposing a particular frame or issue.
Three categories of participants were recruited: those without an interest in genomics, those interested in genomics but not involved in the issue in a professional or organisational capacity, and finally those with a ' direct interest' in the topic, that is, 'non-governmental groups who spoke on behalf of public interests, researchers, funders and regulators of genomic research' (Burgess 2004: 8). Random digit dialling and honoraria were used to recruit the first two populations while the others were recruited through contacts and referrals (Burgess 2003). During the deliberation, participants were asked to describe the scope of genomics, their hopes with regard to it, and their concerns (Burgess 2004: 8). Prominent hopes included improved treatment, diagnosis and prevention of disease, reduced use of pesticides and increased crop yields, while prominent concerns included complex and unpredictable consequences, public misunderstanding and misrepresentation in the media and inequitable distribution of benefits (Burgess 2003: 12-13). On the basis of these results, human tissue biobanking and aquaculture involving genetically modified salmon were chosen as topics for future deliberation (Burgess 2004: 8; see also O'Doherty, Burgess, & Secko 2010).
The final aim we consider is the co-creation of recommendations. Similar to eliciting a range of perspectives, this aim is exploratory in that its results may include novel ideas or proposals. But it also examines specific decisions that could be made, explores possible trade-offs and attempts to identify areas of agreement. Deliberative minipublics falling under this third aim may vary in the extent to which agreement is sought or expected, and in whether the recommendation is merely advisory or is linked to action by an established mechanism. 7 In the example we describe here (participatory budgeting), the extent of agreement required depends on whether decisions are reached by consensus or by voting, and whether a mechanism exists to link decisions to action. In contrast, other deliberative minipublic designs that we would also classify as aiming for co-creation of recommendations might only be advisory (see Bentley et al. 2018).
Participatory budgeting was first developed in Porto Alegre, Brazil, and is now used around the world (Campbell et al. 2018). Participatory budgeting is a form of deliberation in which members of the public deliberate over the allocation of some portion of a public budget (Pin 2016;Pinnington, Lerner, & Schugurensky 2009). Most commonly implemented at the level of municipalities, 8 participatory budgeting generally involves community level deliberations, open to all, where funding priorities and proposals are discussed and community delegates are elected. Delegates from the several communities or neighbourhoods then participate in meetings where they can advocate for their proposals and collectively decide, either by consensus or by vote, which proposals will be funded. City officials attend these meetings in an advisory, nonvoting capacity, and community delegates have the opportunity to oversee the disbursement of funds and implementation of projects. Participatory budgeting, then, is exploratory and decision oriented. Participants can advance novel proposals grounded in their knowledge of community needs and are expected to make decisions about which proposals to fund, which naturally entails the discussion of priorities and values in the context of trade-offs required by budget limitations.
Consider a specific example of participatory budgeting that operated in the city of Guelph, Ontario from 1999 to 2012 (Pinnington et al. 2009;Pin 2016). The participatory budgeting programme in Guelph was led by an organisation called the Neighbourhood Support Coalition (NSC), which was established to coordinate the activities of neighbourhood groups in the city. The impetus for participatory budgeting was the fact that equal distribution among the neighbourhood groups resulted in some having a surplus of funds, while others were unable to maintain their community programming (Pinnington et al. 2009: 464). The participatory budgeting process in Guelph followed the pattern described in the previous paragraph, but with neighbourhood delegates selecting projects by consensus and neighbourhood groups directly spending the funds rather than overseeing city officials (Pinnington et al. 2009: 467). The portion of the municipal budget of Guelph that the NSC could disburse was never greater than 0.1%, which is significantly smaller than in South American examples of participatory budgeting (Pin 2016;Pinnington et al. 2009). As a result, projects funded through Guelph's participatory budgeting process tended to be small-scale, such as festivals, newsletters or community food programmes rather than the infrastructure projects typical in Porto Alegre (Pin 2016;Pinnington et al. 2009). After 2012, the participatory budgeting process in Guelph was replaced with a small grant competition to which neighbourhood groups can submit proposals (Pin 2016). 9 Summing up, each of the three goals we considerapproximation of the counterfactual public will, eliciting a range of perspectives and co-creating recommendations -is illustrated by actual deliberations. Moreover, taken together, the three goals systematically cover a broad range of aims associated with results of deliberative minipublics. In the next section, we suggest that differences among the three aims have important implications for how representativeness and diversity should be understood.

Three claims
In this section, we advance three claims concerning diversity and representation in deliberative minipublics: (1) the importance of statistical representativeness for a deliberative minipublic depends on its aim; (2) for all three aims, counteracting inequities can be a reason for increasing proportions of marginalised groups above what would be expected from random sampling; and (3) mixed aims of deliberative minipublics often justify recruitment strategies that hybridise elements of statistical and cross-sectional repre sentativeness as well as those that oversample for specific minority groups.
The first claim we advance is that the extent to which statistical representativeness should be a priority of a deliberative minipublic varies according to its aim. Recall that statistical representativeness occurs when the sample of participants in a deliberation is proportionally representative of a relevant broader population. This is considered by many to be a desirable feature of deliberation, and Fishkin, for example, argues that deliberative polling among randomly selected samples is superior to alternative deliberative minipublic formats (See Fishkin 2018: 149). We agree that statistical representativeness is preferable when the aim is to approximate the counterfactual public will, because statistical representativeness makes it more likely that polling results will correspond to those of the broader population if it were to be informed and given the opportunity to deliberate. However, the approximation of the counterfactual public will is not the aim of all deliberative minipublics. Our first claim, then, is that the importance of statistical representativeness for a deliberative minipublic can depend upon which aim it pursues. 10 Deliberative minipublics that aim to elicit perspectives provide a particularly clear example. In such cases, the aim is to discover the range of perspectives that would emerge from informed deliberation, and not necessarily to approximate their distribution in the population. In this case, it is important that a broad range of perspectives and values present in the population be represented, although there is no clear reason why they must be represented in the same proportions as the population at large. Indeed, there may be a reason to prefer a more diverse sample of participants, at the cost of reducing the proportions of majority groups, in order to capture a cross-section of all relevant views. For example, organisers of a deliberative minipublic might oversample individuals with relevant lived experiences related to the topic of deliberation or individuals who express views that are socially marginalised. Consequently, when elicitation of perspectives is the aim, a cross-sectional notion of representativeness is the natural starting point. However, it is important not to oversimplify this observation, as it is possible that a deliberative minipublic that aims to elicit a range of perspectives might also be intended to provide information about which hopes or concerns would most commonly arise in the population. And if that were the case, then statistical representativeness would need to be balanced against diversity in recruiting a wider range of perspectives.
Related considerations arise for the third aim, the exploration of decisions. In this case, it is possible that a deliberative minipublic might be primarily focused on enhancing the quality of the decision and that a more diverse range of perspectives in a deliberation is likely to provide ' epistemic robustness' or ' epistemic validity' (Bohman 2006;Caluwaerts & Ugarriza 2012; see also Page 2017). For example, the inclusion of many views and perspectives might increase the pool of available reasons for the group to consider as premises in discussing common problems, and the group may agree upon a decision for different reasons, thus strengthening the decision (Bohman 2006). However, it is again important not to oversimplify the connection between the aims and the desirability of a statistically representative sample of participants in a deliberative mini-public. Deliberation may seek a quality decision that reflects the distribution of values and interests present in the population. Again, such mixed aims might necessitate striking a balance between statistical representativeness and diversity. For example, a deliberation that examines the fairness and sustainability of cancer services with the intention of generating policy recommendations may seek a crosssection of all perspectives to fully grasp the concerns within the population. In addition, statistical representativeness may be desirable if the recommendations are meant to reflect the values of the population. Some organisers may, therefore, wish to combine these features (Bentley et al. 2018;O'Doherty & Burgess 2013; see also Steel et al. 2018: 774-777).
In sum, statistical representativeness should be a priority for deliberative minipublics that aim to approximate the counterfactual public will, but not necessarily for deliberative minipublics that aim to elicit a range of perspectives or co-create recommendations. For these latter two aims, there will often be reasons to sacrifice statistical representativeness for the sake of diversity, at least to some extent, either to increase the chance that an adequately broad range of perspectives will be elicited or because it is thought that diversity is likely to improve the quality of decisions made.
Our second claim is that for all three of the aims, counteracting inequities can be a reason to increase the proportion of marginalised groups in comparison to what would result from random sampling. With regard to eliciting a range of perspectives and exploring decisions, this claim is an extension of the points previously outlined. For example, some deliberation organisers have opted to oversample historically marginalised or disenfranchised groups or those thought to be disproportionately impacted by the issue, while maintaining the population proportions of other groups of participants as much as possible (Burgess 2004: 7;O'Doherty & Hawkins 2010: 202). This might be done to increase the chance that the perspectives of marginalised people are voiced in deliberation, which may broaden the range of perspectives elicited or improve the quality of decisions. But the participation of minority groups in greater proportion that would result from random sampling may also be desirable for reasons of equity (Beauvais & Baechtiger 2016). In the case of participatory budgeting, for example, lower-income communities and individuals often have a greater need for municipal services, either because they are less able to pay for services out of their own pockets or because they are less able to influence political decisions. In such circumstances, overrepresentation in the deliberation of lower-income individuals can be viewed as a slight counterbalance to social inequities prevalent in other arenas of society.
The relationship between equity and deliberative minipublics that aim to approximate the counterfactual public will is more complex. It might seem that concerns about equity could never justify increasing the proportion of certain groups, because the counterfactual public will would be less accurately approximated as a result. However, the discussion of political equality and the example of voter suppression in Section 2 suggests a more complex picture. Sometimes, the distribution of an actual population (e.g., all registered voters in the state of Mississippi) differs from what it would have been were the society more politically equal (e.g., if voter suppression targeted at African Americans did not exist). In such circumstances, either of the two populations might be deemed relevant: the actual population generated by inequitable political and social forces, and a hypothetical population that would have existed in a more politically equal version of the society.
Statistical representativeness refers to some population, and consequently this reference population might be the actual and inequitable population or a hypothetical and more politically equal one. Moreover, the decision to choose either of the options implicitly reflects what the deliberative minipublic aims for. Does it aim to approximate a counterfactual distribution of preferences of an actual population, no matter how inequitable the processes that constitute it? Or is the aim to approximate the counterfactual public will of a population under conditions of political equality? The former aim is somewhat more practical. To continue the example from the previous paragraph, it asks about the distribution of preferences over a set of policy options that would arise in an actual population of registered voters -a population that, say, is racially skewed by a continuing history of voter suppression -were that population to be informed and able to deliberate. The latter aim is more idealistic insofar as it insists that the political inequalities that went into forming the actual population should not be ignored. In the example of voter suppression, one might increase the proportion of African American and other minority registered voters in the deliberation to approximate their numbers in the general population. This procedure would not base its random sample on the actual voter registration list, and participation recruitment would be deliberately biased toward oversampling minority voters.
We do not insist that one of these choices of reference population (i.e., actual and politically unequal or hypothetical and more politically equal) is always the correct one. It might be of interest to learn the counterfactual distribution of informed preferences in an actual population, even if that population were constituted by means that flout political equality. Such results might be of practical use for the purposes of messaging and strategy in an election campaign, for instance. However, we do claim that a deliberative pollor other deliberative minipublic designs that approximate the counterfactual public will -may reasonably opt for the latter, more idealistic alternative. After all, Fishkin's arguments regarding political equality and deliberative democracy point in this direction. If political equality, rather than political strategising, motivates the design of the deliberative mini-public, then political inequities that distort populations and sampling frames become obstacles that should be addressed. Otherwise, there can be no reasonable sense in which the deliberative minipublic gives all an equal chance of participation. To put the matter simply, political equality is a rationale for statistical representativeness in deliberative minipublics only in reference to populations whose membership is constituted by politically equal means.
Our third claim develops consequences of the first two for how participant recruitment should be pursued in deliberative minipublics. Specifically, the complexity of aims brought out in the foregoing discussion suggests that recruitment strategies for deliberative minipublics should often combine statistical and cross-sectional representativeness along with equity-based efforts to increase the proportion of minority groups. To pursue this idea further, note that the complexity of the aims is twofold: aims may differ from one deliberative minipublic to the next, and a single deliberative minipublic may have mixed aims. Section 3.1 emphasised the first type of complexity by describing deliberative minipublics where one of the three aims (i.e., approximating the counterfactual public will, eliciting a range of perspectives and exploring decisions) was prominent. This suggests that recruitment strategies used by deliberative minipublics may vary with their aims, and consequently that random sampling of participants should not be viewed as a sine qua non. The second complexity, relating to mixed aims, is illustrated by the prior discussion in this section. A deliberative minipublic that aims to elicit a range of perspectives on a topic might also aim to provide information about which perspectives arise most frequently. One that aims to co-create recommendations may emphasise decision quality or be more concerned with reaching a decision that parallels what the public at large would have concluded if it were informed and had deliberated. And a deliberative poll may be more or less thoroughly motivated by political equality and consequently more or less concerned about inequities that skew the demographic distribution of the relevant population. Mixed aims naturally suggest hybrid recruitment strategies, such as those that begin with a stratified random sample but subsequently increase the numbers of some categories of people above their proportions in the population for reasons of social equity or because their input is expected to be especially valuable.
Thus, our purposive design approach entails that it is important for organisers of deliberative minipublics to be explicit about their aims, because these are highly relevant to what recruitment strategy, or combination of recruitment strategies, should be adopted. Moreover, when aims are mixed, it is also important to consider which aim should be given priority if trade-offs between them prove necessary. Such reflections might reveal that a deliberative minipublic is in fact attempting to do too much at once, and that some aims should be deemphasised. For example, it might not be feasible for a deliberative minipublic that aims to explore decisions and promote equity by emphasising socially marginalised perspectives to also approximate the counterfactual public will (Beauvais & Bächtiger 2016). In such a case, the latter aim might be scaled back, in which case reports describing the deliberation should be clear that its results do not necessarily represent what the public as a whole would choose if it were informed and had deliberated. Similarly, a deliberative poll that makes no effort to compensate for known inequities that distort the population from which participants are randomly invited should be explicit about its limits with respect to political equality.

Conclusions
Representativeness and diversity are desirable features of participant groups in deliberative minipublics. However, both of these concepts can be interpreted in more than one way, and furthermore the two can lead in different directions. That in turn creates theoretical and practical conundrums about how participants in deliberative minipublics should be recruited. A better understanding of representativeness and diversity, and how to balance them in specific contexts, is therefore central to the future design of deliberative minipublics.
In this article, we have addressed this issue by developing a purposive design approach to representation, according to which the concept of representation appropriate for a deliberative minipublic depends on its aims. This approach proceeds pragmatically from the consideration of possible goals of deliberative minipublics rather than attempting to deduce a conception of representation and a recruitment strategy from a basic principle of democracy, such as political equality. While we do not doubt the importance of political equality, we think the distance between it and the variable circumstances of deliberative minipublics is too great for a deductive approach of this kind to succeed. For example, the link between random sampling and political equality in a deliberative minipublic depends on whether the aim is to approximate the counterfactual public will and on whether the population and sampling frame are skewed by inequities. Our approach also contrasts with arguments for cross-sectional representation in that it can naturally accommodate distinct notions of diversity. Diversity might refer to a larger number of perspectives or to perspectives of socially marginalised people whose experiences are particularly relevant to the topic of deliberation, and which way of thinking about diversity is most relevant can depend on the aims of the deliberative minipublic and details of the context. Finally, while some authors have noted trade-offs among the aims of deliberative minipublics (Beauvais & Bächtiger 2016;Caluwaerts & Ugarriza 2012), our proposal advances the discussion by exploring more systematically the possible aims of deliberative minipublics and linking these aims to concepts of representation and thereby to recruitment strategies.

Notes
1 Some exceptions exist, such as participatory budgeting (see Section 3.2). Cases such as these, in which there is a direct link between recommendations and action, raise questions of political legitimacy. While this issue is not explored here, Min Reuchamps and Jane Suiter (2016) provide examples of such cases. 2 Thus, unlike some (e.g., Smith 2009) we do not limit deliberative minipublics to designs in which participants are recruited by random sampling. Also, while we adopt the term ' citizen representative' for the sake of consistency with other authors, we note that deliberative minipublics frequently do not require citizenship as a precondition for participation (see Pinnington, Lerner, & Schugurensky 2009: 459). 3 For the purposes of this article, we adopt Fishkin's (2018) conception of political equality as the equal chance of influencing political outcomes. For a more thorough examination of political equality, see Robert Dahl (2006). 4 Political equality is not the only possible rationale for a random recruitment of participants. Another is that nonrandom methods are more susceptible to organiser bias (e.g., recruiting individuals who are more likely to agree with the views of the organisers). 5 Thus, we do not agree with Archon Fung's claim that random sampling 'guarantees that actual participants mirror the underlying population demographically' (Fung 2003: 354). 6 For example, adding a catchall category to each of three binary attributes would increase the number of possible intersections from 8 to 27. 7 Deliberative minipublics that aim to approximate the counterfactual public will might also be linked to decisions in this way. 8 Although a national level participatory budgeting scheme now exists in Portugal (https://opp.gov.pt/ english). 9 The NSC has carried on as a nonprofit organisation named the Guelph Neighbourhood Support Coalition (Pin 2016; see http://guelphneighbourhoods.org). 10 Relatedly, Hainz et al. (2016) suggest that the relevant concept of 'public' associated with a deliberative minipublic should be consistent with its aims, although they do not elaborate on the details of which concepts of 'public' go with which aims.