Though deliberation is a critical component of democratic decision-making, existing deliberative processes do not scale to large groups of people. Motivated by this, we propose a model in which large-scale decision-making takes place through a sequence of small group interactions. Our model considers a group of participants, each having an opinion which together form a graph. We show that for median graphs, a class of graphs including grids and trees, it is possible to use a small number of three-person interactions to tightly approximate the wisdom of the crowd, defined here to be the generalized median of participant opinions, even when agents are strategic. Interestingly, we also show that this sharply contrasts with small groups of size two, for which we prove an impossibility result. Specifically, we show that it is impossible to use sequences of two-person interactions satisfying natural axioms to find a tight approximation of the generalized median, even when agents are non-strategic. Our results demonstrate the potential of small group interactions for reaching global decision-making properties.
To our knowledge, we are not aware of other literature on algorithmic or mathematical models for scaling deliberation. However, the problem of scaling deliberation has been discussed in the political science community. Deliberation was initially conceptualized as an exchange of arguments among a small group of rational individuals. Recent developments acknowledge that deliberation should be thought of in richer ways, including as an activity that takes place at the system level, among groups. @cite_11 . In other words, it has recently become possible to think of deliberation as a task that can be broken down into various components and performed at different social levels and by large numbers of individuals. There have also been several practical initiatives for scaling deliberation such as Deliberative Polling @cite_12 , in which a single representative sample of participants is brought together to deliberate, and the 21st Century Town Hall Meeting @cite_10 , in which the entire set of participants are divided into tables of size @math for a single round of deliberation followed by voting.
@cite_10 @cite_12 @cite_11
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Over the last decade we have watched democracy surge and ebb around the world. With its firm commitment to strengthening democratic movements, the United States has encouraged, directly assisted in, and even led many democratization efforts. Yet to maintain a credible leadership role, we must acknowledge that our own democracy has much room for improvement. A healthy democracy depends on the ability of citizens1 to affect the public policies that deeply influence their lives, and ours does not currently allow citizens their rightful voice in decision making. Special-interest groups have captured the processes for democratic input. They have skewed the agenda toward extreme positions and alienated many citizens who would tend toward a middle ground. For this reason and many others, citizens distrust their elected officials, don’t vote, and are deeply cynical about government. Conversely, policy makers believe citizens hold fast to uninformed opinions and operate from self-interest. In the end, the gap between people and the decision-making processes that affect their lives continues to widen. Despite this state of affairs, our experience working with citizens in all regions of the country leaves us confident that people want to get involved and change things for the better. Unfortunately, the traditional methods our government has used for involving citizens give little inspiration for the public to reinvest in civic life. Public hearings and typical town hall meetings are not a meaningful way for citizens to engage in governance and to have an impact on decision making. They are speaker-focused, with experts simply delivering information or responding to questions. Little learning occurs, for citizens or decision makers, because airing individual concerns too often devolves into repetitive ax grinding, grandstanding, or even a shouting match between various stakeholders. In the end, decision makers don’t know which points of view have the most salience for 'Deliberative democracy' is often dismissed as a set of small-scale, academic experiments. This volume seeks to demonstrate how the deliberative ideal can work as a theory of democracy on a larger scale. It provides a new way of thinking about democratic engagement across the spectrum of political action, from towns and villages to nation states, and from local networks to transnational, even global systems. Written by a team of the world's leading deliberative theorists, Deliberative Systems explains the principles of this new approach, which seeks ways of ensuring that a division of deliberative labour in a system nonetheless meets both deliberative and democratic norms. Rather than simply elaborating the theory, the contributors examine the problems of implementation in a real world of competing norms, competing institutions and competing powerful interests. This pioneering book will inspire an exciting new phase of deliberative research, both theoretical and empirical.