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
1514522744 1480441807 2963204789 1971118040
Are we the kind of creatures who are suited to govern ourselves through deliberation? We seek to answer one important component of this question: how do individuals respond to deliberation in groups with varying levels of disagreement? We use a natural experiment in which approximately 3000 individuals were divided into small groups composed of about 8-10 persons. These groups deliberated for one day about health care reform in California. We demonstrate that there is a non-monotonic effect of disagreement upon deliberative quality. Elements of deliberative quality include mutual respect, understanding, proferring of reasons and arguments, equal opportunity for discursive engagement, and neutrality. Deliberative quality is maximized at moderate levels of disagreement and lower at high levels of ideological agreement or disagreement. Furthermore, individuals exhibit higher levels of persuasion in deliberative contexts of moderate disagreement. These findings support the view that many individuals have elements of a political psychology that is well suited for deliberation. They do not recoil when encountering disagreement nor do they especially value deliberating with those who see the world in very similar ways. Instead, they regard as most successful deliberations with moderate levels of difference -- perhaps those in which they were acquire new information, perspectives, or reasons. Beyond our substantive finding, this paper offers a methodological template for experimental studies of deliberation. '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. We present theoretical and empirical results demonstrating the usefulness of social choice functions in crowdsourcing for participatory democracies. First, we demonstrate the scalability of social choice functions by defining a natural notion of epsilon-approximation, and giving algorithms which efficiently elicit such approximations for two prominent social choice functions: the Borda rule and the Condorcet winner. This result circumvents previous prohibitive lower bounds and is surprisingly strong: even if the number of ideas is as large as the number of participants, each participant will only have to make a logarithmic number of comparisons, an exponential improvement over the linear number of comparisons previously needed. Second, we apply these ideas to Finland's recent off-road traffic law reform, an experiment on participatory democracy in real life. This allows us to verify the scaling predicted in our theory and show that the constant involved is also not large. In addition, by collecting data on the time that users take to complete rankings of varying sizes, we observe that eliciting partial rankings can further decrease elicitation time as compared to the common method of eliciting pairwise comparisons. A voter sits on each vertex of an infinite tree of degree @math , and has to decide between two alternative opinions. At each time step, each voter switches to the opinion of the majority of her neighbors. We analyze this majority process when opinions are initialized to independent and identically distributed random variables. In particular, we bound the threshold value of the initial bias such that the process converges to consensus. In order to prove an upper bound, we characterize the process of a single node in the large @math -limit. This approach is inspired by the theory of mean field spin-glass and can potentially be generalized to a wider class of models. We also derive a lower bound that is nontrivial for small, odd values of @math .