The non-linear q-voter model

We introduce a non-linear variant of the voter model, the q-voter model, in which q neighbors (with possible repetition) are consulted for a voter to change opinion. If the q neighbors agree, the voter takes their opinion; if they do not have an unanimous opinion, still a voter can flip its state with probability $\epsilon$. We solve the model on a fully connected network (i.e. in mean-field) and compute the exit probability as well as the average time to reach consensus. We analyze the results in the perspective of a recently proposed Langevin equation aimed at describing generic phase transitions in systems with two ($Z_2$ symmetric) absorbing states. We find that in mean-field the q-voter model exhibits a disordered phase for high $\epsilon$ and an ordered one for low $\epsilon$ with three possible ways to go from one to the other: (i) a unique (generalized voter-like) transition, (ii) a series of two consecutive Ising-like and directed percolation transition, and (iii) a series of two transitions, including an intermediate regime in which the final state depends on initial conditions. This third (so far unexplored) scenario, in which a new type of ordering dynamics emerges, is rationalized and found to be specific of mean-field, i.e. fluctuations are explicitly shown to wash it out in spatially extended systems.Comment: 9 pages, 7 figure

Erasing Red Lines: Part 3 - Building Community Wealth

Erasing Red Lines of discrimination and inequality from our map is a monumental task that will require transformational systems-change. As community-based organizations are demonstrating the possibilities of alternative systems in specific geographic places, the questions of (1) how to bring those efforts to scale, and (2) how public policies might change in response to the lessons learned from those efforts, require greater attention. Building on the previous installment of this series, this report engages with aspects of these two questions by: (a) further unpacking some of the beliefs, values, and goals that define the current economic system; (b) summarizing and synthesizing selected ideas from the literature to describe mental models that might underwrite a “next system”; and (c) relating a public policy case study from Buffalo, NY, in which a City-run program was redesigned to be a vehicle for bottom-up community empowerment as opposed to a tool for top-down command-and-control. The case study shows how the program redesign implicitly reflects, and explicitly embraces, some of the “next system” mental models that are outlined in the report. For these and other reasons, the program has received (inter)national recognition, and researchers have argued that it might offer budding insights for how local governments can begin reorienting their existing policies away from goals of growth that support the status quo, and toward goals of equity and community wealth-building. The report concludes with a summary of the case study’s practical lessons for policy development moving forward

Measuring voting power in convex policy spaces

Classical power index analysis considers the individual's ability to influence the aggregated group decision by changing its own vote, where all decisions and votes are assumed to be binary. In many practical applications we have more options than either "yes" or "no". Here we generalize three important power indices to continuous convex policy spaces. This allows the analysis of a collection of economic problems like e.g. tax rates or spending that otherwise would not be covered in binary models.Comment: 31 pages, 9 table