Related papers: Maximal modularity and the optimal size of parliam…
Modularity is a quantity which has been introduced in the context of complex networks in order to quantify how close a network is to an ideal modular network in which the nodes form small interconnected communities that are joined together…
In exponentially proliferating populations of microbes, the population typically doubles at a rate less than the average doubling time of a single-cell due to variability at the single-cell level. It is known that the distribution of…
Can one hear the 'sound' of a growing network? We address the problem of recognizing the topology of evolving biological or social networks. Starting from percolation theory, we analytically prove a linear inverse relationship between two…
Liquid democracy is a novel paradigm for collective decision-making that gives agents the choice between casting a direct vote or delegating their vote to another agent. We consider a generalization of the standard liquid democracy setting…
Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is…
When delegations to an assembly or council represent differently sized constituencies, they are often allocated voting weights which increase in population numbers (EU Council, US Electoral College, etc.). The Penrose square root rule…
Liquid democracy is the principle of making collective decisions by letting agents transitively delegate their votes. Despite its significant appeal, it has become apparent that a weakness of liquid democracy is that a small subset of…
We address the problem of selecting $k$ representative nodes from a network, aiming to achieve two objectives: identifying the most influential nodes and ensuring the selection proportionally reflects the network's diversity. We propose two…
On the basis of a formula for calculating seat shares and natural thresholds in multidistrict elections under the Jefferson-D'Hondt system and a probabilistic model of electoral behavior based on P\'{o}lya's urn model, we propose a new…
Apportionment is the act of distributing the seats of a legislature among political parties (or states) in proportion to their vote shares (or populations). A famous impossibility by Balinski and Young (2001) shows that no apportionment…
There is both theoretical and numerical evidence that the set of irreducible representations of a reductive group over local or finite fields is naturally partitioned into families according to analytic properties of representations.…
This research paper talks about using complex mathematical tools to study and figure out the behavior of biological populations in porous media. Porous media offer a unique environment where various factors, including fluid flow and…
Elections for public offices in democratic nations are large-scale examples of collective decision-making. As a complex system with a multitude of interactions among agents, we can anticipate that universal macroscopic patterns could emerge…
Some argue that political stability is best served through a two-party system. This study refutes this. The author mathematically defines the stability and rigidity of electoral systems comprised of any quantity of electors and parties. In…
Primary law of the European Union demands that the allocation of the seats of the European Parliament between the Member States must obey the principle of degressive proportionality. The principle embodies the political aim that the more…
Using population data of high spatial resolution for a region in the south of Europe, we define cities by aggregating individuals to form connected clusters. The resulting cluster-population distributions show a smooth decreasing behavior…
We introduce a 2-state opinion dynamics model where agents evolve by majority rule. In each update, a group of agents is specified whose members then all adopt the local majority state. In the mean-field limit, where a group consists of…
Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the…
The Cambridge Compromise composition of the European Parliament allocates five base seats to each Member State's citizenry, and apportions the remaining seats proportionately to population figures using the divisor method with rounding…
The Majority Rule is applied to a topology that consists of two coupled random networks, thereby mimicking the modular structure observed in social networks. We calculate analytically the asymptotic behaviour of the model and derive a phase…