Related papers: A Fibonacci sequence for linear structures with tw…
In this paper, we derive several formulas of counting families of non-intersecting paths for two-sided ladder-shaped regions. As an application, we give a new proof to a combinatorial interpretation of Fibonacci numbers obtained by G.…
The outcomes of democratic elections rest on individuals' decision-making that is driven by their varying preferences and beliefs. Individuals may prefer consensus to gridlock, or gridlock to consensus, and information may be fractured via…
We consider a setting with agents that have preferences over alternatives and are partitioned into disjoint districts. The goal is to choose one alternative as the winner using a mechanism which first decides a representative alternative…
The Fibonacci sequence $\mathbb{F}$ is the fixed point beginning with $a$ of morphism $\sigma(a,b)=(ab,a)$. Since $\mathbb{F}$ is uniformly recurrent, each factor $\omega$ appears infinite many times in the sequence which is arranged as…
We analyse the structure and behaviour of a specific voting network using a dynamic structure-based methodology which draws on Q-Analysis and social network theory. Our empirical focus is on the Eurovision Song Contest over a period of 20…
This paper provides a serious attempt towards constructing a switching-algebraic theory for weighted monotone voting systems, whether they are scalar-weighted or vector-weighted. The paper concentrates on the computation of a prominent…
This paper formalizes the lattice structure of the ballot voters cast in a ranked-choice election and the preferences that this structure induces. These preferences are shown to be counter to previous assumptions about the preferences of…
We present a model for quantitatively identifying swing voters in congressional elections. This is achieved by predicting an individual voter's likelihood to vote and an individual voter's likelihood to vote for a given party, if he votes.…
A binary matrix can be scanned by moving a fixed rectangular window (submatrix) across it, rather like examining it closely under a microscope. With each viewing, a convenient measurement is the number of 1s visible in the window, which…
A class of determinants is introduced. Different kind of mathematical objects, such as Fibonacci, Lucas, Tchebychev, Hermite, Laguerre, Legendre polynomials, sums and covergents are represented as determinants from this class. A closed…
We consider multicolor urn models with multiple drawings. An urn model is called linear if the conditional expected value of the urn composition at time $n$ is a linear function of the composition at time $n-1$. For four different sampling…
In this paper, we construct Pell matrices, analogous to Fibonacci matrices, to study algebraic properties of Pell numbers via linear algebra. This framework yields identities involving the trace, inverse, and determinant, as well as matrix…
In this paper, we discuss a voting model with two candidates, C_0 and C_1. We consider two types of voters--herders and independents. The voting of independents is based on their fundamental values; on the other hand, the voting of herders…
Fibonacci numbers can be expressed in terms of multinomial coefficients as sums over integer partitions into odd parts. We use this fact to introduce a family of double inequalities involving the generating function for the number of…
A recently proposed model of social interaction in voting is investigated by simplifying it down into a version that is more analytically tractable and which allows a mathematical analysis to be performed. This analysis clarifies the…
Candidate control of elections is the study of how adding or removing candidates can affect the outcome. However, the traditional study of the complexity of candidate control is in the model in which all candidates and votes are known up…
Many hardness results in computational social choice make use of the fact that every directed graph may be induced as the pairwise majority relation of some preference profile. However, this fact requires a number of voters that is almost…
We investigate winner determination for two popular proportional representation systems: the Monroe and Chamberlin-Courant (abbrv. CC) systems. Our study focuses on (nearly) single-peaked resp. single-crossing preferences. We show that for…
We analyze the winning coalitions that arise under Bloc voting when voters preferences are single-peaked. For small numbers of candidates and numbers of winners, we determine conditions under which candidates in winning coalitions are…
We study a binary dynamical process that is a representation of the voter model with opinion makers. The process models an election with two candidates but can also describe the frequencies of a biallelic gene in a population or atoms with…