Extending difference of votes rules on three voting models.

This paper combines social choice theory with mathematical optimization by applying various group decision concepts to a classical problem of combinatorial optimization, namely the famous traveling salesperson (sales- man) problem. The aim of the latter is to find a tour through all vertices of a given graph along edges of minimal total cost. In this contribution we replace the measure of additive edge costs by the social acceptance of different edges and the resulting tours. In particular, for four different voting rules, the Borda rule, Approval voting, Plurality rule and Simple Majority rule, we will investi- gate the social acceptance of tours derived from global and local decisions. It will be shown that these two decision approaches can lead to widely varying results.

When Do Conflicting Parties Share Political Power? An Experimental Study

The evaluation of majority rules in a legislative bargaining model

Short-Term Deviations from Simple Majority Voting

Dynamic Stability and Reform of Political Institutions

This chapter explores the debate about the debate and two procedures that US senators use to extend and close the debate: filibuster and cloture. I first outline the history of the filibuster and cloture. Within the debate about the debate are two controversies: the senate as an exclusive deliberative body, and the meaning of majority rule. I show how the exclusive deliberative body theory envisioned by James Madison, Alexander Hamilton, and George Washington has devolved to where the Senate has become more like the House. Majority rule, because of changes made to cloture, has become more like what the framers of the Constitution likely envisioned: simple majority rule.

Let P(n, 4) denote the probability that there is a pairwise simple majority rule winner on four candidates with n voters under the impartial anonymous culture condition. Similarly, let Pt(n, 4) denote the probability that the complete ranking obtained by pairwise simple majority voting on four candidates with n voters is transitive under the impartial anonymous culture condition. We obtain representations for P(n, 4) and Pt(n, 4), and computed values for each for odd n with 3 ≤ n ≤ 19.

public choice theory to familiarize themselves with the masterworks in political theory. [6, 99-101] With this call for broader scholarship in mind, we were impressed in a recent reading of Aristotle's Politics with two aspects of his thought that, in our opinion, should be brought to the attention of modern scholars. First, we examine Aristotle's commentary on voting rules and propose a resolution of an important conflict in the literature interpreting his position on majority rule. Second, we examine Aristotle's general, but not unqualified, belief, presented mainly in analogies, that the collective wisdom of a people was superior to that of the lawgiver's. The main question that we address is whether this superior wisdom was to be embodied in the degree of restrictiveness in the voting rule or in the limits of suffrage. We show that under the former interpretation Aristotle hypothesized an important link between the restrictiveness of the voting rule and the amount of information that is brought to bear in making collective decisions. This is a link perhaps overlooked by modern writers on public choice, and we examine its effect in a model of the optimal voting rule, originally developed by J. M. Buchanan and G. Tullock, to observe its impact on the minimum cost decision rule. [7, 63-84]

Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements but only up to a global phase ambiguity. This work proposes a novel approach to achieve ambiguity-free signal reconstruction using the magnitude of affine measurements, where an additional bias term is used as reference for phase recovery. The proposed scheme consists of two stages, i.e., a support identification stage followed by a signal recovery stage in which the nonzero signal entries are resolved. In the noise-free case, perfect support identification is guaranteed using a simple counting rule subject to a mild condition on the signal sparsity, and the exact recovery of the nonzero signal entries can be obtained in closed-form. The proposed scheme is then extended to the sparse noise (or outliers) scenario. Perfect support identification is still ensured in this case under mild conditions on the support size of the sparse outliers. With perfect support estimation, exact signal recovery from noisy measurements can be achieved using a simple majority rule. Computer simulations using both synthetic and real-world data sets are provided to demonstrate the effectiveness of the proposed scheme.

It is well known that human beings do not always change opinions or attitudes, since the duration of interaction with others usually has a significant impact on one's decision-making. Based on this observation, we introduce a freezing period into the voter model, in which the frozen individuals have a weakened opinion switching ability. We unfold the presence of an optimal freezing period, which leads to the fastest consensus, using computation simulations as well as theoretical analysis. We demonstrate that the essence of an accelerated consensus is attributed to the biased random walk of the interface between adjacent opinion clusters. The emergence of an optimal freezing period is robust against the size of the system and the number of distinct opinions. This study is instructive for understanding human collective behavior in other relevant fields.

We study the dynamics of a class of two dimensional stochastic processes,\ndepending on two parameters, which may be interpreted as two different\ntemperatures, respectively associated to interfacial and to bulk noise. Special\nlines in the plane of parameters correspond to the Ising model, voter model and\nmajority vote model. The dynamics of this class of models may be described\nformally in terms of reaction diffusion processes for a set of coalescing,\nannihilating, and branching random walkers. We use the freedom allowed by the\nspace of parameters to measure, by numerical simulations, the persistence\nprobability of a generic model in the low temperature phase, where the system\ncoarsens. This probability is found to decay at large times as a power law with\na seemingly constant exponent $\\theta\\approx 0.22$. We also discuss the\nconnection between persistence and the nature of the interfaces between\ndomains.\n

This is an advance summary of a forthcoming article in the Oxford Research Encyclopedia of Politics. Please check back later for the full article.Narrowly understood, social choice theory is a specialized branch of applied logic and mathematics that analyzes abstract objects called preference aggregation functions, social welfare functions, and social choice functions. But more broadly, social choice theory identifies, analyzes, and evaluates rules that may be used to make collective decisions. So understood, social choice is a subfield of the social sciences that examines what may be called “voting rules” of various sorts. While social choice theory typically assumes a finite set of alternatives over which voter preferences are unrestricted, the spatial model of social choice assumes that policy alternatives can be represented by points in a space of one or more dimensions, and that voters have preferences that are plausibly shaped by this spatial structure.Social choice theory has considerable relevance for the study of legislative (as well as electoral) institutions. The concepts and tools of social choice theory make possible formal descriptions of legislative institutions such as bicameralism, parliamentary voting procedures, effects of decision rules (e.g., supramajority vs. simple majority rule and executive veto rules), sincere vs. strategic voting by legislators, agenda control, and other parliamentary maneuvers. Spatial models of social choice further enrich this analysis and raise additional questions regarding policy stability and change. Spatial models are used increasingly to guide empirical research on legislative institutions and processes.

There exists a large literature on two-person bargaining games and distribution games (or divide-the-dollar games) under simple majority rule, where in equilibrium a minimal winning coalition takes full advantage over everyone else. Here we extend the study to an n-person veto game where players take turns proposing policies in an n-dimensional policy space and everybody has a veto over changes in the status quo. Briefly, we find a Nash equilibrium where the initial proposer offers a policy in the intersection of the Pareto optimal set and the Pareto superior set that gives everyone their continuation values, and punishments are never implemented. Comparing the equilibrium outcomes under two different agendas – sequential recognition and random recognition – we find that there are advantages generated by the order of proposal under the sequential recognition rule. We also provide some conditions under which the players will prefer to rotate proposals rather than allow any specific policy to prevail indefinitely.

Two main objectives of Computational Textual Criticism are the development of algorithms for tree and text reconstruction under conditions of imperfect copying. Despite recent developments in the field, few comparative studies or benchmarks have been performed, particularly in the case of text reconstruction. On the other hand, recent advancements in Natural Language Processing (NLP) have begun to impact various aspects of the humanities and social sciences. In this paper, we incorporate various NLP techniques (including Large Language Models (LLMs)) to simulate text transmission and benchmark different tree and text reconstruction algorithms. In addition, for text reconstruction, we incorporate LLMs to improve the final result. Our results show that the Unweighted Pair Group Method with Arithmetic Mean (UPGMA) or Neighbor Joining (NJ) methods combined with the Levenshtein metric achieved superior comparative results for tree reconstruction. Moreover, for text reconstruction, we found that the Simple Majority Rule (SMR), UR, and Roos-Heikkilä-Myllymäki (RHM) methods yielded consistent results, and in most cases, the incorporation of LLMs improved the final output.

Submajority Rules: Forcing Accountability upon Majorities