Vote Counting as Mathematical Proof

2015 ◽  
pp. 464-475 ◽  
Author(s):  
Dirk Pattinson ◽  
Carsten Schürmann
Keyword(s):  
Mathematical Proof ◽  
Vote Counting

Mathematical proof that rocked number theory will be published

Nature ◽  
2020 ◽  
Vol 580 (7802) ◽  
pp. 177-177
Author(s):  
Davide Castelvecchi
Keyword(s):  
Number Theory ◽  
Mathematical Proof

How do academics assess the results of multiple experiments?

2018 ◽  
Author(s):  
Olmo Van den Akker ◽  
Linda Dominguez Alvarez ◽  
Marjan Bakker ◽  
Jelte M. Wicherts ◽  
Marcel A. L. M. van Assen
Keyword(s):  
Bayesian Inference ◽  
Secondary Analysis ◽  
Individual Participant Data ◽  
Additional Experiment ◽  
Underlying Theory ◽  
Individual Participant ◽  
Vote Counting

We studied how academics assess the results of a set of four experiments that all test a given theory. We found that participants’ belief in the theory increases with the number of significant results, and that direct replications were considered to be more important than conceptual replications. We found no difference between authors and reviewers in their propensity to submit or recommend to publish sets of results, but we did find that authors are generally more likely to desire an additional experiment. In a preregistered secondary analysis of individual participant data, we examined the heuristics academics use to assess the results of four experiments. Only 6 out of 312 (1.9%) participants we analyzed used the normative method of Bayesian inference, whereas the majority of participants used vote counting approaches that tend to undervalue the evidence for the underlying theory if two or more results are statistically significant.

Electoral laws

2018 ◽  
Author(s):  
Richard L. Hasen
Keyword(s):  
Fake News ◽  
Election Administration ◽  
External Threats ◽  
Electoral Laws ◽  
Political Integrity ◽  
Voting Laws ◽  
Vote Counting

Chapter 2 provides an overview of the legal and political integrity issues raised in the 2016 elections. It begins by describing the now normal voting wars between the hyperpolarized parties, lawsuits aimed at shaping the rules for the registration of voters, the conduct of voting, and the counting of ballots. Restrictive voting laws have increased in number and severity in many states with Republican legislatures, and the judiciary itself often divides along partisan lines in determining controversial laws’ legality. The chapter then turns to the troubling escalation in the wars, from candidate Donald Trump’s unsubstantiated claims of fraud and election rigging to Russian (and other) meddling, the rise of “fake news,” and problems with vote-counting machinery and election administration. It concludes by considering the role that governmental and nongovernmental institutions can play in protecting American election administration from internal and external threats and restoring confidence in elections.

How is science to be carried forward, and its conclusions reported?

2018 ◽  
Author(s):  
Andrew Briggs ◽  
Hans Halvorson ◽  
Andrew Steane
Keyword(s):  
Mathematical Proof ◽  
Good Practice ◽  
Natural World ◽  
Component Part ◽  
Journal Articles ◽  
Scientific Publications ◽  
Direct Role ◽  
Intellectual Activity ◽  
Self Identity ◽  
The World

The chapter appraises science as an intellectual activity that is appropriately carried out on its own terms. Consequently, it is not appropriate to introduce references to God as a component part of a mathematical proof, nor of a system of forces in the natural world, nor of a sequence of impersonal processes in the biosphere. This does not mean that it is inappropriate to be thankful to God and to celebrate all these aspects of the world as gifts. They can be employed as opportunities to express appreciation through studying and understanding them better in their own right. Nevertheless, there may be processes, such as those which shape a person’s self-identity, in which it is appropriate to recognize God’s more direct role. Good practice concerning acknowledgements sections in scientific publications such as doctoral theses and journal articles is then discussed.

scholarly journals Nonlinear stability of two-layer shallow water flows with a free surface

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190594
Author(s):  
Francisco de Melo Viríssimo ◽  
Paul A. Milewski
Keyword(s):  
Free Surface ◽  
Initial Data ◽  
Nonlinear Stability ◽  
Mathematical Proof ◽  
Passive Layer ◽  
Physical Parameters ◽  
Immiscible Fluid ◽  
Dimensional System ◽  
The Cauchy Problem ◽  
The Difference

The problem of two layers of immiscible fluid, bordered above by an unbounded layer of passive fluid and below by a flat bed, is formulated and discussed. The resulting equations are given by a first-order, four-dimensional system of PDEs of mixed-type. The relevant physical parameters in the problem are presented and used to write the equations in a non-dimensional form. The conservation laws for the problem, which are known to be only six, are explicitly written and discussed in both non-Boussinesq and Boussinesq cases. Both dynamics and nonlinear stability of the Cauchy problem are discussed, with focus on the case where the upper unbounded passive layer has zero density, also called the free surface case. We prove that the stability of a solution depends only on two ‘baroclinic’ parameters (the shear and the difference of layer thickness, the former being the most important one) and give a precise criterion for the system to be well-posed. It is also numerically shown that the system is nonlinearly unstable, as hyperbolic initial data evolves into the elliptic region before the formation of shocks. We also discuss the use of simple waves as a tool to bound solutions and preventing a hyperbolic initial data to become elliptic and use this idea to give a mathematical proof for the nonlinear instability.

A Relationship Between the Factor Indivisibility and the Output Elasticity of the Indivisible Factor

2021 ◽  
pp. 232102222098516
Author(s):  
Dipankar Das
Keyword(s):  
Production Function ◽  
Limit Point ◽  
Mathematical Proof ◽  
Wage Equation ◽  
Marginal Value ◽  
Output Elasticity ◽  
New Type ◽  
First Time ◽  
Jel Classifications

The paper puts forth a notion and derives a special type of production function where labour is an indivisible factor and is in the integer space. Thus, Newtonian calculus is not an appropriate method of deriving the marginal value because limit point does not exist. This shows that indivisibility determines the output elasticity. In the first part, the paper propounds a notion regarding how indivisibility determines curvature of the production function. In the second part, the paper incorporates the findings within a production function and derives a new type accordingly. Moreover, it formally derives the standard wage equation considering all the entitlements of labour, namely (a) normal wages, (b) interest and (c) rent of ability. So far, no such mathematical proof is there to support this wage composition. This paper, for the first time, derives this wage equation considering indivisibility of labour. JEL Classifications: J23, J24, J31, D24, C61, E24, L8

scholarly journals The Link Between SRI and Financial Performance: Effects and Moderators

2013 ◽  
Vol 17 (2) ◽  
pp. 105-122 ◽  
Author(s):  
Christophe Revelli ◽  
Jean-Laurent Viviani
Keyword(s):  
Financial Performance ◽  
Meta Analysis ◽  
Socially Responsible Investment ◽  
Empirical Literature ◽  
Empirical Methods ◽  
Socially Responsible ◽  
Responsible Investment ◽  
Counting Approach ◽  
Performance Effects ◽  
Vote Counting

Over the last twenty years, the debate on financial performance of socially responsible investment (SRI) has not yielded a clear consensus, arguing mainly that there was no difference in performance between SRI and ‘conventional’ investment, although SRI could underperform or outperform in some cases. Our research, based on a meta-analysis ‘vote-counting’ approach of the empirical literature, allows us to observe that the effects of SRI on financial performance are multiple. Second, we conclude that the financial performance of SRI is radically changing according to the empirical methods employed by researchers.

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