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In the course of studies of the measure of chaos for the distribution of the prime numbers among the positive integers N arched structures have been found. It is given a brief description of the fine structure of the positive integers…

General Mathematics · Mathematics 2007-05-23 Andrei V. Vityazev , Galina V. Pechernikova

The 2016 Austrian presidential runoff election has been repealed by the Austrian constitutional court. The results of the counted votes had yielded a victory of Alexander van der Bellen by a margin of 30.863 votes as compared to the votes…

Applications · Statistics 2016-10-02 Erich Neuwirth , Walter Schachermayer

Donald Trump was lagging behind in nearly all opinion polls leading up to the 2016 US presidential election, but he surprisingly won the election. This raises the following important questions: 1) why most opinion polls were not accurate in…

Information Theory · Computer Science 2019-01-01 Weiyu Xu , Lifeng Lai , Amin Khajehnejad

We consider the performance of the foremost academic House of Representatives forecasting models in the 2018 elections. In creating open-source implementations of these models, we outline key underlying assumptions. We find that although…

Applications · Statistics 2018-12-03 Henry Bendekgey

The U.S. Supreme Court is currently deliberating over whether a proposed mathematical formula should be used to detect unconstitutional partisan gerrymandering. We show that in some cases, this formula will only flag bizarrely shaped…

Combinatorics · Mathematics 2017-10-27 Boris Alexeev , Dustin G. Mixon

This paper studies statistics of riffle shuffles by relating them to random word statistics with the use of inverse shuffles. Asymptotic normality of the number of descents and inversions in riffle shuffles with convergence rates of order…

Combinatorics · Mathematics 2013-03-12 Umit Islak

We use a method based on machine learning, big-data analytics, and network theory to process millions of messages posted in Twitter to predict election outcomes. The model has achieved accurate results in the current Argentina primary…

Social and Information Networks · Computer Science 2019-10-25 Zhenkun Zhou , Hernan A. Makse

Randomness in scientific estimation is generally assumed to arise from unmeasured or uncontrolled factors. However, when combining subjective probability estimates, heterogeneity stemming from people's cognitive or information diversity is…

Methodology · Statistics 2015-05-28 Ville Satopää , Robin Pemantle , Lyle Ungar

This paper uses daily Behavioral Risk Factor Surveillance System data to estimate the causal effect of the 2024 U.S. presidential election, a highly competitive race whose outcome resolved lingering uncertainty on election day, on…

General Economics · Economics 2025-11-10 Dongyoung Kim , Young-Il Albert Kim , Haedong Aiden Rho

In this article we study asymptotic behavior of the probability that a random monic polynomial with integer coefficients is irreducible over the integers. We consider the cases where the coefficients grow together with the degree of the…

Probability · Mathematics 2022-04-29 Grigory Terlov

We introduce and study isomorphic distances between ordinal elections (with the same numbers of candidates and voters). The main feature of these distances is that they are invariant to renaming the candidates and voters, and two elections…

Computer Science and Game Theory · Computer Science 2026-01-28 Piotr Faliszewski , Piotr Skowron , Arkadii Slinko , Krzysztof Sornat , Stanisław Szufa , Nimrod Talmon

Political advertising on digital platforms has grown dramatically in recent years as campaigns embrace new ways of targeting supporters and potential voters. Previous scholarship shows that digital advertising has both positive effects on…

Computers and Society · Computer Science 2020-12-11 NaLette Brodnax , Piotr Sapiezynski

We consider self-averaging sequences in which each term is a weighted average over previous terms. For several sequences of this kind it is known that they do not converge to a limit. These sequences share the property that $n$th term is…

Probability · Mathematics 2016-10-04 Eric Cator , Henk Don

The prime numbers look like a randomly chosen sequence of natural numbers, but there is still no strict theory to determine 'Randomness'. In these years, cryptography has developed a battery of statistical tests for randomness. In this…

Number Theory · Mathematics 2011-02-19 Wang Liang , Huang Yan

We study the group Russian roulette problem, also known as the shooting problem, defined as follows. We have $n$ armed people in a room. At each chime of a clock, everyone shoots a random other person. The persons shot fall dead and the…

Probability · Mathematics 2017-05-02 Tim van de Brug , Wouter Kager , Ronald Meester

Correlated proportions arise in longitudinal (panel) studies. A typical example is the ``opinion swing'' problem: ``Has the proportion of people favoring a politician changed after his recent speech to the nation on TV?''. Since the same…

Statistics Theory · Mathematics 2007-07-27 Guido Consonni , Luca La Rocca

The increasing cost of electoral campaigns raises the need for effective campaign planning and a precise understanding of the return of such investment. Interestingly, despite the strong impact of elections on our daily lives, how this…

In this paper, we apply genetic algorithms to the field of electoral studies. Forecasting election results is one of the most exciting and demanding tasks in the area of market research, especially due to the fact that decisions have to be…

Neural and Evolutionary Computing · Computer Science 2014-01-21 Ronald Hochreiter , Christoph Waldhauser

This is a short survey on existing upper and lower bounds on the probability of the union of a finite number of events using partial information given in terms of the individual or pairwise event probabilities (or their sums). New proofs…

Probability · Mathematics 2017-10-23 Jun Yang , Fady Alajaji , Glen Takahara

We consider the problem of predicting winners in elections, for the case where we are given complete knowledge about all possible candidates, all possible voters (together with their preferences), but where it is uncertain either which…

Computer Science and Game Theory · Computer Science 2016-03-27 Krzysztof Wojtas , Krzysztof Magiera , Tomasz Miąsko , Piotr Faliszewski
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