Quantification of deviations from rationality with heavy tails in human dynamics

Maillart, Thomas; Sornette, Didier; Frei, Stefan; Duebendorfer, Thomas; Саичев, А. И.

doi:10.1103/physreve.83.056101

Cited by 31 publications

(24 citation statements)

References 31 publications

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“…Here, we assume that with probability p the time of jump j(t) satisfies j(t)∼U(0, T) and with probability 1 − p no such jump occurs. This mirrors the construction of heavy-tailed queueing models in Maillart et al (2011) as well as sharing qualitative features of related models in Zeira (1997) and Fry (2015). In this case it follows that…”

Section: The Probability Modelsupporting

confidence: 57%

Bubbles, Blind-Spots and Brexit

Fry

Brint

2017

Risks

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Abstract:In this paper we develop a well-established financial model to investigate whether bubbles were present in opinion polls and betting markets prior to the UK's vote on EU membership on 23 June 2016. The importance of our contribution is threefold. Firstly, our continuous-time model allows for irregularly spaced time series-a common feature of polling data. Secondly, we build on qualitative comparisons that are often made between market cycles and voting patterns. Thirdly, our approach is theoretically elegant. Thus, where bubbles are found we suggest a suitable adjustment. We find evidence of bubbles in polling data. This suggests they systematically over-estimate the proportion voting for remain. In contrast, bookmakers' odds appear to show none of this bubble-like over-confidence. However, implied probabilities from bookmakers' odds appear remarkably unresponsive to polling data that nonetheless indicates a close-fought vote.

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Section: The Probability Modelsupporting

confidence: 57%

Bubbles, Blind-Spots and Brexit

Fry

Brint

2017

Risks

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“…The absolute value of the slope of this line approximates the scaling parameter α (Mandelbrot, ). Thus, in these graphs, the more the data follow a slowly downward‐sloping straight line (i.e., the less steep the negative slope), the heavier the tail of the distribution—as indicated by a smaller scaling exponent α (Clauset et al., ; Maillart, Sornette, Frei, Duebendorfer, & Saichev, ). Prior to the availability of the more precise fitting procedures that we used in our paper, distributions were considered to follow a power law if the data as shown in Figure generally follow a slowly downward‐sloping straight line when plotted on log–log scales (Clauset et al., ).…”

Section: Resultsmentioning

confidence: 99%

Cumulative Advantage: Conductors and Insulators of Heavy‐Tailed Productivity Distributions and Productivity Stars

Aguinis

O’Boyle

Gonzalez‐Mulé

et al. 2015

Personnel Psychology

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We use the metatheoretical principle of cumulative advantage as a framework to understand the presence of heavy-tailed productivity distributions and productivity stars. We relied on 229 datasets including 633,876 productivity observations collected from approximately 625,000 individuals in occupations including research, entertainment, politics, sports, sales, and manufacturing, among others. We implemented a novel methodological approach developed in the field of physics to assess the precise shape of the productivity distribution rather than relying on a normal versus nonnormal artificial dichotomy. Results indicate that higher levels of multiplicity of productivity, monopolistic productivity, job autonomy, and job complexity (i.e., conductors of cumulative advantage) are associated with a higher probability of an underlying power law distribution, whereas lower productivity ceilings (i.e., insulator of cumulative advantage) are associated with a lower probability. In addition, higher levels of multiplicity of productivity, monopolistic productivity, and job autonomy were associated with a greater proportion of productivity stars (i.e., productivity distributions with heavier tails), whereas lower productivity ceilings were associated with a The first and second authors contributed equally to this manuscript. We thank Berrin Erdogan for sharing data described in Erdogan and Bauer (2009);

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“…Models have been proposed based on queuing theory where incoming messages are replied to according to some prioritisation strategy [6][7][8]. By adjusting a parameter which controls the randomness of the strategy, these models have been shown to create power-law distributed inter-event times with exponents that agree with a number of real-world data-sets.…”

Section: Related Workmentioning

confidence: 99%

Memory and burstiness in dynamic networks

Colman

Greetham

2015

Phys. Rev. E

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A discrete-time random process is described which can generate bursty sequences of events. A Bernoulli process, where the probability of an event occurring at time t is given by a fixed probability x, is modified to include a memory effect where the event probability is increased proportionally to the number of events which occurred within a given amount of time preceding t. For small values of x the inter-event time distribution follows a power-law with exponent −2−x. We consider a dynamic network where each node forms, and breaks connections according to this process. The value of x for each node depends on the fitness distribution, ρ(x), from which it is drawn; we find exact solutions for the expectation of the degree distribution for a variety of possible fitness distributions, and for both cases where the memory effect either is, or is not present. This work can potentially lead to methods to uncover hidden fitness distributions from fast changing, temporal network data such as online social communications and fMRI scans. The mathematics of interactive complex systems has a vital role to play in the interpretation of large-scale social and biological data. Technology which facilitates the collection of vast amounts of information is increasingly becoming available for both academic and commercial purposes; however, in the absence of a detailed understanding of the underlying processes, there will always be a risk of deriving the wrong conclusion from the facts. Complexity science provides numerous models of social, biological, physical and economic systems which combine large numbers of individual components to reproduce the types of behaviour observed on the systemic level. The components in such systems are usually uninteresting in isolation, but when allowed to interact with each other they produce complex non-trivial patterns which in some cases agree very well with empirical results. This poses a challenge for data scientists: given information only about the system as a whole, with all its complex and interactive dynamics, how can one conclude anything about the individual components? To begin answering that question we need to understand, in mathematical terms, the form and extent of the biases that complexity creates.The purpose of the present work is to provide an understanding of how one very simple mechanism, a memory effect (brought about by interaction), will bias the statistical properties of a complex system such as the distribution of communication activity in a social network, or the distribution of brain activity of different cortical regions in a fMRI scan. We consider a hypothetical system of individual agents (nodes) and the instantaneous pairwise interactions which happen between them (edges). By aggregating all of the interactions that occur within some given time window, a network is formed whose structure can be analysed for a deeper understanding of the system. * E. Colman@Reading.ac.uk In general, the length of this time window determines the density of the network; as an incre...

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Quantification of deviations from rationality with heavy tails in human dynamics

Cited by 31 publications

References 31 publications

Bubbles, Blind-Spots and Brexit

Bubbles, Blind-Spots and Brexit

Cumulative Advantage: Conductors and Insulators of Heavy‐Tailed Productivity Distributions and Productivity Stars

Memory and burstiness in dynamic networks

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