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Journal article
Simon's fundamental rich-get-richer model entails a dominant first-mover advantage
Physical review. E, v 95(5), pp 052301-052301
01 May 2017
PMID: 28618612
Abstract
Herbert Simon's classic rich-get-richer model is one of the simplest empirically supported mechanisms capable of generating heavy-tail size distributions for complex systems. Simon argued analytically that a population of flavored elements growing by either adding a novel element or randomly replicating an existing one would afford a distribution of group sizes with a power-law tail. Here, we show that, in fact, Simon's model does not produce a simple power-law size distribution as the initial element has a dominant first-mover advantage, and will be overrepresented by a factor proportional to the inverse of the innovation probability. The first group's size discrepancy cannot be explained away as a transient of the model, and may therefore be many orders of magnitude greater than expected. We demonstrate how Simon's analysis was correct but incomplete, and expand our alternate analysis to quantify the variability of long term rankings for all groups. We find that the expected time for a first replication is infinite, and show how an incipient group must break the mechanism to improve their odds of success. We present an example of citation counts for a specific field that demonstrates a first-mover advantage consistent with our revised view of the rich-get-richer mechanism. Our findings call for a reexamination of preceding work invoking Simon's model and provide an expanded understanding going forward.
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Details
- Title
- Simon's fundamental rich-get-richer model entails a dominant first-mover advantage
- Creators
- Peter Sheridan Dodds - University of VermontDavid Rushing Dewhurst - University of VermontFletcher F. Hazlehurst - University of VermontColin M. Van Oort - University of VermontLewis Mitchell - The University of AdelaideAndrew J. Reagan - University of VermontJake Ryland Williams - Drexel UniversityChristopher M. Danforth - University of Vermont
- Publication Details
- Physical review. E, v 95(5), pp 052301-052301
- Publisher
- Amer Physical Soc
- Number of pages
- 7
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Information Science
- Web of Science ID
- WOS:000400671000001
- Scopus ID
- 2-s2.0-85019035879
- Other Identifier
- 991021806674904721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Physics, Fluids & Plasmas
- Physics, Mathematical