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Bentley's conjecture on popularity toplist turnover under random copying
Mälardalen University, School of Education, Culture and Communication. (CEK)ORCID iD: 0000-0002-7164-0924
Mälardalen University, School of Education, Culture and Communication. (CEK)
KTH.
2010 (English)In: The Ramanujan journal, ISSN 1382-4090, E-ISSN 1572-9303, Vol. 23, no 1, 371-396 p.Article in journal (Refereed) Published
Abstract [en]

Bentley et al. studied the turnover rate in popularity toplists in a 'random copying' model of cultural evolution. Based on simulations of a model with population size N, list length ℓ and invention rate μ, they conjectured a remarkably simple formula for the turnover rate: ℓ √μ. Here we study an overlapping generations version of the random copying model, which can be interpreted as a random walk on the integer partitions of the population size. In this model we show that the conjectured formula, after a slight correction, holds asymptotically.

Place, publisher, year, edition, pages
2010. Vol. 23, no 1, 371-396 p.
National Category
Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-11179DOI: 10.1007/s11139-010-9280-zISI: 000284594000025Scopus ID: 2-s2.0-78649677346OAI: oai:DiVA.org:mdh-11179DiVA: diva2:373833
Note

MERO

Available from: 2010-12-01 Created: 2010-12-01 Last updated: 2014-06-23Bibliographically approved
In thesis
1. Modelling Two-Person Interactions Within and Between Cultural Groups
Open this publication in new window or tab >>Modelling Two-Person Interactions Within and Between Cultural Groups
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The groups with which we associate influence our actions. This is often the case even when they are not deliberately organised but rather based on social categories, such as sex and skin colour, or cultural homogeneity, such as common language or customs. Group membership can cause widespread phenomena such as ingroup favouritism, polarisation of opinion and competition. Previous experiments have shown that these effects can be triggered by even completely arbitrary distinctions between groups. This thesis uses mathematical models to investigate under what circumstances these phenomena can arise.

Using a game theoretical approach, the first three papers address the evolution of ingroup favouritism. Previous models have focused on the prisoners’ dilemma, interactions where the socially optimal behaviour is to co-operate, but where it is in the individual’s self-interest not to. The results presented here suggest that co-ordination problems may have been more important than those of co-operation in the evolution of an ingroup bias. In particular, this applies to common goals that require trust. It is also demonstrated in a behavioural experiment that such trust is most common within groups, but that it can emerge between groups through group reputation.

The fourth paper focuses on a model on how cultural groups in contact can develop common norms, rather than polarise into different norm groups, by assuming a confirmation bias. The model is empirically tested on demographic and linguistic data from Mauritian Creole, a natural language developed from the mixing of parent languages.

In the fifth paper, the group is defined by common preferences (e.g. for pop songs), which are transmitted in a random copying model. The competitive success of the groups, with respect to their size, is recorded on a toplist, the turnover rate of which is derived.

In the final paper, people match up in pairs between groups according to their preferences, and all stable matchings are found under a specific assumption of bounded rationality, when people’s individual behaviour may be affected by the consequences for fellow group members.

Place, publisher, year, edition, pages
Västerås: Mälardalen University, 2013
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 136
Keyword
Mathematical modelling, cultural evolution
National Category
Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-16500 (URN)978-91-7485-100-7 (ISBN)
Public defence
2013-02-22, Lambda, Mälardalens högskola, Västerås, 13:15 (English)
Opponent
Supervisors
Available from: 2012-12-19 Created: 2012-12-10 Last updated: 2015-11-13Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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