Granular DeGroot Dynamics -- a Model for Robust Naive Learning in Social Networks
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866910308959780864 |
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| author | Amir, Gideon Arieli, Itai Ashkenazi-Golan, Galit Peretz, Ron |
| author_facet | Amir, Gideon Arieli, Itai Ashkenazi-Golan, Galit Peretz, Ron |
| contents | We study a model of opinion exchange in social networks where a state of the world is realized and every agent receives a zero-mean noisy signal of the realized state. It is known from [Golub and Jackson 2010] that under DeGroot dynamics [DeGroot 1974] agents reach a consensus that is close to the state of the world when the network is large. The DeGroot dynamics, however, is highly non-robust and the presence of a single ``stubborn agent'' that does not adhere to the updating rule can sway the public consensus to any other value. We introduce a variant of DeGroot dynamics that we call \emph{ $\frac{1}{m}$-DeGroot}. $\frac{1}{m}$-DeGroot dynamics approximates standard DeGroot dynamics to the nearest rational number with $m$ as its denominator and like the DeGroot dynamics it is Markovian and stationary. We show that in contrast to standard DeGroot dynamics, $\frac{1}{m}$-DeGroot dynamics is highly robust both to the presence of stubborn agents and to certain types of misspecifications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_11768 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Granular DeGroot Dynamics -- a Model for Robust Naive Learning in Social Networks Amir, Gideon Arieli, Itai Ashkenazi-Golan, Galit Peretz, Ron Probability Discrete Mathematics Social and Information Networks Physics and Society 91D30, 60C05 We study a model of opinion exchange in social networks where a state of the world is realized and every agent receives a zero-mean noisy signal of the realized state. It is known from [Golub and Jackson 2010] that under DeGroot dynamics [DeGroot 1974] agents reach a consensus that is close to the state of the world when the network is large. The DeGroot dynamics, however, is highly non-robust and the presence of a single ``stubborn agent'' that does not adhere to the updating rule can sway the public consensus to any other value. We introduce a variant of DeGroot dynamics that we call \emph{ $\frac{1}{m}$-DeGroot}. $\frac{1}{m}$-DeGroot dynamics approximates standard DeGroot dynamics to the nearest rational number with $m$ as its denominator and like the DeGroot dynamics it is Markovian and stationary. We show that in contrast to standard DeGroot dynamics, $\frac{1}{m}$-DeGroot dynamics is highly robust both to the presence of stubborn agents and to certain types of misspecifications. |
| title | Granular DeGroot Dynamics -- a Model for Robust Naive Learning in Social Networks |
| topic | Probability Discrete Mathematics Social and Information Networks Physics and Society 91D30, 60C05 |
| url | https://arxiv.org/abs/2102.11768 |