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1. Suppose that we have the following "updating" matrix for a 4-person network. 0.3 0 0.4 0.37 1 0 0 0 0 0.5 0 0.5 0 00 1 A = (a) Labeling nodes 1-4, represent this updating matrix with a drawing of a directed network. Note that you will need to include self-links. (b) Which agent puts the least amount of weight on her own prior beliefs? Which one puts the most? For the one with the most, what happens to her beliefs over time? (c) Assuming this network reaches consensus (which is not guaranteed), what will its con- sensus belief be as too?

1. Suppose that we have the following "updating" matrix for a 4-person network. 0.3 0 0.4 0.37 1 0 0 0 0 0.5 0 0.5 0 00 1 A = (a) Labeling nodes 1-4, represent this updating matrix with a drawing of a directed network. Note that you will need to include self-links. (b) Which agent puts the least amount of weight on her own prior beliefs? Which one puts the most? For the one with the most, what happens to her beliefs over time? (c) Assuming this network reaches consensus (which is not guaranteed), what will its con- sensus belief be as too?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Suppose that we have the following "updating" matrix for a 4-person network. [0.3 0 0.4 0.3 1 0 0 0 0 0.5 0 0.5 0 1 0 0 A = (a) Labeling nodes 1-4, represent this updating matrix with a drawing of a directed network. Note that you will need to include self-links. (b) Which agent puts the least amount of weight on her own prior beliefs? Which one puts the most? For the one with the most, what happens to her beliefs over time? (c) Assuming this network reaches consensus (which is not guaranteed), what will its con- sensus belief be as t→ ∞o? (d) Discuss your answer in (c) in terms of "naive" learning. What is "naive" about this process? How would fully-Bayesian learning update in a more sophisticated way?
Transcribed Image Text:1. Suppose that we have the following "updating" matrix for a 4-person network. [0.3 0 0.4 0.3 1 0 0 0 0 0.5 0 0.5 0 1 0 0 A = (a) Labeling nodes 1-4, represent this updating matrix with a drawing of a directed network. Note that you will need to include self-links. (b) Which agent puts the least amount of weight on her own prior beliefs? Which one puts the most? For the one with the most, what happens to her beliefs over time? (c) Assuming this network reaches consensus (which is not guaranteed), what will its con- sensus belief be as t→ ∞o? (d) Discuss your answer in (c) in terms of "naive" learning. What is "naive" about this process? How would fully-Bayesian learning update in a more sophisticated way?
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