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In "Definitions", isn't 1. already guaranteed by the fact that knowledge spaces are closed under union? Because K is the set of feasible subsets of concepts... Antoine Ponsard (talk) 06:28, 13 December 2013 (UTC)[reply]

Er, yes, the second bullet and numbered item 1 appear to be the same as each other. Maybe an appropriate fix would be to say that a learning space is a family of sets that obeys those two properties, without calling them additional properties, and then observe that every learning space is a knowledge space? But feel free to just take out the redundant property and state that a learning space is a knowledge space that is also accessible, if you think that would be clearer. —David Eppstein (talk) 07:35, 13 December 2013 (UTC)[reply]

I am sorry not to have a specific reference, but around 2000 I ran across and article written a mathematical biology journal by a Russian engineer/mathematician which defined "Mass Media" along the lines of a limited sphere of allowed concepts. It seems to me that the same type of math would apply. — Preceding unsigned comment added by 172.78.105.9 (talk) 05:27, 29 May 2017 (UTC)[reply]

Falmagne and his co-authors have done some work applying similar theories to mass-media influence in political campaigns that may be related to your question. See:

• A stochastic model of preference change and its application to 1992 presidential election panel data. M Regenwetter, JC Falmagne, B Grofman, Psychological Review, 1999
• The tune in-and-out model: A random walk and its application to a presidential election survey, YF Hsu, M Regenwetter, JC Falmagne, Journal of Mathematical Psychology, 2005

As I understand it the first paper defines a model in which each potential voter has a preference that can be described as a weak ordering on the candidates, and in response to media messages can change that ordering in small incremental steps (merging two groups of candidates that were consecutive into a single group that is tied in the ordering, or splitting a tied group into two consecutive groups). The second paper modifies the model by assuming that a voter can either be paying attention to media messages (allowing the sort of changes described above) or not paying attention (in which case their preference is frozen). The structure of the system of possible states of a voter, and transitions between those states, resembles in many important respects the structure of a knowledge space. I don't suppose the Russian would be Sergei Ovchinnikov? He has also worked with Falmagne (and me) on this topic. —David Eppstein (talk) 06:14, 29 May 2017 (UTC)[reply]