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Università di Firenze |
Abstract
We
present a model of opinion formation of individuals with respect to a set
of products. We show that from the analysis of individual's opinion
we can reconstruct the knowledge networks of preferences and anticipate
the judgement about an unseen product.
In
geometrical words, one represents agent's preferences as a vector in an
hypothetical taste space, whose dimension and base vectors are unknown.
A product is represented by a similar vector (in dual space). Agent's opinion
on a given product is given by an operation analogous to the scalar product
between preferences and properties.
Therefore,
products acts like a basis, and opinions as agent's coordinates on such
a basis. However, differently from usual geometrical problems, we do not
know what the basis is, if it is complete, etc. We assume that all these
``internal'' degrees of fredom are hidden, and that the only observable
if Agent's opinion on a set of products.
The
main result of our analysis, is the possibility of extracting informations
about the hidden degrees of freedom, and in particular the dimensionality
of hidden space, from the opinion database. In this way customer's surveys
can be used as tools for studing brain functionality.
This
study is also important for establishing the importance of personal informations
and the need for their protection.