Hybrid schema

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The hybrid schema is a simulation model that tries to use swar schema norm spec's to help solve for maxhi schema optima. The idea is that each pubwan participant has a norm set represented in the pub wan database. This normset specifies which parameters that participant wants to maximize or minimize, along with information about which parameters have highest priority. To operate the hybrid schema, both participants and pubwan virtual object's are represented as vertices in a graph. Both participants and objects are assumed to have attractions and repulsions between them. There is assumed to be an "attractive force" between a participant who wishes to maximize some parameter p, and an object whose specification sheet indicates an unusually high value for parameter p. The magnitude of this force is larger given a larger value of the parameter in the object, and also larger given a higher priority according to the partitipant's norms.

I'll use myself as an example of a pubwan participant. This makes sense, since as far as I know, I'm the only one in existence. :-P I'll use edible grocery items as pubwan virtual objects. For the present discussion, the specification sheet will consist of the "Nutrition Information" on the package, combined with the price of the package. Here is my normset for this class of virtual pubwan objects:

Aran Velema
calories minlo minhi
total fat minlo minhi
saturated fat minlo minhi
polyunsaturated fat maxlo maxhi
monounsaturated fat minlo minhi
cholesterol minlo minhi
sodium minlo minhi
potassium maxlo maxhi
fiber maxlo maxhi
sugar minlo minhi
protein maxlo maxhi
price minhi minlo

For our analysis, the amounts of the various nutrients would be "per container," not "per serving." These can be obtained simply by multiplying the "per serving" amounts by the "servings per container" given in "Nutrition Information" on most packaged foods sold in the U.S. "Aran" would represent my current norms, and "Velema" would represent my norms if my income were higher. Running an attraction/repulsion (swar schema) simulation with the Aran and Velema participants and a few thousand grocery items might yield some insights on consumer utility.

The value of "adjacency" between a vertex representing a participant and one representing a pubwan virtual object (in this case a packaged food item) could be the specification, times 1 or -1 (depending on whether it is maximized or minimized, respectively), times 1 or 2 (depending on low or high priority, respectively). In addition to adjacency values based on normsets, there should be adjacency relationships between food objects, Along the lines of "like repels like." Protein grams repel protein grams, Vitamin A units repel Vitamin A units, etc. This ensures that the immediate neighbors of a participant vector not only represent the participant's preferences and priorities, but also comprise a diversified "food portfolio."

In short, in the hybrid schema attractive or repulsive forces between individuals and goods reflect norm set's, while forces between goods reflect complementarity (attract) or substitutability (repel) of goods.

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