This site is associated with projects to make society work through the development of social systems software. For these projects, a profile is a sequence of numbers which describe a person. A linear profile is one in which can be transformed into an equally correct one with a linear transform, as defined in the field of linear algebra.
For the purposes of these projects, the linear profiles are verifiable in that the users cannot directly edit the records containing them, to make themselves appear better or different than they are.
This is one of several sites for the application of mathematical methods in society. Some of the others are:
- estimation for decision making
- error covariance minimization
- bipartite matching
- social combinatorics
- social network optimization
Other methods are discussed in sites created to explain and promote various aspects of social technology.
Most of these methods involve some form of profile. When the goals are social, these are often personality profiles, but from these many others can be derived, as long as the profiles are linear. The question of linearity is discussed elsewhere.
For example, a profile for a job can be derived as a weighted sum of the profiles of individuals who do that job, weighted according to job satisfaction and performance.
A profile for a place to live can be derived as a weighted sum of the profiles of individuals who live there or near there, weighted by proximity and their satisfaction of the area as a place to live.
A profile for a person’s place in the social network can be derived as a weighted sum of the profiles of nearby individuals in the network, weighted by familiarity and compatibility.
If the person’s individual personality profile were expressed in, say, a 10 component vector, then 30 additional components can be added from those of the person’s job, place to live and position in the social network. If a very large and diverse sample of these 40 component vectors are supplied, factor analysis can be used to reduce the dimensionality of the space back to 10. These could be a much more accurate profile description of the individual. This process may be iterated, with significant improvements each time, provided sufficiently large and diverse samples of individuals are used.
The results of this kind of analysis are not only accurate profiles for individual people, but for jobs and places to live. Since they are all derived from the profiles for individual people, they are in the same abstract space, which makes it easy to use weighted matching procedures to find suitable jobs and places to live for people. The use of weighted bipartite matching to find lovers or spouses, part of a person’s social network, is discussed elsewhere.