Pseudoscience of Criminal Predisposition of an Individual Based on Facial Characteristics, Mathemati
The concept of anthropological criminology is focused primarily on the premise that a criminal potential is inherited. Lombroso's general theory suggested that such a "born criminal" would bear certain physiological abnormalities or specific characteristics. Nowadays, this concept is perceived as rather controversial and does not have much of a scientific support. To this day, a correlation between criminal predisposition of an individual and physiological characteristics was not proved to be existent.
Cesare Lombroso, born Ezechia Marco Lombroso, 6 November 1835 - 19 October 1909, founder of the Italian School of Positivist Criminology
For this particular little thought experiment, let us presume that there could indeed be found some correlation between criminal predisposition and facial characteristics of an individual. The question would now be how to objectively quantify it. As there is a clear lack of any analytical solution to this problem, we are left solely with enumerating methods. Then, we will be able to at least come with a probability solution.
Let us assume that we have acces to a database of convicted criminals, D, with n subjects. For each subject, there is a vertical vector VA, of enumerated specific facial characteristics and a vertical vector VB, of crime convictions, binarily enumerated as 0 or 1 for each crime. For example, let us say that the subject n was convicted of theft and theft is the third of r crimes in vector B. Subject n would then have vector VAn=[c1,c2,c3,...ci] and vector VBn=[0,0,1,0,...r*0].
The general principle of analysis would then be as follows. As input, we will use a known specific vector VAn. Vector VBn would be unknown. We would have to create a number of subdatabases of database D, based on the vector VAn. For given value of ci, we would create a subdatabase Ci, of ni subjects, which would fit the range of (ci +- given tolerance). A predisposition αr of subject n, for the crime ωr could then be described as follows.
(left) probability for specific crime r, (right) probability vector (vertical)
SINGLE-FEATURE METHOD:
For each facial feature given from vector VAn, we would have to create specific subdatabase Ci. Let us say we have m facial features. Then, we will have m subdatabases. As sum through all those databases, we shall be given a percentage of crime convictions, based on single facial features. The mathematical form for analysis would be:
DOUBLE-FEATURE METHOD
For this method, we would need to create specific subdatabases of database D, fitting not one, but two criteria. For example, (c1 +- given tolerance), (c2 +-given tolerance). Then as sum through all possible valid combinations, we shall be given a percentage of crime convictions, based on coupled criteria of facial features. The mathematical form for analysis would be:
TRIPLE-FEATURE METHOD
In principle, a double-feature method with a third iteration, selecting triplets instead of couples of facial features. A more complex method, creating subdatabases that fits three criterias, for example: (c1 +- given tolerance), (c2 +- given tolerance), (c3 +- given tolerance). As a sum through all possible valid combinations, we shall be given a percentage of crime convictions, based on triplets of facial feature criteria. The mathematical form for analysis would be:
CONCLUSION
Such methods of elementary arithmetics could tell us once and for all, if there really is a correlation between facial features and crime predisposition of an individual. Although, other factors would be needed to be taken into account, such as race, nationality, geolocation, social status, age, gender.. These factors should divide the master database, for the sake of statistical accuracy.
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