## Network Theory and Ordered Set Theory Used for Addressing Crime in Jamaica and Haiti

Kevin Blake

Assistant Superintendent of Police

Jamaica Constabulary Force

Ministry of National Security

#### Abstract:

Law enforcement organizations are always seeking to find the most efficient and cost effective ways of utilizing limited resources. Hence targeting offenders based on some priority value is one means by which maximum impact is obtained with minimum resource. Several mathematical techniques have been developed to help law enforcement operatives to do just that. In this presentation we will demonstrate how network theory has been used to identify criminal networks in Jamaica and Haiti. We then used Ordered Set Theory to represent these criminal organizations in a hierarchical structure and to calculate the probability that a criminal network is broken. We describe the application of these techniques in a law enforcement operation in Jamaica.