CRIME IN THE HOOD Violent victimization of whites by blacks is modeled in a racially mixed inner-city neighborhood. Its evolution is traced from the first black to move in, to the last white who moves out. The probability of a white being violently attacked is developed as a function of a neighborhood's racial composition. It is shown to increase nonlinearly, approaching unity as a neighborhood becomes predominately black. A crisis of violence John is white. He is married with two children. He wears a blue collar when he leaves his shabby, inner-city house to go to work. Life has been a struggle for John, but now he faces his most difficult challenge. John's neighborhood is turning black. In John's city, neighborhoods do not integrate, they go black. He has seen it happen elsewhere. He knows what to expect. John and his family will soon face intolerable hardships. They will have to move. Inevitably the last whites able to leave, will. High among their reasons will be fear -- fear of becoming victims of violent crime. As his neighborhood turns black, John and his family will notice many changes, but none will be more dreaded than the prospect of being violently victimized. We will model violent crime in John's neighborhood, tracing its evolution as the community goes from all white to all black. We will chart the course of victimization from insidious beginnings to the threshold of intolerability. We will show that initially the swelling danger will be barely noticeable, but from the beginning there will be an underlying acceleration that ultimately will drive the risk to extreme levels. The data The data reveal two causes of white victimization by blacks. First, a black is 3 times more likely than a white to commit violent crime. However, as a neighborhood turns black, this factor could increase black-on-white violence at most by a factor of 3, and then only when a neighborhood is virtually all black. The observed level of white victimization is much too high to blame on general tendencies of blacks to be violent. A more important reason is simply that blacks prefer white victims. The best and most complete evidence comes from the Justice Department. Its annual National Crime Victimization Survey (NCVS) canvasses a representative sample of about 80,000 Americans, from roughly 43,000 households. From this survey, a picture of crime is painted by its victims. The last full report of the NCVS was issued in 1994. From it we learn that blacks committed 1,600,951 violent crimes against whites. In the same year, whites committed 165,345 such offenses against blacks. Despite being only 13 percent of the population, blacks committed more than 90 percent of the violent interracial crime. Less than 15 percent of these had robbery as a motive. The rest were assaults and rapes. The asymmetry of interracial crime goes still deeper. More than half the violence committed by blacks is directed against whites, 57 percent in 1994. Less than 3 percent of the violence committed by whites is directed against blacks. Population and NCVS statistics reveal that in 1994 a black was 64 times more likely to attack a white than vice versa. In the city, the races live mostly apart from one another, so that the most convenient victims of thugs are others of the same race. Only a hunter's mentality could account for the data. Given a choice, a black thug will select a white victim. Ironically, so will a white thug. Modeling the Hood The real world is too complicated for us to describe exactly. We can learn about it by describing a simpler system, or model, that mimics it. The model should include the essential features of the real system, and yet be mathematically accessible. Refinements can bring us closer to the truth, but we never quite reach it. We approach truth asymptotically. To model Johns neighborhood, we face a problem immediately. A neighborhood is itself an abstraction. Where does it begin? Where does it end? We simply regard John's neighborhood as a black and white universe with a total population N, a black fraction fB, and a white fraction fW. Divide the number of criminally violent victimizations perpetrated by blacks in a year, by the black population and call this quantity, pB. It is related, but not equal, to the probability that a randomly selected black is a violent criminal. It would be that probability if criminals always acted alone and committed only one violent act per year. Since we are interested in victimization, pB is the more relevant quantity. The corresponding quantity for whites is pW. The probabilities calculated below refer to a one-year period. First we look at the probability, FB, that a particular white, say John, will be victimized at least once by blacks. The white population in the hood is NfW. Consistent with NCVS data, we assume that if presented with a convenient choice, both black and white thugs will select white victims over black. Then, the number incidents involving white victims and black perpetrators is pBfBN. For simplicity, we assume single-victim incidents. (This does not preclude victims from being attacked more than once a year.) The probability that John will be the victim in Incident 1 is 1/(NfW). The probability that John will not be that victim is 1-1/(NfW). The probability that John will not be the victim of Incident 2 is also 1-1/(NfW). If each incident is independent of the others, the probability that John will not be victimized by blacks this year is (1-1/(NfW))^(pBfBN). The probability that John will be victimized within the year is then...... ...to see all the rest of the equations, data and graphs, click on link at top.