Just some brief comments about the benefit of armed and law abiding citizens.
Given a rational robber/thief/burglar: the law breaker is more likely to prefer easy targets to difficult targets. If a potential target announces their enhanced difficulty they create a deterrent for the criminal. This is not a complicated or confusing prediction of human behavior. However, the premise will not always hold. Some thieves will be irrational. Some thieves will believe the risk is justified by the reward and some will be unaware of the risk. However, as a general proposition, making the criminal aware of the heightened degree of risk will in many cases deter the criminal who will then seek a less troubling target.
Given a rational robber/thief/burglar: the law breaker is more likely to prefer easy targets to difficult targets. If a potential target announces their enhanced difficulty they create a deterrent for the criminal. This is not a complicated or confusing prediction of human behavior. However, the premise will not always hold. Some thieves will be irrational. Some thieves will believe the risk is justified by the reward and some will be unaware of the risk. However, as a general proposition, making the criminal aware of the heightened degree of risk will in many cases deter the criminal who will then seek a less troubling target.
