“Variance-Covariance matrix” unnecessarily redundant

Stop saying “variance-covariance matrix.” It’s just “covariance matrix.”

A covariance matrix is a symmetric matrix in which each element i,j = covariance(X_i, X_j), where X_i is a random variable. By definition the diagonal elements i,i = covariance(X_i, X_i) ≡ variance(X_i). That is always true of a covariance matrix, so there is no need to (re-)state that. I.e., adding the prefix “variance-” to the term “covariance matrix” never adds information. Except, perhaps, to suggest that the speaker does not fully understand this.

(I’ve heard some suggest that referring to it as a “variance-covariance” matrix helpfully reminds people that the diagonal is the variance of each variable. But if the reader or writer doesn’t already understand that then they’re not going to get very far with the topic.)

Disarm Police – Part II

American police should not be allowed to routinely carry weapons because the established risks to the public outweigh the benefits. Police are held to lower standards and face minimal consequences for misuse of force. And American policing attracts people who are disposed to being physically abusive.

Arming cops is worse than arming average citizens because private citizens face both civil and criminal liability for using force. Even a fully justified use of force can send a citizen through the ordeal of arrest, jail, and a criminal trial. It is hard to overstate the consequences of being put through the criminal justice system: A public arrest cannot be expunged from the internet. There is no compensation for the financial damage of being jailed, or the costs and curtailment of rights that accompany posting bail for the months or years it takes to get a trial. Legal fees to defend oneself in court cannot be recovered even if one is vindicated. These severe consequences deter people from unjustified acts of violence.

In contrast, thanks to qualified immunity, American police face no civil liability for misuse of force. In theory police face criminal liability for unjustified violence, but in practice this risk is also negligible: Police are not immediately arrested for acts of violence. Instead police officers are given paid vacation and public anonymity while their union lobbies their colleagues in law enforcement against filing criminal charges, and their brothers in blue pick over evidence to justify their behavior and publicly vilify their victims.

The public is supposed to believe that law enforcement agencies are competent to investigate and correct their members for acts of abuse. But those administrative trials are conducted in secret, and their results are almost always kept confidential. The most serious adverse consequence is for an officer to (eventually) lose his job and have to find one with a different law enforcement agency.

This asymmetry in process and consequences is too extreme: Justified use of force by a private citizen can cost them years of time, hundreds of thousands of dollars, and can haunt them forever. Unjustified use of force by a cop can cost … maybe having to find another job.

I can see two obvious ways to restore some balance here:

1. Require that every use of force incident be presented to a grand jury but don’t let the jury know whether the suspect is a cop.
2. Send every use of force incident to a prosecutor that is independent of mainstream law enforcement: i.e., a prosecutor who does not otherwise depend on the cooperation of police to conduct his job.

Hold cops to the same criminal standards as other citizens who use lethal force. Or don’t give them lethal weapons.