In the context of NonViolence, we seek to avoid punishment. Instead, we try to only reward those who deserve rewards, and ignore everyone else (typically we LimitDamage). Is ignoring someone de facto punishment then, since it is the opposite of rewarding someone?

No. Punishment is an action. It requires direct intervention in someone's life in an attempt to control them. Ignoring someone makes no judgment over another person, and more to the point does not attempt to control that person. We may ignore someone not just because we dislike them, but because we aren't interested in them, don't know who they are, don't have the time to pay attention to them, or don't know how to react to them (even positively). Conversely, punishment is clear and unambiguous. Similarly, rewarding is clear and unambiguous.

To accept the argument that ignorance was punishment, we might accept the argument of this [disturbed] individual who believes women are punishing him by not sleeping with him--a not infrequent assessment, sadly. That may be an absurd case, but the point still holds. Punishment and reward are unambiguous; taking no action says nothing and thus remains ambiguous.

For example, here we have separated these cases such as with RewardReputation, PunishReputation, and DissuadeReputation, where dissuade is an near synonym for ignore since the latter strategy attempts to create no reputation.

Of course there is a distinction, but does the distinction make a difference? In the United States, driving an automobile is a privilege, not a right. Would you say that withholding the privilege of driving from someone is a punishment? If it isn't, what is it? If you had five children, and one acted up, so you didn't give them dessert that night, and the other four were well-mannered, so you did, is that a punishment? (Would the child agree?) If it isn't, what is it? --anon.

Withholding a driver's license is an overt, unambiguous action. It is not "not rewarding" someone, as the license has to be physically removed from someone. It is a punishment, which is why it looks like a punishment.

Yet in the original context, the question was whether it was punishment to allow the wicked to suffer the deleterious results of their own wickedness - to fail to protect the cruel from the self-damaging consequences of their own cruelty. By this definition, it seems that this is not the case, that you must do something in order to punish someone, that you cannot punish someone by standing idly by while they maim themselves. Is this the case? --anon.

People hurt themselves all the time. To claim it was punishment to let them do this to themselves implies that you are responsible for their actions, and thus you are compelled to intervene in other people's lives. As a corollary, other people are compelled to intervene in your life.