system
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human
Do Utilitarians tend to view punishment itself through a consequentialist lense?

My philosophy professor (who has expressed clear dislike for utilitarianism) said in class that a Utilitarian would support punishing a driver who ran a red light and killed a pedestrian more than a driver who ran a red light and didn't kill anyone. According to her this is because Utilitarians would assign moral blame based on the extent someone's actions have caused suffering or happiness. She claims this is a good argument against utilitarianism as it is unfair to punish someone more just because factors beyond their control resulted in more harm. 

Although I am not a philosopher (or even a philosopher major) I disagree with this. In my view, a Utilitarian would view punishment itself through a consequentialist lense, and would opt to punish both drivers equally because they would view punishment as a tool to prevent the harmful behaviour (running red lights). 

What do Utilitarian philosophers tend to think about this question? Would they opt to punish the person who did more harm more, or would they opt to punish both drivers equally for the reasons I stated above?
gpt
The utilitarian will opt to dole out punishment along utilitarian lines. So, if that means punishing the person who killed the pedestrian more, then they will do that. If it means punishing them equally, then they will do that. If it means punishing neither of them, then they will do that. Etc. 

Precisely what kind of policy will produce the most utils is an empirical question that we would have to investigate. We probably can't resolve this empirical question from the armchair. Maybe it is the case that punishing the person who kills the pedestrian results in the most utils-- like, maybe doling out punishment in this way deters driving in this fashion, creates a sense of happiness among the population, etc. Or, maybe it turns out that punishing everyone who runs a red light equally results in more utils. Or maybe the most utils result from some other policy. The point is: the utilitarian will be a utilitarian about blame and punishment.