NEGATIVE UTILITARIANISM says reduce the most suffering and concentrate on that

Negative Utilitarianism teaches that reducing the most pain and suffering in the world is the true morality. It puts increasing happiness in second place.

Alleviating suffering is harder and more unpleasant than making people happy. If everybody practices Negative Utilitarianism they will not be happy and sickness will increase. Or so it seems. But people can be happy despite doing unpleasant work. People can be happy to eat chewing gum that tastes awfully sour.

It has the same problems as Utilitarianism though it is a bit more intelligent than it.

CONSEQUENTALISM AND JUDGING
 
Judging, condemning something as wrong and deserving of punishment and disapproval, disproves all forms of consequentialism.

Bernard Williams in his Morality (page 110) perceives something interesting that is in all manifestations of Utilitarianism. It is that the actions of evil people have to be dealt with by evil actions. The good have to punish them by reducing their happiness. The good have to do evil. But often it will happen that the good the Utilitarian works for will not have been worth the bad that had to be done to bring it about. The doctrine lead to more misery than happiness. If punishment is right then Utilitarianism is nonsense.
 
William’s argument disproves Negative Utilitarianism and Ideal Utilitarianism as well.
 
The argument has led some Utilitarians to assert that Utilitarianism should only be taught to a few (page 111, 112). The members of this few would need to be spread out in society so that each one is among absolutists to prevent the escalation of evil. But this damage limitation principle demanded by Utilitarianism still manages to contradict Utilitarian philosophy. It is asking people to promote error and moralities which are based on habit and feelings instead of on reason which is really furthering artificial morality and hypocrisy which will deaden the happiness of the non-Utilitarian world. Utilitarianism has to put the Utilitarian group of believers before everybody else. That's whose happiness they have to think about – nobody else’s. They cannot promote their philosophy or be happy or know how many Utilitarians there should be so the presence of the dissenters from Utilitarianism can only distress them. It seems to be hypocritical for them to publish books on their philosophy and to promote it.
 
It could be answered that the infliction of pain on evil people is necessary to stop worse evil and it could be said that they could be happy even with the pain and it is up to them to learn how. It could be said that if you feel you cannot be punished in life that will actually distress you at some point. But if it is up to people to make themselves happy no matter what is done to them or if they are in prison then the greatest happiness of the greatest number ethic is wrong. It would follow that their happiness is their concern and not yours.

It is supposed, “All consequentialist ethics imply that you can never judge anybody. The person who looks to be doing bad may really be doing what he thinks is right and may not be able to explain to you his reasons. You have to think the best of him. That is a dangerous position and shows the hypocrisy of believers in consequentialism who sent people to jail to be punished. No wonder jail makes them worse.”

But criminals are given a chance to speak up for themselves – that is what trials are for. If a person steals a cheque from an employer because he is grossly underpaid, that excuse is not going to work in his favour if he explains this in court. It is only going to add more stigma to his already tarnished reputation. And how can the criminal use this defence if he is in any way a consequentalist for it will mean propagating a principle that will lead to most employees stealing on the grounds that they imagine themselves to be underpaid? But as we have to take people’s word for these things we have no choice but to judge him as guilty. And since we know human nature from being human ourselves we will frequently have an accurate idea of what a person meant to do.