Does Utilitarianism require that your units of happiness are fulfilled?

Utilitarianism in its most basic form is the greatest amount of happines for the greater good. Defined in units of happiness, basically: the more the merrier. It is based solely on actions and their outcomes. What happens if there is no happiness and no matter the act, no utility becomes of it. What then?

Does that mean that, we are utility empty? I will admit I did take a few philosophy classes and while the concepts still seem abstract, I did catch the basics (or so I thought I did.) Ok. Lets take an example:

One of the problems I remember in the discussion of utility was the subject of capital punishment. While taking the life of someone as punishment is a bit harsh, it does take from the total utility of the world, does it not? Well, you are reducing the units of happiness from the person in the electric chair because the KNOW they are going to die a horrible death. No utility in his corner at all. You are also taking from the utility of the family of the convicted. They are heartbroken by losing their son, brother, cousin, uncle, parent, whatever. While this convict may not be the best person in the world (innocence project aside, lets say he did it, end of story) he was still someone's family member, no matter what. Lost utility for many years to come. Everytime a family member or close friend thinks back upon this person, lost utility units right there. Further, the people who have to do this deed are supposed to be good people, after all, we do not hire convicts and killers and psychopaths to run prisons and be baliffs, guards, etc. They have GOT to lose some of their utility in participating in the act of the capital punishment. Bottome line, lots of lost utility. No doubt.

Conversely.......

The streets are rid of a (possibly) career criminal, the jails are not supporting this convict and the families this person has affected in a bad way (good vs evil argument here?) are happy that he is getting his just desserts. So, where do the scales balance? Well, we have to sacrifice the one for the greater good of the group. Therefore, the sacrifice of the one makes the utility of the whole group better....so the argument goes.

Now, lets think about a totally different scenario but the same basic concept. You have a group of people on an island. In order for the most people to survive and be comfortable, one of them has to be pushed into the pirahna infested waters that surround the island. Due to the ritual involved, it has to be done in such a way that the person pushed into the waters shall perish lest the pirhana god come and devour them all. (Island religion, go figure.) They use the concept of utility to choose the member to be "discarded." While all of them are equal otherwise, how is that you would choose one when all are equal contributing members to the society? Should it be the weakest? The oldest? The youngest? What would you do in this situation?

Were it your family, what choice would that be? Difficult? Yes. For me, I would not want that burden. However, a choice has to be made or everyone will be reduced to zero units of happiness due to the peril of the whole group. While I am very thankful that choices like that are not made in my little corner of the universe, there have been societies that have had to make life or death choices for survival and if you look at the very core of what those choices were, I am certain you can find utility played a part in them.

Off my soapbox now, what are your opinions on utility and what do you attribute to the greatest happiness for the greatest good?

(Sorry folks, random tags so I can generate some discussion here.)