I assume utilitarianism to be the doctrine that one should act to maximize the overall amount of "happiness".
Next to the fact that it's not quite clear
what happiness is supposed to be and how it could be measured (to maximize it)
what the target group should be (whose overall amount of happiness is to be maximized)
it's also unclear
what the overall amount should be and
if this is the relevant target size.
Maximizing the overall amount means maximizing the arithmetic mean. But this is possibly not what one wants to achieve. As more often than not, the median would be a better target size, i.e. the "happiness in the middle".
But maybe this still isn't the whole story: happiness - even when the median is maximized - could nevertheless be distributed unfairly, e.g. in the case of too many or too extreme outliers or possibly measured as some kind of Gini coefficient.
Is there a modern version of utilitarianism that takes all of this into account?