maximin

one common mistaken anti-utilitarian argument is that the social welfare function ought to be max-min.

At the other extreme is the Max-Min, or Rawlsian utility function.[7] According to the Max-Min criterion, welfare is maximized when the utility of those society members that have the least is the greatest. No economic activity will increase social welfare unless it improves the position of the society member that is the worst off.

we can trivially see the obvious irrationality of max-min by considering two scenarios:

scenario x:
999,999 people: thriving
1 person (we’ll call her alice): very unwell

scenario y:
1 million people: infinitesimally better than “very unwell”.

max-min says that scenario y is better, because alice is infinitesimally better, while making any number of people any amount worse off.

this is obviously untenable, since the percentage of people preferring scenario x approaches 100% as population increases.