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balancing utilitarianism

suppose you have multiple values ("i want to be healthy but also i want to eat a lot of fries") or a value applying to multiple individuals ("i want both alice and bob to be happy"), but sometimes there are tradeoffs between these values. how do you resolve such situations ?

a simple weighed sum might suffice in many cases, but i feel like there are cases where this is not sufficient.

for example, consider a population of 5 persons, who you care about equally, and consider a simple scalar value you have for them, such as happiness.

now, consider the following three options:

• all individuals get 0.5 utility ("fair")
• one individual gets 0.9 utility, the other four get 0.4 utility ("bully")
• one individual gets 0.1 utility, the other four get 0.6 utility ("scapegoat")

if we are to use a simple sum, all three of these situations sum to 2.5 total utility; yet, i feel like something ought to be done to favor the fair situation over the other two (and then probably to favor the bully situation over the scapegoat situation?)

what i propose to address this is to apply a square root (or other less-than-one exponent) to the utilities of persons before summing, which has the effect of favoring more equal situations. in this case, we get:

• fair: 3.54 utility
• bully: 3.48 utility
• scapegoat: 3.41 utility

which does seem to produce the desired effect: in this situation, it maps to how i feel about things: fair > bully > scapegoat