balancing utilitarianism

posted on 2022-02-04

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

posted on 2022-02-04