I suppose if a parent were also an economist, he might seek to split the inheritance among his kids so as to maximize the net happiness.
-- Leaving any money at all to an addict, etc is likely to decrease that child's happiness in the long term, and will certainly not increase the happiness of the other children, so that is out.
-- A child who has a low net worth is likely to get more utility (and happiness) from each dollar received than a child who has a high net worth, all other things being equal. The rich child might enjoy the $1000 ermine seatcover for his Lamborghini purchased with Dad's gift, but it's very likely that more net happiness is purchased if the poorer daughter uses the same $1000 to keep the heat on through a couple of winters. The counterargument is that stepping in to "subsidize underperformance" just encourages more of the same. But as far as extending this whole argument to government social programs, I'd offer:
1) Parents are probably better at making judgements as to the reason a child has "done well" or not. Governments seldom even try.
2) With an inheritance, the money is the personal property of the decedent, and they have complete discretion as to what to do with it. The money was not taken from one group to be given to another, no person or group who doesn't get the money is made objectively worse off than they otherwise would have been.
-- What if the unequal gifting itself results in unhappiness-- If the rich son with the Lamborghini resents the fact that Dad gave more money to his poorer sis than he got, and this resentment decreases his own happiness? That's a possibility. Maybe our economist decedent applies a weighting factor: unhappiness resulting from envy or a misplaced sense of entitlement counts less. After all, Mr Moneybags could have chosen to be happy that his sis now had enough wintertime heat, instead of fixating on the fact that he didn't get an even share of the loot.
