There are different forces at play here (not 'ambition-sensitive' ones), but it's a case where randomness fails miserably. Obviously, the 3-month-old should get it -- indeed, this is how scarce organs are actually distributed.
How is giving to somebody who had something and used it and not giving it to somebody who hadn't had the same opportunity fair?
It is not fair to count the octogenarian's past good fortune against them in what should be a fair contest. But we do it, because when handing out organs we don't care about fairness, we care about viable lifetime remaining.
When searching for fairness a lot of people seem to believe that good luck in the past means it should be harder for you to have good luck in the future. Ironically, this is very unfair.
It matters whose costs we're measuring here and it matters how we measure that. See what responses you get when, e.g., you change the problem to be deciding who gets the liver among two twins who are identical except that one is, say, a Republican and the other a Democrat, or some other situation where the only difference in utility is which of two opposed groups would be aided by their survival.
Then compare the responses you get to how much that person approves or disapproves of the respective beliefs.
The 3-month-old has done nothing of value. Most likely, he will be just typical. There is a good chance that he will be a loss for society. His parents can probably just make another kid, and that kid would be a lot less sickly.
I think the conclusion is obvious. The octogenarian should get the organ.
Obviously it's also chosen based on moral "merit" where cases are less clear-cut -- say a 40-year-old rapist on death row vs. a 40-year-old family man and pastor. Again though, it's pretty obvious that a coin-flip isn't any good. Most people would choose the latter over the former.
You can say to use a utilitarian standard, but that simply begs the question of whose utility, as these can be in direct conflict and in practice, people choose their own or their in group's utility.
Also, even when we set up some political system to enforce this inequality, we often have ended up making a different concentration of power in the positions that actually run that system, destroying the very equality that was supposed to be created. Money is just one form of power and different kinds of power are generally convertible.
The coin flip is no good if you believe wicked people should not be held in equal regard to those who have done nothing wrong. But it is perfectly fine if you believe the only thing that matters is a truly fair outcome.
Her 10 or 15 years is worth more, because we can already know that she is a good person. The young person could haunt us for decades.
Also, why should we extend life? Well, some people are worthy of it. So again, my grandmother wins.
I see no benefit the maximizing the value of random abstract people. Merely maximizing total longevity fails to distinguish desirable people from undesirable people. This is partly why death row exists; in that case we certainly aren't maximizing longevity, and we are declining the obvious choice to extend life.
If maximizing life were really the goal, we could ban birth control or even force people to become pregnant.
Past accomplishments count. My grandma has earned the organ.
Octogenarian Einstein/Tesla vs random 3-month-old? Is it still obvious?