Random Distribution of Goods

In my Moral Philosophy exam today I answered a question relating to the distribution of goods by random procedure, and whether there was any grounds on which such a method was justifiable. I think it's somewhat already a common-place practice. In Wales they apparently allocate some cancer treatment drugs based on a postcode lottery. It was my weakest exam answer because I genuinelly don't seem to have formed a strong opinion on either side of the argument.

The main argument that justifies such a practice rests on the proposition that, by randomly distributing a good, everyone has an equal chance of obtaining it. It's a "fair method" of ensuring everyone can lay some claim to the good; you don't have to fulfil specific criteria in order to be considered for the process (apart from, obviously, there being an existing reason for you to want/need the good in question). Let's consider an example, that might elucidate this further.

Suppose the good in question is something indivisible, like a human organ - let's say, a liver. Since only one person can have the liver, there needs to be some method of selecting who will have the organ. Now, because there may be many people in need of a liver transplant, a proponent of the random selection process might say, in order to not discriminate against anyone and in order to give everyone a fair shot at this life-saving procedure, we should employ a lottery whereby a patient is randomly selected from all those that need a liver, and hence they are the ones that receive the good.

I find it really difficult to write about this method because there seem to me to be too many things to take into consideration, and also I think I expose myself to the risk of sounding elitist or 'like a right cow', for want of a better term.

But here are my problems with the method:
1) Does everyone really have an equal claim to the good? Suppose a third of the people on the liver transplant list are alcoholics. Do they really have an equal claim to the liver as does, say, a promising tennis star who happened to just get an infection?

Proponents of the theory suggest everyone ought to have an equal, or at least roughly equal, claim to the good in order for them to be considered by the lottery, but what does this mean? How do we judge what constitues an 'equal claim'? On what basis? Surely the whole point is just to give everyone an equal chance...

2) In employing the random selection procedure, are we just ridding ourselves of the moral responsibility of making ethical choices? We can't decide for ourselves how best to distribute the good, so we'll just leave it to chance...

On the other hand, perhaps random selection isn't all bad. Evolution operates on a random mutation 'policy', for want of a better word, so maybe we are just following in nature's footsteps.

Anyway, I am running out of interesting things to say on this topic. But basically, I can't make up my mind whether or not it is good or bad. I think in some cases it is necessary - until we have enough resources to go around I guess someone will always miss out on 'the good', and it is better that a few get it than that none get it. I wish I could just form a strong opinion on it though.