(1) Price mechanisms.There are no other options that I can think of.* This is another fact we have to deal with. You can say that all of these are in a sense "unfair," which is just one more reason "fairness" is relatively meaningless. People willing to spend money prefer (1); the apathetic prefer (2); the time-rich prefer (3); those in power and the well-connected prefer (4). They all, of course, tend to think their method is the most fair.
(2) Random lottery.
(4) Dictatorial fiat.
The most common in our society is (1). Liberals (and sometimes conservatives as well) like to complain about using prices to allocate resources because it shifts the balance towards those with money, which seems dirty to many people. This can be a valid complaint, but it means that if we are to abandon market pricing we must adopt one of the other solutions. The challenge for those who do not like market-based allocation is not to show that it is bad, but to show that it is worse than the other options for resource allocation.
Speaking of which, Nick Gillespie has a post on Hit & Run today about Cincinnati's use of queuing to determine who gets into magnet schools. It is, quite predictably, a miserable failure. Also predictably, it still benefits the relatively wealthy, because they have the option of spending time waiting in line when they could be working. My home county used to (and may still) run a number of magnet-like programs which used a lottery method. They were also a travesty. They ended up filling these supposedly selective programs with students who weren't any more capable or interested than the average student. The federal government, of course, is currently pursuing allocation by fiat to the tune of several trillion dollars, and there's simply no way you'll convince me that that's either efficient or just.
I tend to like (1) because I think it's the best at encouraging people to create more things, thus alleviating scarcity. I admit though that pricing is not always the optimal method. However, I am no longer interested in hearing condemnations of markets unless they are accompanied by an explanation of why lottery or queuing or fiat are more appropriate for the circumstance.**
* Contests and feats of skill might be an alternative, but in anything more complicated or subjective than, say, the discus throw, the necessity of judging puts you back in the territory of allocation by fiat. You've just pushed the problem back a step from "You get the goodies because I say so" to "You get the goodies because you won the contest and you won the contest because I say so." A contest (or application process, as we tend to call them) may be more or less objective, but at some point the winners win because either the guy who wrote the rules, or the guy who interprets the rules, or both, says they win.
** Identifications of inefficiencies and constructive criticisms of how to make a market run more smoothly are always welcome but please don't tell me that it just isn't fair! unless you're prepared to defend the viability of another option. Such complaints will ignored dash nine.
Update: An anonymous commenter made me realize that I did not make clear the extent of "dictatorial fiat." By this I don't just mean a plutocrat or prince or poobah deciding who gets what, but any situation in which a person (or people) controls a resource and decides what to do with it themselves. I would include under this banner a CEO allocating budget to departments of their firm, a child handing out invitations to their birthday party, and parents distributing belongings to their children through a will (although perhaps the executor or court system might step in and impose their own fiats as well). That caveat brings me to another point, which is that these systems can be mixed together, although I think in most cases one mode prevails. You may have most items of a batch sold off at market, but some given away to friends, or you may need to wait in line for the chance to enter a lottery.