The impossibility of keeping everyone happy

I wrote a while back about the potential benefits of restricting student choice. I’m feeling even more inclined in that direction after the annual group consulting project (GCP) round. We try to offer students a choice over which project to do but it is hard to make everyone happy. In fact, I can state more strongly that it is impossible and refer to a Nobel prize winning economist to do so.

Each year there are usually one or two projects that are particularly popular, so they are over-subscribed. We ask students to provide first, second or third preferences to allow for the fact that they may not get their first choice. We then allocate students randomly (literally, we use random numbers) to their first choice projects. Those who don’t get first choice go to their second choice, assuming there is still a slot, and so on. This seems the fairest approach but inevitably some people think they’ve been hard done by.

The complainers are usually the more narcissistic students, so perhaps no amount of analysis will convince them. But there is some comfort (for me) in knowing that Arrow’s Impossibility Theorem shows that any political decision process has its flaws.

Kenneth Arrow showed in the early 1960s that under reasonably general conditions there is no way of transforming individual utility functions into a single social welfare function without violating a number of reasonable criteria for success. (One of the criteria is non-dictatorship, which arguably is untrue for the MFin – though I’m reluctant to think of myself as a dictator.) It has become known as Arrow’s Impossibility theorem, one of the most famous elements of public economics.

The theorem has been used to show that politics is not just about ends but processes. There are legitimate reasons for disagreeing about how people’s views are aggregated and combined. We have a refendum coming up in the UK next month on using the alternative vote system in preference to the existing first past the post approach. There are vigorous arguments for and against change, reflecting the fact that no voting system is perfect – it depends which criteria for selection you think most important.

Another of the criteria is Pareto efficiency, which is widely used in economics as a weak measure of social justice. A Pareto optimum is one in which no outcome can be improved without making someone else worse off. This is actually very restrictive and if applied in real politics would paralyse most government policy. Another major intellectual, Amartya Sen, argued in 1970 that it should be dropped as a criterion in one of his many fascinating articles “The impossibility of a Paretian liberal”.

For the MFin, there could be a number of ways of allocating the scarce resource of a desired project. One could of course auction it, a market mechanism that seems rather fitting. But doubtless some would object to the extra cost and to the differing ability to pay.

I hope that we have a system that commands general, if not universal, support. The test would be if the people who complain would support the system if they happened to get their first choice, but we can’t run that experiment. Each year I do learn quite a lot about people from the way they respond to getting, or not getting, what they want.

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