Most people agree that carbon dioxide emissions need to be drastically cut. One way to do this is by emissions trading.

The idea is to cap the total emissions that are allowed and then allocate permits to countries allowing them to emit up to a certain limit. If a country produces less than its limit, it will have leftover permits it can sell to countries that want to increase their emissions.

The end result is a market that should encourage countries to invest in technologies that reduce emissions (provided the permits are priced correctly).

One problem with emissions trading is the initial permit allocation: how should the emissions be divided between countries in a way that is fair?

The two most widely discussed options are by auction and grandfathering. In an auction, countries with the deepest pockets can buy the most permits. Grandfathering distributes permits based on historical emissions, so countries that have emitted more in the past get more permits for the future. Both options have their fair share of critics.

Now Ji-Won Park, Chae Un Kim and Walter Isard at Cornell University in Ithaca have another suggestion. Their idea is to allocate the permits using a Boltzmann distribution, which they say is fairer than other methods.

First a bit of background about Boltzmann distributions. Imagine a gas made up of a large number of particles that each have a certain energy. Now imagine you plot the fraction of particles with a given energy.

Your plot will be a Boltzmann distribution and it describes the most probable distribution of the system. That idea of the ‘most probable distribution’ is what makes it fair for emissions trading. “When introduced to international emissions trading, the Boltzmann distribution provides a simple and natural rule for permit allocation among multiple countries,” say the Cornell group.

The Cornell group’s idea is to think of the particles in the system as countries and to think of the energy as their potential to be allocated a permit.

The Boltzmann distribution then gives the probability that a given permit is allocated to a particular country.

That’s not entirely bonkers. Many economists are turning to ideas in physics to describe the complexities of business, finance and trade. Various econophysicists have even explored the suggestion that economies behave with properties that have a formal mathematical link with thermodynamics. In that case, it’s only natural to imagine that Boltzmann-type distributions will crop up.

The suggestion is that if these distributions are good enough for nature, then they should be good enough for us.

But the danger, of course, is swapping one bone of contention for another. In this case, the point of issue is likely to be the precise mathematical form of the allocation potential, which can have dramatic effects on a country’s final allocation.

The Cornell group make some suggestions about solving this.

But whether the international community could ever agree on a fair allocation system is moot. International agreements are like sausages: no matter how much you like the end product, you don’t want to know what goes into them.

And the likelihood that a Boltzmann-type allocation system could come out of a process like that is surely tiny.

Ref: arxiv.org/abs/1108.2305: Permit Allocation In Emissions Trading Using The Boltzmann Distribution