numbers, not adjectives — D. J. C. MacKay

3  The Themis Mechanism: price elicitation

A central task of the Themis Mechanism is for the Coalition Authority (CA) to determine the emission price (and other governing quantities) on an annual basis. This page explains the elicitation process.

The goal is to determine the carbon price which maximises the impact of the coalition on the environment. Rather than a democratic vote, with majority decision and compulsion to comply, it is done by an elicitation process based on voluntary coordination. This process is more suitable for a coalition of sovereign nations.

The CA asks every nation for their preferred price \(p_i\). Based on these price preferences, the CA must determine the best price \(\hat p\) based on a compromise: if the price is low, then many nations are expected to join the coalition (all the nations who expressed a preference for at least that price), but the impact is low because the price is low; conversely, if the price is high, the impact will be low because only few nations are expected to join (the nations whose price preferences was at least that high). The best price will be somewhere in the middle.

It’s important to realise that this process necessarily excludes nations from the coalition. That’s not really a choice, but dictated by the properties of task. Exclusion is necessary because sovereign nations can’t be compelled to do anything they don’t want. Unanimity would result in too low a price, and single nations gaining too much power. Non-members will be sanctioned by the coalition.

To formalise the process, introduce the coverage \(c\), the fraction of emissions covered by coalition members. In the plot below, a histogram is shown of the coverage weighted price preference in dark blue. Also shown is the achieved coverage \(c(p)\) in light blue and the price \(p\) in green. And finally the objective, the total price paid, \(p\times c(p)\) in red, which is maximised to find the Themis price \(\hat p\). The total price paid is a proxy for the impact of the coalition on the environment.

This great visualisation was written by Philipp Hennig.

Large absolute emitters have a large influence on the price. For example, China’s vote has more influence than India’s, although the two nations have equally sized populations. That’s caused by the objective measuring the impact on the environment.

You may think that nations could collude to gain more power over the price. But this is a false intuition. In fact, since the procedure depends only on the quantiles of the weighted price preference distribution, the procedure has the important game theoretic strategy proofness (SP) property, which means that no nation can manipulate the outcome in their favour by not telling the truth.