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Mathematics for Politics

How to model the division of the Arctic territories

Egor Borsuk from the HSE International Centre of Decision Choice and Analysis has developed a software that can resolve international territory disputes. He has tested the programme on the disputed Arctic region. The researcher spoke about his innovation at the XXI April International Academic Conference on Economic and Social Development and in an interview for IQ.HSE.

 — Why did you begin with the Arctic region?

The division of the Arctic territory is a global issue that has yet to be addressed and solved. Some decades ago, very few countries were interested in this territory of extremely severe climatic conditions — back then, it would have been too expensive to explore it.

However, the Arctic Region is too rich in natural resources to remain ignored: although it makes up less than 6% of the earth’s landmass, the Arctic Region accounts for about 13% and 30% of untapped oil and gas, respectively. Therefore, once this area became more accessible due to global warming, the region’s attractiveness rose considerably.

Today, the Arctic region is divided amongst Russia, the USA, Canada, Denmark, and Norway. The areas extending 200 nautical miles from these countries’ shorelines into the Arctic are called exclusive economic zones (EEZ). Waters beyond these zones is considered open sea, i.e., it doesn’t belong to any nation.

In 1996, the international Arctic Council was established. One of this forum’s aims is to consider claims over some territories. The resource potential of those territories is of interest to many countries, triggering conflicts of interest. The latter can be addressed by means of mathematical methods, distributing area given individual nations’ needs and the locations of natural resources.

 — What and who are you talking about?

Natural resources include oil, gas, fish, and sea routes. The territory is the area located at a latitude of 63 degrees and higher in the north. The stakeholders are six nations located there: the United States, Russia, Canada, Greenland (Denmark), Norway, and Iceland.

The whole territory was split into equal plots, about 50 km² each. Over 42% (12.5% after taking into account the EEZ) of them remains free for distribution among the countries. They have to be distributed to meet the maximum simultaneous needs of each stakeholder.

 — Have outcomes of territorial disputes ever been modelled before?

I’m only aware of the research conducted by the HSE International Centre of Decision Choice and Analysis—there about eight models developed by different mathematical methods.

 — Are you offering a first-of-its-kind model?

All the models have their own approach and advantages, but they all share one main problem — they fail to take into account the countries’ level of interest in natural resources. We tend to believe that oil, gas, fish, and sea routes are equally needed by every nation. This is not quite correct, and my model takes this into consideration. Moreover, the model provides a consistent solution: none of the distributed area would be surrounded by other countries’ territories, but it should be adjacent to the shore of the state that receives it.

 — How can we estimate the level of nations’ interest?

I couldn’t find any objective data, so I had to develop my own method. As a rough estimate, I analyzed the ratio of the number of Google links for the query ‘country–Arctic–resource’. For instance, the words 'USA Arctic Oil’ were used to estimate the USA’s interest in oil. I assumed that the more the country needs a natural resource, the more references there will be for this query.

The level of interest varies from one (low) to seven (high). The calculations using a special formula yield quite plausible results. For instance, Russia appears to be more interested in oil than in fish, while fish was more important than oil for smaller countries, like Greenland,.

Nations’ interest in Arctic resources

 — What other data were used and what was the final result?

We have developed a software that allows us to verify the efficiency of the model. We have tested only the actual Arctic data, but the software can be used for many other purposes, helping us address any other territorial dispute. You just need to apply other parameters, such as countries, distances, descriptions of the free territories, the level of interest in them, satisfaction from obtaining them, and so on.

This will result in various outputs, showing maps of resources and territories, telling us how useful the territories would be for the countries, providing animation, histograms, spreadsheets with data on envy-freeness, and so on.

 — Does mathematics study envy as well?

Yes, envy-freenessis a mathematical characteristic which is used in addressing territorial disputes. When Stakeholder A has obtained something, but in fact he wishes he had obtained what Stakeholder B received, it means Stakeholder A envies Stakeholder B. Conversely, envy-freeness can guarantee that no nation would like to exchange its territories with another nation, and this is part of the criteria for a successfully resolved dispute.

 — Has this criteria been met for the Arctic Region?

No, it hasn’t. The best of my solutions reports four instances of envy from the United States and Iceland. Within the Arctic Circle in question (i.e., the area to the north the latitude of 63 degrees latitude), the United States are surrounded by large countries — Russia and Canada — and compared to them, the US receives a smaller territory. This results in envy. The same happens to Iceland, which is surrounded by Greenland and Norway.

Unfortunately, the actual data have not let us develop an envy-free solution so that nobody envies the others.

 — Are mathematical models and division of territories just a theory or there are any practical cases?

There are no practical cases from what I know. I haven’t found any evidence about them in open sources.

 — Why not? What seems to be the problem: mathematics or politics?

Both. Mathematics hasn’t come up with any methods to provide an ideal solution to this problem. All the solutions we have now leave something to be desired. It is rather hard to apply mathematics to political issues, as politics has its own rules. I have never delved too deeply into them, but I don’t doubt that mathematical models are used in one way or another when it comes to the division of disputed territories — people simply do not mention it.

 — What is the status of your research? Is the software ready for use?

The model is up and running, but the solutions it produces will not be optimal. We have yet to improve our solution-seeking methods. Moreover, the model needs upgrading, as calculations take too long. We will also have to make our software more user-friendly.
IQ