Any urban dweller knows that few things have the capacity to make us as miserable as our neighbours can. If fate plants you next door to someone inconsiderate, noisy, hostile or otherwise vexatious, their unpleasantness is made worse by the fact that you’re stuck with them: nobody gets through life without, at some point, ­entertaining fantasies of retribution vis-à-vis the folks next door. The same is true, as the most rudimentary scrutiny of history books will attest, of countries. ­Because their disputes can often end in large numbers of buildings being knocked down and hot metal being fired, many ­attempts have been made over the centuries to construct a framework for states to resolve their differences peacefully.

One of the less likely efforts was wrought by an accidental alliance of a Russian king and a Scottish-American millionaire. The Permanent Court of ­Arbitration is the enduring result of The Hague Peace Conference of 1899, called by Tsar Nicholas II, apparently fretful about an increasingly militarised planet (it certainly worked out badly for him). The spectacular building constructed to house the PCA – the Hague’s Peace Palace – was underwritten by the steel magnate Andrew Carnegie, who wanted to invest in mankind’s betterment. The Palace, and its glorious gardens – in which Carnegie imagined the world’s finest minds being inspired to find peaceful solutions – were the result of an international design competition, and were opened in Carnegie’s presence on 28 August, 1913. Exactly 10 months later, a young Bosnian Serb nationalist raised his pistol on a Sarajevo footpath: though we tend to assume that peace is a universal human desire, it’s difficult to nurture.

Nevertheless, people try, and with occasional success. In July 2009, a five-person arbitral tribunal empanelled by the PCA delivered, beneath the stained glass windows of the Peace Palace’s Great Hall of Justice, a decision in a dispute between the government of Sudan and the Sudan People’s Liberation Movement (SPLM). At stake were the borders of Sudan’s oil-rich Abyei region, over which much blood had been spilt – a month before the PCA made its ruling, at least 22 Sudanese soldiers died in clashes with SPLM militias, and Al-Jazeera reported that most of the population of the region’s capital city (also called Abyei) had been displaced by fighting. The PCA’s ruling, by which both sides had agreed in advance to abide, reduced the size of the Abyei region, and awarded control of the Heglig oil fields and the Nile oil pipeline to Khartoum. “Both parties,” says Judith Levine, a legal counsel at the PCA, “came to us at the end of a 25-year civil war that had left two million dead, and asked us to resolve it, and quickly.”

Agreement over Abyei was a key step towards the full implementation of the 2005 peace deal that aimed to end Sudan’s interminable civil war, and which provides for a 2011 referendum in which Abyei’s people will decide whether they want to remain part of Sudan proper, or join the autonomous region of Southern Sudan (it is expected they will choose the latter, which explains SPLM’s desire for a settlement, even at the cost of resource-rich land). Each side was asked to appoint two people to the five-person arbitration committee. When agreement couldn’t be reached on the fifth, the PCA’s secretary-general chose someone.

“Our role then,” explains the PCA’s deputy secretary-general, Brooks Daly, “was to make sure we had chairs in the right place, translators who could speak Arabic, Dinka and English, security, catering, all the nuts and bolts.”

“We had to be very sensitive,” recalls Aloysius “Louis” Llamzon, another legal counsel. “A lot of witnesses were tribesmen who’d never travelled north of Khartoum before, all wearing their traditional dress. Some of them had to pray five times a day, so we had to figure out which way Mecca was so they could lay their mats on the lawn.”

Unusually for a case of this sort, proceedings were broadcast live online, and were avidly watched back home.

“It seems obvious,” says Daly, “but it was regarded as a great innovation in ­arbitration, which is usually done in camera. Suddenly, interested parties in Sudan – and international law nerds from around the world – could watch a live case for the first time. And it’s still on our website [pca-cpa.org], so it can be used in lectures.”

Daly, 41, is a Californian who arrived here via a Los Angeles law firm and the International Chamber of Commerce in Paris. Levine, 34, is from Sydney and previously practised in New York. Llamzon, 32, is a Yale Law School graduate from the Philippines (10 other nationalities are represented among the PCA’s 17 legal staff). All are hearteningly enthusiastic, leafing through folders of old cases – such as the 1928 decision that decided that the Pacific island of Palmas (now Miangas) was Dutch (therefore now Indonesian) rather than American.

“It’s an old institution,” says Daly, regarding the original green velvet wallpaper and William Strutt painting of Isiah 11:6 (“The wolf shall also dwell with the lamb”) in his office. “And it’s an old building, though a beautiful one. Yet we’re creeping up on the cutting edge of dispute resolution. In the last 18 months, our caseload has exploded.”

Other recent cases have included the 2007 ruling on a maritime boundary ­between Guyana and Suriname, which necessitated searching for and disinterring a marker stone from a 1930 survey. “It wasn’t quite where either side thought,” smiles Daly, “so everyone saved face.” Some nifty diplomacy was called for though. “Guyana wanted to see some colonial maps owned by the Dutch government,” explains Daly. “Suriname [a former Dutch colony] objected to this in case it made them subject to other border disputes, so we asked them to help us pick the expert who studied the maps. The tricky bit then was that the expert had to speak Dutch, but to keep the Guyanese happy and avoid implicating the Dutch government, they couldn’t be Dutch. So we went recruiting in South Africa and the north of Belgium.”

The PCA’s current docket runs to 35 pending cases including disputes between states and investors or other private parties, disputes within states, and good, old-fashioned disputes between states (the PCA is in “the very early stages”, according to Daly, of taking a role in a spat ­between Croatia and Slovenia over their mutual border). Asked why the PCA has become quite so overrun – as recently as 2000, the PCA had just five cases on the go – Daly responds with the optimism that animates the entire enterprise.

“It’s a pragmatic way out,” he ­enthuses. “And in long-running disputes especially, it can help deflect criticism from political leaders trying to resolve things without looking like they’ve sold out – they can say that they’re merely abiding by the decision of a neutral legal overlooker.” According to all recent ­reports, the peace in Abyei is holding.

The Peace Palace is decorated with the artefacts and artworks donated by the PCA’s 110 member states (it is not necessary to be a member state to apply to the PCA for help). The original building is abutted by modern extensions – the Peace Palace now also houses the International Court of Justice, the Hague Academy of International Law, and the immense Peace Palace Library. It also boasts a good restaurant, where the PCA’s current secretary-general, Christiaan Kröner, explains his view of the organisation’s present and future over lunch. “I was brought up,” he explains, “with the idea that sovereignty is alpha and omega, so from that point of view, it’s fascinating.”

Kröner, 64, is a career diplomat who has been the Netherlands’ ambassador to Washington, Paris, Rome and Tel Aviv, among other postings. He has occupied his present position – by tradition, the PCA’s secretary-general is always Dutch – since 2008. “The Abyei case is exactly the kind of thing I mean,” he continues. “It was unprecedented for a breakaway movement to go into arbitration with its own government, to agree on a boundary which may become a border.”

Kröner admits to a certain crusading – if understated and diplomatic – zeal about the PCA’s possibilities. “For years,” he says, “this organisation has had a sleeping beauty aspect to it. But because of globalisation, we are being called upon a lot more. There are a lot more bilateral investment disputes, simply because there’s a lot more bilateral investment, and there’s a lot more attention paid to obscure conflicts which have been going on for years, because communications have become much faster and more accessible.”

The PCA has secured host country agreements with South Africa, India, Costa Rica, Argentina, Singapore and (pending ratification) Lebanon. The hope is that obviating the need for disputants to travel to the Hague will make arbitration more accessible. In 2010, the PCA will open its first overseas office in Mauritius – where they are likely to have little difficulty recruiting staff.

“We have to spread the gospel,” he says. “International law is still perceived as an invention of former colonial powers. But the combination of diplomacy and international law can be a very powerful tool. There is an idealistic ­dimension to this, but I am an idealist. If the international legal order can be strengthened, more countries can be persuaded to resolve things peacefully.”