For 50 years, property has sat at the centre of every negotiation on Cyprus, and every time it has been deferred to a “comprehensive settlement”. In a recent article for the Turkish Cypriot daily Kibris Postasi, I argued that Turkish Cypriots should return to, and reclaim their rights within, the Republic of Cyprus. The hardest part of that return is property. Yet return is also what makes the property problem solvable.

Economics may offer a way through, from an unexpected direction. Tayfun Sonmez and Utku Unver, two Turkish-born economists at Boston College in the US, together with Nobel laureate Alvin Roth, designed a system for kidney transplants that today saves thousands of lives in many countries.

The problem is simple. A patient needs a kidney; her husband is willing to donate, but they are not compatible. In another city there is another such pair. If the donors match crosswise, they swap, and both patients receive a kidney. Such pairwise matches are rare. The breakthrough was to move from pairs to cycles and chains: A’s donor gives to B, B’s to C, C’s to A. An altruistic donor can start a chain that makes dozens of transplants possible. The larger the pool, the more cases are solved. All of this happens without money: selling a kidney is banned, but exchanging one is allowed.

Now apply this to Cyprus. Consider four families. Ahmet owns a house in Limassol but has lived since 1974 in Andreas’ house in Kyrenia. Andreas lives in Paphos, in a house owned by Mehmet. Mehmet lives in north Nicosia, in a house built on Eleni’s land. Eleni lives in Limassol, in Ahmet’s house.

All four want to stay where they have lived for half a century. But no two of them hold each other’s property. Consequently, no bilateral deal is possible. In a common pool, a single four-way exchange gives each family title to the home it lives in. Nobody moves. Fifty years of uncertainty end with four signatures.

Two rules matter. Nobody ends up worse off than today. And anyone can say no: those who refuse are not penalised.

How would it work? Under the Republic of Cyprus, with international support, a single bicommunal exchange centre can be set up. Independent valuation converts each property into points, and a compensation fund covers any differences. An algorithm searches for cycles and chains at regular intervals. Today, the Immovable Property Commission in the north and the Guardian of Turkish Cypriot Properties in the south work separately, case by case. It is like searching for a compatible kidney one hospital at a time: most patients would never find a match.

It is true that there is more Greek Cypriot property in the north than Turkish Cypriot property in the south, so this mechanism alone cannot solve everything. But being unable to solve the whole problem is no reason not to solve part of it.

The imbalance is not fate. The lesson of kidney exchange is that a bigger pool solves more cases. There is public land on both sides that could be opened for development. In addition, the UK has twice offered to hand back around half of its base areas once the Cyprus problem is resolved: Tony Blair’s government in 2004, as part of the Annan Plan, and Philip Hammond, as foreign secretary, in 2015. Both could act as altruistic donors.

This proposal also helps to answer the most challenging question in the talks: owner or user? A Greek Cypriot owner wants her home back; a Turkish Cypriot family lives in it. A “donor” property from the pool offers that family an equivalent home. The family moves, and the owner returns. Nobody loses.

The Bosnian experience is helpful here. Displaced people there were given the right to reclaim their pre-war property, and by 2004 around 93 per cent of claims had been resolved. Yet many who regained their homes sold, exchanged or rented them rather than returning. The right to return does not mean everyone returns. However, it is crucial to recognise this right, as it frees people to choose. This proposed system aims to do exactly that: those who want to return can, and those who do not can choose exchange or, failing that, compensation. When people are free to choose, peace stops being something imposed on them and becomes something they own.

Time matters. The 1974 generation is now in its late 70s and 80s. Every year, owners die without knowing the fate of their property, and with each death the problem is divided among more heirs. Waiting is not neutral.

Where should the political will be sought? A return to the Republic is no one’s favour; it is the ground that the world and the Greek Cypriot side already accept. The Republic has always held the position that it is the state of all Cypriots.

The first step, therefore, lies with the Turkish Cypriot side. The Republic’s task is then to make the return work. In the meantime, a clear signal from the Republic, with no ifs and no buts, that it welcomes this return, and would support a system like this, would make that first step much easier.

A personal note: As a Turkish Cypriot, wherever I have lived in the world, in the UK or elsewhere, I have carried the weight of Greek Cypriot property on my back. I want nothing that belongs to anyone else. A debt is a debt.

Perhaps an idea that saves lives can also help heal a 50-year-old wound.

Engin Kara is a professor of economics at Cardiff University, UK