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Lets go (note, these are my rough picks – they aren’t associated with anyone else, and they definitely don’t exist in a professional capacity) :
I aim to sketch out a few thoughts I have based on the study of economics. If there is a political scientist out there (or anyone else for that matter), I would be more than happy to hear about the multitude of logic flaws in my description 
To start with I should describe the general international relations (market
) failure involved in a relationship like the Israel-Palestine relationship (therefore, I am not saying that the following this ARE happening – I am saying that they are indicative of the type of situation).
The way I see it there is a prisoner’s dilemma going on. Both countries would prefer it if Israel was not closing off its borders, and if Palestine did not support people who were shelling areas in Israel. However, it is a “dominant strategy” for Israel and Palestine to do each of these things. Fundamentally, if one side tried to lighten things up, the other side would take advantage of the situation – so they both end up worse off.
Now this is no good – and it suggests that there could be scope for an independent third party to come in and enforce the “pareto superior” equilibrium with no closed borders and no shelling (Note: I realise that this is a HUGE simplification – Palestine does not necessarily fully control the shelling, and Israel cannot be forced to just “open its borders”. However, it is a useful EXERCISE to get an idea of the issues – I do not expect to be able to solve anything from this).
So here we have assumed that the goal of an objective third party is to get “pareto optimal” outcomes, given current allocations of “resources”. Given this view, there could be scope to broker an agreement. However, this view misses a very important element – the drivers of the allocation of resources, and the payoff associated with each nations actions.
Think of it this way. If the third party stuck to the view that they would try and come up with a “pareto optimal” solution, the stronger party could take advantage of the situation by declaring war, taking land, and then asking the impartial body to mediate. In this case, the solution may be pareto optimal relative to the current allocation – but it may be construed as “unfair” relative to the initial resource allocation.
As a result, the third party has to take this into account when stating action – or else their rule of “static pareto optimality” will lead to suboptimal outcomes overtime. This makes the issue a whole lot more difficult.
In this case, there is a “rights based” element to the negotiations. The different nations believe that they have a justifiable claim over the same territory.
Fundamentally, as long as the third party believes that there is a justifiable rights based claim on land – it would be more difficult for them to define a pareto optimal outcome.
Now, in this case so much depends on the value judgments implicit in our third parties view. How long can the historical claim on land be? Is there some intrinsic right to this land beyond the third parties aim to avoid the “strong attack weak” scenario – fundamentally here I am asking whether prior ownership of the land creates some value over it. If it does – then the situation we are in is even fishier.
Conclusion
Fundamentally, we have decided that the long-term conflict between these two countries (not just the war) is the result of a prisoner’s dilemma.
Our third body (the UN) is unable to mediate effectively because dynamic considerations, and because the joint claim over land makes pareto improvements more difficult to come by.
If the general situation wasn’t difficult enough to solve we have the added complication that the UN is actually a set of varying value judgments – not an objective social maximiser. In this case, the whole idea of policy actually being put in place to improve outcomes for both parties in this type of situation seems slight.
However, we will see in the current case.
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