Of course in such a case they would do the swap voluntarily if they could. Then the situation before the 3-for-5 swap was not Pareto optimal, and the situation after the swap is Pareto optimal. It’s possible to make a trade that makes both sides better off, let’s say for example that perhaps a swap of 5 bushels of rice for 3 bushels of beans makes both islanders happier, and there’s no subsequent swap that would improve the welfare of both. So the distribution where each has only one is probably NOT Pareto optimal. Well, rice and beans is a tasty combination that makes a complete protein, whereas rice or beans alone make a dull and unhealthy diet. Now imagine one island has big piles of rice and the other has big piles of beans. The 1-3 distribution was already Pareto optimal, as is 2-2 - there’s no way to help one person without hurting the other. But - and this is the key point - we haven’t accomplished ANYTHING in terms of Pareto optimality. We can just recognize that under certain rules of optimality - say, one where we simply add up the “utility” of the two islanders - and given some other assumptions about how utility works and how adding works, we can say that moving a tree takes us from suboptimal to optimal. Of course the ethics of such social planning are hotly contested, but we don’t need to get into that here. Now, if you were to uproot a tree from Island 3 and move it successfully to Island 1, under many definitions of optimality you would be making things more optimal - you’d be taking one person from the brink of starvation to a satisfying situation, while only harming the other a small amount. (the coconuts are the only food source on these islands in my silly made-up example). Island 3 has three trees 90% of the time two trees deliver enough coconuts that the hermit living there doesn’t eat anything from the third tree (the coconuts just rot on the ground), but occasionally the third tree brings him some pleasure as he’s in the mood to gorge himself that day. You pass through the region briefly and have an opportunity to make changes - you are what economists call the “social planner.” Let’s say Island 1 has 1 coconut tree, which delivers barely enough food for the hermit’s survival. But most economic situations are not zero-sum.Ī nice way to see the difference between “optimal” and “Pareto optimal” is to imagine two hermits on desert islands. In a two-player, zero-sum game, all distributions are Pareto optimal, helping one person always hurts the other. The name comes from the great Italian economist Vilfredo Pareto, who developed the concept of “Pareto optimality.” A distribution of goods is Pareto optimal if it is impossible to give one person more without giving someone else less. A recent article in 538 proposed the name “ Pareto Game” for the situation where a player puts up a stat line that no one in NBA history has exceeded in each category.
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