4 ms·

I can try to answer any questions you might have. The article highlights two main contributions of Arrow. One is a question of how a society can make collecti

I can try to answer any questions you might have. The article highlights two main contributions of Arrow. One is a question of how a society can make collective decisions. A classical answer is "utilitarianism" -- if a collective decision makes me happy more than it makes you sad, then we should do it. This requires society to be able to be able to measure exactly how happy something makes me and how sad it makes you. What if we can't make those kinds of measurements? Arrow shows that (under reasonable assumptions) we're stuck. There is no good rule to decide. His other contribution was to "general equilibrium". A set of markets are "in equilibrium" if we can find prices so that supply and demand are equal in every market simultaneously. Do such prices exist, even in theory? Arrow showed that the answer is yes.

earthboundkid 7y ago
I don't have the background to actually ask this question, but don't general equilibriums turn out to be NP-hard, meaning that the market can't always compute the solutions with a reasonable about of information exchange?
- QuesnayJr 7y ago
  In Arrow's version the inputs are continuous rather than discrete, so I don't know if NP-hard is the right criterion. There is a discrete version that is NP-hard, but I'm not sure you even have existence for that case. The continuous version of general equilibrium is as hard as solving an arbitrary continuous system of equations, which is probably pretty hard. There are a bunch of criticisms of general equilibrium. Some of these were begun by Arrow himself. If you have prices that are out of equilibrium, can you adjust them to be in equilibrium? If you see the whole demand curve, then you could. But imagine you just know that there is unfulfilled demand for some goods, and excess supply for other goods. If you just make small adjustments in prices to lower excess demand or supply, will you eventually converge on market-clearing prices? Arrow showed that the answer is: it depends.

earthboundkid 7y ago

I don't have the background to actually ask this question, but don't general equilibriums turn out to be NP-hard, meaning that the market can't always compute the solutions with a reasonable about of information exchange?

QuesnayJr 7y ago
In Arrow's version the inputs are continuous rather than discrete, so I don't know if NP-hard is the right criterion. There is a discrete version that is NP-hard, but I'm not sure you even have existence for that case. The continuous version of general equilibrium is as hard as solving an arbitrary continuous system of equations, which is probably pretty hard. There are a bunch of criticisms of general equilibrium. Some of these were begun by Arrow himself. If you have prices that are out of equilibrium, can you adjust them to be in equilibrium? If you see the whole demand curve, then you could. But imagine you just know that there is unfulfilled demand for some goods, and excess supply for other goods. If you just make small adjustments in prices to lower excess demand or supply, will you eventually converge on market-clearing prices? Arrow showed that the answer is: it depends.