Danish math major
Yes.I agree that the original post keeps going after removing differences in values because they don't remove differences in marginal value, which is what matters.I am providing an example where properly removing the differences in marginal value results in no trade.You are using a nonstandard definition of goods. Would you equally object to a market with only blueberries, apples and bananas on the basis that there is only one good available (fruits)?The example world can be modified easily to use any utility function of the form a·red points + b·yellow points + c·blue points.
Yes.The comment was meant as a proof by example that you can have no trade in a world with comparative advantages, if everyone has the same marginal value of all products the result is no trade.Diminishing marginal returns are indeed enough to make marginal values different between people.
People could trade making each others numbers bigger, it's just that it will never be beneficial for both.Letting people increase others numbers by decreasing their own number doesn't change the results
Example world without trade.Every person gets at birth assigned an array of 3 integers a blue number, a yellow number and a red number. Every person has 3 attributes: the speed they can increase a red number (by spending that amount of time counting out loud), the speed they can increase a blue number, and the speed they can increase a yellow number. They can increase their own numbers or anyone elses. (Note we are not assuming everyone has the same amount of red, blue and yellow points at birth or that they are all equally fast at producing them). Everyone knows that there are no ways to become better at increasing your numbers.Everyone has the following utility function: red points + blue points + yellow points.This world has no trade! But it does have comparative advantages!
Two of the removed features are removed incompletely.Differerences in preferences. What is important for trade is the marginal preference. So to remove this motivation to trade one mus assume the marginal value (both intrinsic and instrumental) to be equal for everyone for all goods, which i think can only happen in some very weird cases (eg all gods have no instrumental value and utility is a linear combination of the products).The difference in peoples productive capacity (which doesn't by itself result in trade (it does when assuming diminishing marginal value to personal consumption of the same product)) is not captured completely by their human capital, it is their all their capital. So normal capital differences could cause trade in any situation where human capital could.Trade can also be used to facilitate coordination, cooperation and information.Trade can allow parallelization of work (a kind of cooperation), and can in general let you play with time (eg work to create a product with the intention of trading it for something later (when you have better information about what you want))
Does you intuition still hold in the [Least Convenient Possible World](https://www.lesswrong.com/posts/neQ7eXuaXpiYw7SBy/the-least-convenient-possible-world) where costs of creating new beings is 0?
At least the big Brittish schools this doesn't clearly hold based on the experience of people i know. Granted the evidence i have is consistent with them only caring about silver or better.Also my impression for the Russian schools was that not speaking Russian was a problem they were happy to work around (which certainly isn't true everywhere)
The Danish team leader (the closest source to these events i have talked to) seems to (personally) believe the cheating allegations in 2010 or at least that the evidence was insufficient. Also note their non participation in 2017 and 2018 for reasons not known to me and in 2020 likely because the event was online
The comparison to chess is maybe more accurate than you think.See stuff like:Beginnings: The first IMO was held in Romania in 1959. It was initially founded for eastern European member countries of the Warsaw Pact, under the USSR bloc of influence, but later other countries participated as well. (source https://en.wikipedia.org/wiki/International_Mathematical_Olympiad)Also classic geometry is (to my knowledge) taught more generally in many eastern European countries (and make up 1/6-1/3 of the imo).Also the note about incentives being larger in North Korea also applies to much of eastern Europa to a lesser degree, where qualifying for imo is seemingly enough to get access to any university (source: Sankt Petersberg university gave an open offer at Baltic Way (a regional math competition), and i know someone who used something like that to get into Moscow university)(Romania, Serbia, Poland, Russia, Ukraine Hungary are the eastern european countries with consistently good results)
One possible way to get at the hack of ignoring unlikely possibilities in a reasonable way might be to do something similar to the "typical set" found in information theory. Especially as utility function maximization can be reformulated as relative entropy minimization. (Epistemic status: my brain saw a possible connection, i have not spent much time on this idea)