> Except that it does affect the positions of others, by pushing them down the list. If there were another opening at someone's preferred school, that doesn't m

> Except that it does affect the positions of others, by pushing them down the list. If there were another opening at someone's preferred school, that doesn't mean that someone would get it. Others likely want it, and one may be ranked higher. But by voluntarily swapping in this way, the results of each of the schools' lotteries are discarded, and others are disadvantaged as a result. You're creating a strawman and arguing against that. I am talking about the exact situation that is covered in the article. This is what the article says: Suppose a student loses the lottery at their number one school (school A). But they win the lottery at school B. And suppose that another student likes school B best. But loses the lottery at school B, and wins the lottery at school A. Then these students won each other’s jackpot. And so they both want to trade. The article continues: With these trades, more than 600 further students could get a place at their top choice school, it later turned out. So many students wanted to trade. This prospective trade wouldn't disadvantage anyone. It would only swap positions to increase people's choices and positions.