[Nobel Laureate Thomas] Schelling observed that by skating without a helmet, a player increases his team's odds of winning, perhaps because he can see and hear a little better, or more effectively intimidate opponents. The down side is that he also increases his odds of injury. If he values the higher odds of winning more than he values the extra safety, he will discard his helmet. Yet when others inevitably follow suit, the competitive balance is restored - everyone faces more risk and no one benefits. Hence the attraction of helmet rules.
As in hockey, many of the most important outcomes in life depend on relative position. Because a "good" school is an inescapably relative concept, each family's quest to provide a better education for its children has much in common with the athlete's quest for advantage. Families try to buy houses in the best school districts they can afford, yet when all families spend more, the result is merely to bid up the prices of those houses. Half of all children will still attend bottom-half schools.
Sports are inherently zero-sum games. Because economics looks at positive-sum games, such as trade and growth, sports can be a dangerous metaphor for economics.
In the case of schools and house prices, I would make several remarks.
1. If we have vouchers and a market for schools, then the money that parents are willing to spend to get their children into better schools would be spent on schools, not houses. Assuming that this produces a supply response, the result would be some overall increase in education quality.
2. It could be that with markets and vouchers, the better schools would get more expensive and the poor would not be able to afford them. I call this a "segregation equilibrium," and I suspect that it explains some of what we observe in higher education today. Affluent parents want to send their children to "good schools," meaning schools that are attended primarily by other affluent children, which means that demand is a positive function of price.
3. If "segregation equilibrium" is a problem, then voucher programs should include a "luxury tax" on high-tuition schools, with the money used to boost vouchers for low-income families. In the worst case, if low-income parents continue to get priced out of the market for high-end schools, they at least can use their larger vouchers to procure better teachers and facilities for the schools that their children do attend.