is winner-take-all broken?

Olympic athletes use a huge amount of sponsor money — not to mention legal and illegal performance aids — to reach gold. Soon we will have genetically engineered physiology to reach even greater records. Schools compete for an annual #1 ranking. They spend more and more money to bid for the best professors and build the best facilities, driving up tuition. Coding theorists run massive simulations to find the best code to compete for the one spot in standards. But is the second place athlete, school, and code that much worse? No, usually they are nearly as good as #1.

I’ve often wondered whether many problems in the world are not variations of attempting “exact optimization” — this being the only way to guarantee success in a winner-take-all reward system.

In engineering at least, when any kind of iteratively converging algorithm is run, the prototypical behavior is a fast convergence to a neighborhood of the solution, and then a really long process of getting to the exact one. In choosing exact optimization, a practically “good enough” solution is rejected in favor of expending a huge amount of resources to obtain the last 1% of the gap to optimality.

Where there is no bound to performance, a winner-take-all competition encourages ever-higher performance, driving progress. In reality, there is no system without some constraint that imposes a bound. We hope that rational allocation decisions will cause us to collectively halt at an approximate solution and move on to something else. However, this requires cooperative strategies. Winner-take-all is not stable for cooperative strategies, so we end up collectively committing resources disproportional to the amount of improvement we get in any observable metric. With the exception of the lone winner in each competition, everybody else suffers massive misallocation.

There are a number of absurd problems that arise from not developing a reward system consistent with a “soft” metric that gives some value to anything but the top rank.

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