Who Gets What – And Why? Alvin E. Roth

This book received a good review in Mathematics Today, and I always like to read books by leading experts. In this case, Roth is a winner of the Nobel Prize for Economics for his work in market design: a leader in designing and implementing sorting algorithms for kidney donation, medical job applications and school place allocations.

He gives detail of how algorithms are developed, how they are applied and why they provide a stable solution, as well as the importance of the stability of this solution for that allocation to function well and prevent systems disintegrating and failing to serve the people within them well. Of course only systems that don’t “naturally” reach sensible stable solutions will attract the interest of a market designer.

I didn’t approach this book with an entirely open mind as to the motivations of the author though. Due to the current political drive to make everything into as free a market as possible, I am wary of economists applying market theories to parts of life where it does not intuitively apply. But Roth has the flexibility to talk about goodness of match for the purpose of his reason, not just financial value. But sometimes that viewpoint can be valuable, when we fall into the alternative universe of US healthcare…

If a hospital sends a non-directed donor, the NKR promises to end one of its chains at that hospital. That ensures that the hospital doesn’t “lose” a transplant by sharing its donor. Keep in mind that hospitals earn revenue on their transplants; they’re commercial enterprises as well as caregivers.

But oddities of US healthcare aside, this is a well-written book, giving an insight into how matching works when markets are designed. and the value of this to our institutions.

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