Do School Lotteries Work?
I've been following the Brighton & Hove school lottery case for a while (see here) and, indeed, written about it in print (see here, subscription required).
In other words, the reason it failed is not because it's a lottery (though of course equal chances don't guarantee equal success) but because it wasn't a lottery. It's important to realize that restrictions on who can enter a lottery, for example, can go a long way to 'fixing' the outcomes and therefore cancel out the benefits.
For more on these issues, see the books by my friend Olly Dowlen and Conall Boyle's recent book specifically on school lotteries.