I would read The Bitcoin Standard. It discusses this and much more. It's a great resource.

Thank you, zapped :)

Thank you, zapped

Ok i know im replying months late here. But maybe its helpful for anyone stumbling on it. Check out "The Book of Satoshi". It's not specifically on the halving but goes into detail about and discusses the important writings from and discussions with Satoshi early on. Includes a lot of quotes and message board threads where they debated various potential functions features and implementation of bitcoin. Among that is was a discussion on the supply formula. Very interesting to read a sorta behind the scenes on bitcoin's origins!