I'll be constantly improving this when I have more time.
Market Scoring Rules (MSRs): MSRs replace the double-auction system (with bids and asks) with a simple update rule. Its optimal for a lot of things (particularly blockchain trading), but mostly for PMs, where people don't want to reveal (potentially secret) information by placing bids and asks that go unfilled. In a PM we want traders to be able to trade immediately and often. For details on how this works see my Excel demo (feedback appreciated): https://github.com/psztorc/Truthcoin/raw/master/docs/LogMSR_Demo.xlsx
Multidimensional Markets: Normally, with a PM, you be on something you think will happen. Multidimentional markets let you bet on 2 of 2 or 3 of 3 or N of N things, all happening together. Why do this? Firstly, MSRs make it cheap to do so, and preserve the option to bet on only 1 of 2, or 1 of 3 things. Software can make it psychologically cheap to do this. The costs are low. The benefits, however, are high. With mathemagic, we can move marginal, joint, and conditional probabilities around, and example the real-world relationship between two or more events. Ie, would the economy improve more under Fed policy 1 or 2? Would a stock price be higher with CEO Joe or CEO John?
I wrote some papers which some have found useful:
https://github.com/psztorc/Truthcoin/raw/master/docs/2_PM_Types.pdf
https://github.com/psztorc/Truthcoin/raw/master/docs/3_PM_Applications.pdf
And why not read a blog post by none other than Hal Finney, possible inventor of Bitcoin?:
http://www.overcomingbias.com/2008/07/intrades-condit.html
More blog posts about conditional markets:
http://www.overcomingbias.com/2008/04/if-i-had-a-mill.html
http://hanson.gmu.edu/futarchy.html
http://www.overcomingbias.com/2013/04/diagnosis-futures.html
http://www.themoneyillusion.com/?p=15446