LMSR Made Interactive
02 August 2014The Logarithmic Market Scoring Rule (LMSR) is the rule which governs the price of trades on SciCast. SciCast’s predecessor, DAGGRE, produced a tutorial video on the LMSR.
I thought it might help if people could play with the LMSR directly, to get a feel for how it behaves. I looked around at my options for making interactive mathematical plots, and decided that the best option for the amount of time I was willing to put in was Mathematica CDF files. You’ll need the CDF player installed.
You should have two sliders, “start” and “tradeto”, as well as a graph with two curves on it, one red, the other green. If not, something has gone awry. Sorry.
The value of “start” represents where the trade is starting from; the current state of the market. “tradeto” is the value of the trade you’re considering making (this assumes power mode). “start” and “tradeto” are depicted visually on the graph by vertical lines labelled “S” and “T”. “start” controls a second line, labelled ▽.
Where T intersects with the Yes (green) and No (red) lines, there is a number which is the points you’ll gain (positive) or lose (negative), if the question resolves as Yes, or No, respectively. Between the S and ▽ lines, any trade you make has the potential to earn more than it risks. Everywhere between those lines has decimal odds of ≥2.0.
I have a number of other interactive graphs I’m planning to put up, but I’m still tweaking them. If you’ve got access to Mathematica, and you’d care to root around in my scicasting repo you can find my more-or-less in progress Mathematica notebook where I’m developing them.
On a programming note, these graphs are the most complicated things I’ve ever bothered to do in Mathematica. I’m pleased to discover that a lot of the horrifying looking Mathematica code I’ve seen on their blog, and elsewhere on the Internet over the years, was much worse than it had to be. Apparently nobody believes in adding whitespace to format things nicely. On the downside, it still hurts to read.