Project description

If you see a market on manifold that is at 20%, and you think the true probability is 25%, how much should you bet to maximise your long term profit* and provide as much information as possible? There is basically a correct answer to this, which is to bet in a way which is "Kelly optimal", i.e. it maximises expected log(portfolio value). Currently it's fiddly and annoying to work this out.

My project is to create a tool for conveniently calculating this. At a minimum** this will be a website where you put in your username, the market you are betting on, and your estimate of the true probability, and it tells you how much to bet.

The impact case for this is:

- I personally want something like this. I sometimes can't be bothered to work out the correct size of bets and so don't bet or just bet a token amount. Making it more convenient to do Kelly betting by default will make at least me participate in prediction markets more, and more rationally. Hopefully this will also be true of other people

- Markets learn at the optimal rate when individual bettors use Kelly betting. So if this makes more people bet in a way that is closer to Kelly optimal, then this should improve the accuracy of prediction markets

- This will increase the incentive for people who aren't prediction market fanatics to contribute information, by giving them a tool they can just blindly trust to bet a sensible amount rather than having to learn any prediction market specific theory. Currently if you sign up for manifold because you have inside info on a particular market you might be tempted to bet everything (and possibly lose it all), or just bet a token amount (and provide little information), neither of which are ideal

What is your track record on similar projects?

I'm a software engineer by trade. Currently I work on the EA Forum, you can see some of my code here: https://github.com/ForumMagnum/ForumMagnum/pulls?q=is%3Apr+author%3AWill-Howard

I also use manifold fairly actively and have thought about bet sizing a lot: https://manifold.markets/WilliamHoward?tab=portfolio

How will you spend your funding?

The funding is solely to incentivise me to do this. I have already started this project but I'm not currently prioritising it relative to other things, so without this funding it will take much longer

*This is not strictly true, maximising expected log(wealth) actually doesn't maximise expected wealth, but directly maximising expected wealth tends to result in losing it all. The justification for Kelly optimal betting is actually very long and complicated and not well agreed upon, but it does seem "obviously correct" in the sense that it does better than any other strategy at growing your wealth while not having any risk of losing it all. There is some good discussion of this on lesswrong, see here for starters: https://www.lesswrong.com/posts/HFLuBv8NrBEysRGLZ/why-bet-kelly-1

It is true that Kelly betting optimises the rate at which markets learn information, which is perhaps a better justification from an impact perspective: https://people.cs.umass.edu/~wallach/workshops/nips2011css/papers/Beygelzimer.pdf

**I am planning to do more than this to make it more convenient to use, such as:

- a chrome extension

- trying to get this added to the actual manifold site

Additionally the potential scope of things you could model in order to make the bet sizing more accurate is quite large:

- The opportunity cost of betting in a particular market (e.g. if you are able to get an average return of 5% a month, you shouldn't accept a 5% expected return in a market that resolves in 10 years)

- Accounting for market dynamics (e.g. will the market quickly correct to my probability so I can sell out, or will I have to wait for the resolution?)

- Accounting for the manifold loan system, and also informal loans between users

- etc

But the minimum I'm committing to is a simple calculator that works for binary prediction markets, and accounts for the most important factors. By default I expect to do more than this