TL;DR: Set yourself some challenges, put money at stake, and win big if your achievements are unusually surprising!
I read G.K. Chesterton's essay "[A Defence of Rash Vows](http://www.online-literature.com/chesterton/the-defendant/2/)" recently, and it got me thinking about what it might look like for a group of people to collectively make vows (which you could also call commitments, or challenges) that were challenging, but not too challenging. I came up with the following format:
Contestants each set themselves n challenges (for integer n>0 of their choice), and contribute $X * n^2 to a prize pool for some chosen X.
A prediction market is made for each challenge, resolving YES if it's completed before the competition is over and NO if not.
At some randomly chosen point early in the competition, a snapshot is taken of each market's probability (after they've had time to settle, before contestants have had time to make much progress).
When the competition ends, the prize pool is paid out to everyone who completed a challenge, in proportion to the log snapshot probability of all challenges completed - in other words, in proportion to how surprising their achievements were.
For example, let's say that Alice, Bob, Charlotte, Dennis, and Emily all complete one challenge. Their respective achievement odds were 1%, 2%, 10%, 50%, and 80%. The total prize pool is $100000.
In base 2 log odds (i.e. converted to info-theoretical bits of surprise), these are:
Alice: -6.64385619
Bob: -5.64385619
Charlotte: -3.321928095
Dennis: -1
Emily: -0.321928095
These are their relative shares of the prize pool, so they get paid as follows:
Alice: $39239
Bob: $33333
Charlotte: $19619
Dennis: $5906
Emily: $1901
These are rounded down, with $2 left over - the organiser might keep this as a fee.
Each contestant only completed one challenge here, but this generalises to arbitrary amounts of challenges per contestant - just sum the total bits of surprise (or, equivalently, the total payouts).
Thus, you're incentivised to commit to completing challenges that are difficult (so you get a larger share) but not too difficult (so you actually stand a chance). The quadratic entry fee structure means you need to choose your challenge(s) carefully.
Does this actually work? I dunno, but let's try!
This competition has a base entry fee of Ṁ1000. I'm setting myself 5 challenges and putting Ṁ25000 in the prize pool to get the ball rolling.
If you want to sign up, send me the challenges you're setting yourself (in the comments, or DM me here or on Discord) and managram me your stake (i.e. Ṁ1000 * (number of challenges)^2)! Feel free to only set a small amount at first and increase your stake later. Make sure it's something challenging but achievable, and something you can prove (if not publicly, then at least to me).
The deadline for challenge submissions is the 11th of October (any time zone). The deadline for achieving your challenge is the end of 2024 (if it comes down to the exact time, we'll use this market's close time).
You can find the competition details here.
1,000🏅 Top traders
| # | Name | Total profit |
|---|---|---|
| 1 | Ṁ62 | |
| 2 | Ṁ35 | |
| 3 | Ṁ26 | |
| 4 | Ṁ23 | |
| 5 | Ṁ22 |
Let's try this! Put me down for the following challenges:
Wasabipesto will publish 10 new blog posts on wasabipesto.com
Writing is generally good for me and I keep meaning to do it more. It helps me focus my thoughts and my blog framework makes it easy to build interesting visualizations from data to support my writing. I have 5 posts so far in addition to my basic "about" pages, most of which were recycled from writing I had already done. I also have one post in-progress but haven't touched it for a few weeks.
Wasabipesto will finish reading 3 more books in 2024
For the past few years I have read 7-9 books per year, but this year I've only completed two so far this year. As much as I am amused by Tumblr, any time I'm on my phone and not reading a book is effectively wasted time for me. I got about halfway through one book (Cryptonomicon) before dropping it and I'm about halfway through one now (The Mercy of Gods) - if I complete either one they could count. I track my completed books here.
Wasabipesto will complete the next major update to Calibration City
I haven't been working on Calibration City (AKA Themis) as much as I would have liked. The fetch script needs updates and I have plans for a few new features that I haven't even started on. Knowing me, this will turn into major rewrites of the entire system taking months. Hopefully this will incentivize me to actually ship something in a reasonable timeframe. The repo is public here, and the site is here.
Assuming I'm reading the rules correctly, for my 3 entries I'll submit my M$9000 to @NcyRocks.
@wasabipesto And yes, you seem to have read the rules correctly. (I wonder if this format might be more effective with a linear rather than quadratic pricing structure, but I'll leave that for next time - maybe for 2025 New Year's resolutions.)
@NcyRocks Updates:
Just today I published my tenth new blog post, marking this one complete! I should have been writing more consistently but I got it in under the wire.
I've not actually completed my third book (Almost Nowhere) so this one will remain incomplete. I sped through Mercy of Gods and The Northern Caves but spent multiple weeks just not reading at all.
As I suspected, I never actually started the next CC project. It's still one of my top priorities, but it's a big, intimidating one to start.
The past few months have been quite hectic, and I'm glad I was able to accomplish at least one of these goals. Without this competition I don't think I would have done even half as much. I would be interested in trying a similar contest in the future!
@wasabipesto Well done indeed! I didn't finish a single one of my challenges 🫠 so you get the whole amount!! (Assuming you got it in by the market's close time ~15 hours ago? I realise now that it closed on the 31st pretty much everywhere and relatively early in the day in most places, so let me know if that feels unfair.) Maybe now other people will want to join in 😅
I don't have the Ṁ34000 right now, but I'm hoping that all the New Year's resolutions (the Manifold kind, not the challenge kind) should give me and my bot enough to pay you back, so I hope you're okay with waiting a day or two. (Or if you didn't complete your last blog post in time, then I didn't actually specify what happens if neither of us complete anything! 😬 Returning your Ṁ9000 seems fairest to me).
@NcyRocks I only had 7/10 posts live 15 hours ago - you can see my exact commit history here.
I did assume that the deadline would be midnight somewhere in the US, and that these last posts would count. I saw that line in the description about the market close time, but I should have checked the timezone to see when exactly that was. If I had thought to check, I would have spent last night wrapping them up instead of playing Balatro!
I'm okay either way, a refund seems reasonable given the circumstances. I'm also perfectly fine waiting for payment either way.
@wasabipesto I've decided to should stick to the letter of the description (apologies for making it so unintuitive) but to also give you an extra Ṁ8000 for joining in with this experiment, effectively splitting the prize pool in half. I hope that's an acceptable compromise.
I've made a set of New Year's Resolutions in a different market here: /NcyRocks/nc-youngs-crystallised-new-years-re so if you want to do this kind of challenge again, I've already got a bunch of challenges picked out! (I'd have to make a different market, though, and I'd want to change the pricing structure a bit.)
Some observations:
Committing to one 50% likely challenge for Ṁ1000 has an EV of about Ṁ4533 - come on guys, take my money!
Assuming the market is 100% efficient, the optimal likelihood for a challenge is 1/e ≈ 36.8%. (Which would currently have an EV of Ṁ4672!)
I'm not sure the market is very efficient, but maybe I should shut up and put as much faith in myself as you guys seem to have.
@resourceabet I just managed 12. I’ve been going to the gym semi-regularly but haven’t practiced pushups for ages.