Quadratic Funding: What’s a good opening move (as white) for chess beginners?
0
resolved Feb 18

Quadratic Funding markets are deprecated

This is a test of quadratic funding markets as a potentially more robust move selection mechanism for the "Manifold Plays Chess" series.

I'm still wrapping my head around how this thing works. First of all, it's more like a tipping (or, uh, funding) vehicle instead of trading for profits. Anyone can add a new choice to suggest a presumably good move, then contributors can "tip" their preferred choice, with the choice creator getting the donations, but there's also a matching pool which captures "excessive tipping" and sends it to other choices (as well as the market creator, I think?). So, the funds raised get distributed in a more democratic manner than regular free response markets. Seems like an interesting way to fund the creation of conditional binary markets for each suggested move (the funds raised for each move could get added as liquidity, or as an initial YES bet, but how to enforce it of the contributor who got the tips?). Anyway, seems to me there's still many quirks to understand and iron out.

The goal is to prevent "Resign" or any other bad blunders from getting picked, no matter how well funded an attacker might be. They could suggest a blunder and tip it up through an alt (or vice versa), but some of that (if excessive) would subsidize the other, more popular moves. However, I think attackers could still exploit it by using many different accounts to fund it.

When this experiment ends and I resolve (the button says "Pay out matching pool"), I suppose I'll get back some of the $500 subsidy cost and then any tips on the 3 suggestions I made (including the one decoy). So I'll send a manalink worth any excess amount, if any, to whoever ends up running "Manifold Plays Chess 3" (whether they use this mechanism or not). Or if no one gets that project going, maybe I'll post the manalink as a comment here. If an attacker somehow manages to steal the pot, shame on you! Right, I mean you all, honest players who didn't fight for it (just kidding! 😜 ).

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Please don’t throw any more mana into the matching pool, the [Contribute] button top-right. It’s a mana-eating black hole, I have no way of re-resolving to distribute those funds. At least until @Austin or someone fixes it.

Also, even if it get fixed, it’s not a great cause. @jack doesn’t need your charity.

https://manifold.markets/harfe/manifold-plays-chess-3-what-will-wh Maybe people here would be interested in picking a first move in the new "Manifold Plays Chess" iteration.

Thanks all. That was quite interesting and kinda weird. 🙃

@deagol And here I was naively thinking you wanted a good opening chess move 🤣

Uh after I resolved, it let me add 20 more to the pool but now I can’t resolve again 🤔 😂 cc @Austin

@SamuelRichardson I did! But for begginers.

Here’s a new summary accounting by user, but this time I’m truncating bonuses as shown by the interface, and netting things out by consolidating self-tipping by Jack and recovering most of the subsidy for me.

ᛗ148 net losses by

80 @deagol (includes 94 of the 500 to subsidize match bonuses net of

    300 from PolyArb recovered subsidy

    102 match bonuses recovered by e4 and d4

    4 unused due to truncation)

41 @JuJumper

8 @Jason

19 other donors

ᛗ148 net profit by

75 @jack (includes 64 from match bonuses, net of 300 recovered to me)

    consolidated from 10391 Jack, -10016 Jack2, -300 PolyArb (recovered subsidy)

36 @GiorgiGiorgi (includes 10 from match bonus)

27 @SamuelRichardson (includes 5 from match bonus)

8 @StevenK (includes 2 from match bonus)

2 @citrinitas (includes 13 from match bonus)

I guess all these could change in the next 4h, but probably not by much? Finally, if I focus on the matching bonuses shifts due to Jack2’s actions, I see it ended up costing me an extra 31 for subsidy protection services (after the 300 refund) while they jacked (heh) another 29 from a few “leeches”, and threw 6 Anton’s way. Sweet racket! 😝

Ah a little whale fight I guess, took a bit from @jack‘s loot 😱🍿

ah no that’s coming back to me… thanks, @PolyArb !

@deagol Oops I used the wrong account and I guess trades in QF markets aren't reversible.

@jack is that a problem? do you want me to tip back? lol this is all pretty nuts

@jack like, your intention was to tip me 300 back, but it’s a bit more with the extra bonus.. so what to do?

@deagol That's fine, don't worry about it.

Here’s a summary accounting by user/entry of where things stand 24h before close (I’m rounding figures while the interface above shows them truncated):

Totals: 166 net matched (from pool subsidy i.e me)

created 13 entries, total 103 direct tips received + 166 match received = 269 gross raised

(tipped 13 entries, total 103 paid)

@deagol 122 net raised (-44 net paid after subsidy paid)

created 3 entries, total 27 direct tips + 108 match = 135 gross raised

-e4 18 direct + 95 match=113

-d4 8+14=22

-Nf3 1+0=1

(tipped 5 entries, total -13 paid)

(subsidized 500, total -166 match paid, 334 remains in pool)

@citrinitas 7 net raised

created 2 entries, total 9 direct + 9 match = 18 gross raised

-Resign 6+6=12

-Resign 3+3=6

(tipped 6 entries, total -11 paid)

@Jason -8 net paid

created 2 entries, total 9 direct + 0 match = 9 gross

-Resign 6

-Nc3 3

(tipped 6 entries, total -17 paid)

@GiorgiGiorgi 47 net raised

created 2 entries, total 24 direct + 24 match = 48 gross

-Suggest backgammon 23+24

-b4 1+0=1

(tipped e4, total -1 paid)

@SamuelRichardson 38 net raised

created g4 (Grob’s Attack) 23+16=39 gross

(tipped d4, total -1 paid)

@StevenK 7 net raised

created 2 entries, total 6 direct + 6 match = 12 gross

-Wiggle Ra1 3+3=6

-Offer draw 3+3=6

@jack 9 net raised, created e5 5+4=9 gross

@JuJumper -41 net paid (tipped 3 entries)

@Fion -8 net paid (tipped 2 entries)

@AllanLacy -5 net paid (tipped e4)

@Gigacasting -3 net paid (tipped 2 entries)

@BionicD0LPH1N -2 net paid (tipped e4)

@harfe -1 net paid (tipped Resign)

It seems @citrinitas recruitment campaign hasn’t paid off (yet?). I suspect potential accomplices didn’t care much for such strongly worded arguments as, “you pay me because I was first” …is there no honor among thieves? But who knows, there’s one day left and plenty up for grabs in the pot.

Still, don’t think we should use this system due to the total lack of control on resolution payouts.

And just then @Jack2 showed up.

So it seems they’ll get 381 out of the matching pool, which from the previous accounting had 334 remaining unclaimed, which means they stole 47 of the other entries’ claims, I think?

@deagol Reclaiming your subsidy as requested :) I will tip you back most of it

I know, just figuring out the accounting. Thanks!

Recruitment campaign: I was hoping for N^2 chaos but it didn't really manifest

I think we've eaten most of the subsidy at this point? My ui is showing them adding up to 496 but that might just be rounding errors. I have no idea how the market works at this point, can the bonus go down if something else is voted up?

@citrinitas Yes, I think the bonus is just what would be paid if the market resolved as is, it's not locked in at all.

@citrinitas yes the whole 500 should have been used, the 4 leftover is because the UI not even rounds but truncates the green numbers. Not sure if that’s intended as what will actually get distributed or a funky page design thing.

My calculation is that the huge e5 donation would have deserved a match of 604: payout of (sqrt(4)+sqrt(1)+sqrt(10000))^2=103^2=10609, net of (4+1+10000)=10005 direct donations, gives 604 bonus, but that could only happen if the pool were deep enough, so adding that 604 with all the other entries’ bonuses gives ~792.5 which must be reduced by ~37% to 500, pro rata for all entries, and truncating those does match what the UI shows.

Oh crap all that’s changed now that there’s more donations..

@deagol I wonder why there was no subsidy for me?

@Jason If only one person funds an answer with X mana, then the target value is

(sqrt(X))^2

...which is just X. The subsidy only kicks in once you start getting into quadratic weirdness, when you have multiple people funding an answer.

@citrinitas @Jason The bonus subsidy match achieved by two donors tipping x and y turns out as twice the geometric mean of the tips, derived from the difference between the quad payout (binomial expansion) and linear payout (direct tips):

match bonus = (x^0.5+y^0.5)^2 - (x+y)

= x+2·(x·y)^0.5+y - (x+y)

= 2·sqrt(x·y) = 2·GM(x,y)

For n>2 donors it gets a tiny bit nastier but generalizes to those extra terms in the squared multinomial expansion, and that’s when the quadratic effect takes place since that grows roughly at n^2 times the average tip:

[sum(xi^0.5)]^2 - sum(xi)

= sum[2·(xi·xj)^0.5] (∀ i≠j)

= n·(n-1)·AM(all possible GMs taking 2 of the n tips)

This of course within the limit of the matching pool subsidy(ies), otherwise reduce the bonuses pro rata to fit. Like, at this moment my 500 initial subsidy in the pool can only cover ~38% of the bonus potential, which is over ᛗ 1308.

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