Final score is YES: 683.71, NO: 222.02, so that's a decisive win for YES.

Thanks for betting on this market, all 75 of you! (Even though my NO team lost...) Glad this little square root concept was fun. I guess I'll make some more self-resolving markets in the future!

@Conflux

let

GetID = Json.Document(Web.Contents("https://manifold.markets/api/v0/slug/will-team-yes-have-more-total-sqrts")),

Source = Json.Document(Web.Contents("https://manifold.markets/api/v0/bets?contractId=" & GetID[id])),

#"Converted to Table" = Table.FromList(Source, Splitter.SplitByNothing(), null, null, ExtraValues.Error),

#"Expanded Column2" = Table.ExpandRecordColumn(#"Converted to Table", "Column1", {"amount", "shares", "outcome", "userUsername"}, {"amount", "shares", "outcome", "userUsername"}),

#"Grouped Rows" = Table.Group(#"Expanded Column2", {"userUsername", "outcome"}, {{"Cost", each List.Sum([amount]), type number}, {"Shares", each List.Sum([shares]), type number}}),

#"Filtered Rows2" = Table.SelectRows(#"Grouped Rows", each [Shares] > 1E-10),

#"Added Custom" = Table.AddColumn(#"Filtered Rows2", "ShareRoot", each Number.Sqrt(Number.Round([Shares],10))),

#"Grouped Rows1" = Table.Group(#"Added Custom", {"outcome"}, {{"SumSqRt", each List.Sum([ShareRoot]), type number}, {"SumShares", each List.Sum([Shares]), type number}, {"SumCount", each List.Sum([Cost]), type number}, {"RowCount", each Table.RowCount(_), Int64.Type}, {"Holders", each _, type table [userUsername=text, outcome=text, Cost=number, Shares=number, ShareRoot=number]}})

in

#"Grouped Rows1"

Alright, we've got 9 hours to go, and it's not looking good for Team NO. I did the math, and currently Team YES has about 451.4 total sqrt while Team NO has about 138.9. The gap is 312.4, which would require a single whale to buy 97618 NO shares to close the gap at a current cost of about M$92.5k. If AlexRockwell decided to defect, he'd only have to buy 81646 NO shares, a cost closer to M$76k. Both of these moves would only be safe if executed right before market close, since if any trade was executed after these, enough shares could be bought for cheap that YES would probably trivially take the lead again. Also, I expect YES to take an even larger lead.

Although, a team of NO bettors could still do well. A team of 8 bettors would only have to buy 1526 shares of NO each, total cost M$7k. That's pretty reasonable! I wouldn't count team NO out. It still moves the market to 0.3%, though. A 16-bettor team needs 381 shares each, total cost about M$1150, only moves the market to about 42%. Costs a lot though. Realistically some defectors would probably be part of the plan - pluck off a few top YES shareholders and the 8-bettor numbers start looking fairly reasonable.

So who wants to try to make this happen in the last nine hours of the market? Anyone?

@Conflux by "Costs a lot though" I actually meant, like, "16 bettors is a lot though"

@Conflux Also, remember, you just need to believe in this 5%!

@Conflux i'd be down

@Conflux sure id help

@Conflux This plan seems like it can easily be foiled with a few well-placed limit orders. Once you send the market below 50%, betting against limit orders becomes more beneficial to Team Yes than Team No. Especially if the NO bettors already have thousands of shares.

@JosephNoonan Oh yeah, I didn’t factor in the limit orders. Kinda crushing actually to this plan

I've made two variants:

Using the sum of square roots instead of a simple sum introduced an interesting dynamic to this market. Pretty early on, someone bought a large number (>500) of NO shares and was the largest shareholder. This caused the market probability to go way down, making YES shares cheaper. Traders pretty quickly took advantage of this and started buying cheap YES shares, which in turn caused the total number of sqrt(YES shares) to go up. But since these shares were distributed among many traders, while most of the NO shares were concentrated in a single trader's hands, the sum of sqrt(YES shares) surpassed the sum of sqrt(NO shares) long before the total number of YES shares surpassed the total NO shares. Since the market probability is roughly equal to the relative number of total shares, not total sqrt(shares), we ended up in a situation where the total number of sqrt(YES shares) was higher than the total number of sqrt(NO shares), despite the market probability still being way below 50%. Which of course made the true probability (as opposed to the prob displayed by the market) of a YES resolution much higher than 50%, since anyone could join the team that was currently winning for a cheaper price than the team that was currently losing, thus causing the YES team to pull ahead even further. And anyone could easily predict that this would happen, making it even more likely that people would bet YES, making the probability of a YES resolution even higher, and so on.

Eventually, enough people bought YES to bring the market above 50%, but at that point, the YES team was so far in the lead that it wasn't worth it to bet NO, even if the shares were cheaper. And that's how we got to the situation we are currently in, where, unless some big shake-ups happen, YES looks likely to win in a landslide. This probably wouldn't have happened in a market based on the plain old total number of shares of each side, since there, a large bet holds a lot more weight in the resolution, so it's not as beneficial to bet against it, and it can't be outweighed by a large number of small bets without moving the probability back up to balance things out.

The moral is, you shouldn't bet large amounts early on in a market like this, since the situation that resulted was predictable by thinking through the consequences of the bet. Buying a large number of shares can actually decrease the probability that the market resolves in your favor.

Also, one of the ways a big shake-up could happen is if a YES bettor made the same mistake, and bought this market up to some ridiculously high probability. The same situation would occur: People would be incentivized to buy NO, based on the idea that "Sure, YES is in the lead, but the chances of a NO victory can't be that low", the opportunity to sell them for a profit, or because they forsee this entire dynamic playing out (so, in some ways, it can be a self fulfilling prophecy). With the NO shares being so cheap, NO bettors would get a lot of them and could end up with more sqrt(shares) than the YES bettors.

So uh...., no one do this.

It seems that this market is being misunderstood (given the statistically significant deviation between YES and NO holders). This market should be at 50%, if I'm not mistaken.

@8 I haven’t done the math, but the YES/NO gap looks hard to whale rn. But maybe if NO shares get cheaper it’ll be worth it!

@Conflux ah, i see

@8 If an enterprising NO holder wanted to get more bang for their buck, they could pay other people to buy NO, so that could be one avenue

@8 No, the probability is only 50% before anyone starts betting. Pretty early on, we got to a situation where the sum of the square roots of the numbers of YES shares held was way larger than the same sum for the number of NO shares held. That made it likely that YES would win, which caused people to buy even more YES shares, resulting in a feedback loop that keeps increasing the probability of a YES resolution.

A way you could intuitively think of it is that 50% is an equilibrium of the market, but it's an unstable equilibrium, so once we get perturbed away from a 50/50 chance of a YES resolution, the probability increases further. That's oversimplifying it, since the probability that the market resolves YES isn't actually a function of the displayed probability at all (e.g., due to the dependence on the square roots rather than a simple sum, it depends on the specific distribution of shares across users), but it gets the basic idea across.

Team YES is strong and bold
Their shares will shine like gold
While Team NO may falter and decline
YES will come out on top, it's a sign