The Keynesian Beauty Contest is a game theory experiment where a group of players are asked to guess a number between 0 and 100. The winner of the contest is the player(s) who guess closest to *half* the average of all the guesses.

This is an attempt to perform this experiment on Manifold. At close I will resolve the market to *the option that is closest to half the rounded average of the probability weighted value of the options*.

For instance if there are only two options, 25 with 25% chance and 50 with 75% chance I would resolve to (0.25*25+0.75*50)/2=21.88~=22. Since 25 is closest to 22, the market would resolve to 25.

~~I've added options for all the multiples of 10 to start with. If I've set this up right, you will be able to add your own answers. Keep these guidelines in mind when adding additional options (or your option will not be included in the experiment):~~

~~The option must be an integer between 0 and 100, inclusive.~~~~The option must be written in digit form (to avoid duplicates).~~

~~Should it not be possible to add options, please request the option you want added in the comments, and I'll add it.~~

**As we have reached the limit of how many options can be added, no further options will be added. Every option except 92 and 93 is available.**

### Fine print

Percentages will be read visually from the market page.

Should invalid options be added, the resulting average will be divided by the sum of probabilities of

*valid*options, to ensure consistent values.For the resolution of this market "Other" will always be considered an invalid option. The only reason to bet yes on "Other" would be to speculate on options added in the future.

Each day starting Sep 9th I will add the option which would currently win, if it is not yet part of the options.

In case of discrepancies between the textual description and the spreadsheet calculation, the spreadsheet will decide.

Here is a screenshot of a spreadsheet with formulas, showing how the final value will be calculated:

### Similar markets

### References

## Related questions

If you are invested in NO of 0, I recommend to buy (and possibly immediately sell) 1M of 100,99 and other high options. It will increase the liquidity of those options, making it harder to bring them down.

@Irigi Every time I buy NO 0, I push up the probabilities of all the other options by a tiny amount. That's enough to make it not resolve 0.

I think this market will resolve around the 5-10 range. I respect buying yes for numbers in the 2-4 range. But 0 and 1 are clear losers to me. People read the market title, think they're clever because they know this toy example from economics, and don't take into account the dynamics on manifold. I will happily keep taking your money.

Just to be clear @Toby96 , the probabilities that are fed into the calculation are NOT rounded, correct? As in, if there’s a 0.2% for “85”, then that isn’t rounded down to 0%?

@BenjaminShindel Probability will be used exactly as they are displayed on the Manifold page.

In your example 0.2% would be used. It would not be rounded to 0. Same for probabilities >99% (though that's much less likely to be relevant).

If anyone is curious about the raw values, they can be found here.

They aren't the numbers to be used in judging, but are useful to tell how much movement is required to shift the eventual outcome.

There is some interesting dynamics going on now. If every option except 0 has a probability of 0.1 % the average becomes 4.865 which rounds to 5.

It seems that a bet on any value lower than that relies on very big no orders on many options. I'm not sure how much mana is required to push from 0.1% to 0.0% but unless we get some serious whale action this seems unlikely.

@Toby96 I do expect quite a bit of serious whale-bot action late. After all, NO on every option 51-100 is *absolutely guaranteed* to pay off on resolution; the only reason not to buy it now is opportunity cost on the mana. As we get closer to resolution, the opportunity cost goes lower. Anyone buying YES on 51-100 to manipulate the market at the last minute will simply be shoveling money to those taking the guaranteed returns of buying NO on those options.

@StevenEhrbar Yes, they will be "shoveling" one mana towards the whales for every 1K mana they tie up. 5-10K mana easily takes out all the whales on the site (assuming they even bother to chase the tiny returns).

I was worried about this possibility. Seems like @Toby96 has a balance of about M$322, and I think adding options costs M$25.

Maybe Toby should ask for managrams from the requester? Also, is there a limit on the number of options?

@AndrewHebb I've added all options up to 91, but Manifold has either bugged or I've reached the limit for number of options that can be added. I'll try adding the remaining ones again later, but otherwise this is it.

As for the Mana, I don't really want to request mana for adding options, as that would change the rules. That being said, if somebody wants to donate Mana, that's fine.

It also helps if people actually trade the added options since I get a 3m bonus for each unique trader for each option.

@Toby96 oh! that's cool that you get mana back for each option, not for the market overall! that makes me less worried you're wasting your mana creating a bajillion options, haha

You can run the following code in dev tools to get the current average:

let data = {};

const divs = document.querySelectorAll(

"div.relative.isolate.h-full.w-full.flex.flex-col"

);

divs.forEach((div) => {

let spanElements = div.querySelectorAll("span");

option = spanElements[0]?.innerText || "";

percentage = spanElements[3]?.innerText || "";

if (option.match(/^\d+$/)) {

option = parseInt(option);

if (option >= 0 && option <= 100) {

percentage = parseFloat(percentage);

data[option] = percentage;

}

}

});

let sum = 0;

let total = 0;

for (let key in data) {

sum += key * data[key];

total += data[key];

}

const weightedAverage = sum / total;

const optimalChoise = Math.round(weightedAverage / 2);

console.log(data);

console.log({ weightedAverage, optimalChoise });