One benefit of the Mira way that I think others are haven't mentioned is that if you are confident the variable will end up in between the highest and lowest points, you can compute the EV as $$\sum_{x \in answers} p_a v_a$$.

I definitely agree with your sentiment. I feel like this artificially smooths out the distribution to "reduce noise around boundaries." (Is that even beneficial?) It makes the markets more complicated to both bet in (for bettors) and parse (for lurkers).

For example, I could have a (in my opinion very similar) market with numerical buckets, where I take the actual result and add some normally distributed noise with standard deviation equal to the size of one bucket. Then, instead of resolving to the answer, I resolve to (actual answer + noise). It achieved the same effect of reducing variance within answer choices, but I think it's much easier to see that the concept is a little silly.

@CharlesLien I think the problem with what you are describing is that the outcome for any one bucket is still a binomial variable, and therefore has the maximum variance possible for a random variable with a particular expectation supported on [0,1]. By introducing a chance that a bucket resolves to %, the variance can be less, and you can predict a very similar quantity while giving traders a better Sharpe ratio.

i think it is fine if Mira does it since there is only

one Mira and it is a bit her brand but I would be a bit annoyed if more people start doing it because it is unnecessary and complicates things while adding little value

Sharp cutoffs are much easier to reason about. With interpolation, you have to do annoying math to figure out what optimal bets to make, or you eyeball it and guess and hope what you did was reasonable. And for people looking at the market, they have to eyeball and guess what the market prices mean.

In a market with sharp cutoffs, if a trader believes something could be in bucket 2 or 3, then they should bet on both in proportion to their beliefs - very easy to reason about.

So the thing about reducing noise is kinda meaningless, in a sense, because people aren't limited to betting on one bucket, they can and should bet on multiple!

It is true that people's payouts will change sharply if the resolution goes from just below to just above a threshold, and it is nice to avoid that. But imo the interpolation has far more downsides than upsides - tacking on interpolation onto a mutually exclusive buckets interface is not a good mechanism to do it. If Manifold built a first-class system for numeric, continuous predictions, it could work much better.

I don't really like this - leverage lets you use your capital efficiently

One reason you might feel this way is that my markets are not the optimal way to "play Manifold".

Binary markets that don't close before resolution go to 0% or 100% as traders milk the last bits of AMM liquidity. This means the central bank pays dearly for binary option markets. Whereas, my markets are much friendlier and the central bank often pays hardly anything at all.

In my Sudoku market( /Mira/will-a-prompt-that-enables-gpt4-to ), somebody noticed that "despite the volume, hardly any mana changed hands". Part of it is: Since I was subsidizing it, and I was willing to put M$100k+ subsidies into the market, I wanted to make sure that I got my money back if predictors didn't give me any value.

Since my subsidy was added around 50%, and most trading took place around 50%, and since it resolved 50%, I got my subsidy back since the "expected case" occurred. Only spectacular failures or spectacular successes would've cost me. I should've used a linear interpolation there too, to create more trading volume, but it indicates a general principle.

You feel that my markets are inefficient because you get less money from them. But instead of saying "and therefore we should use binary markets", you could also say "and therefore Manifold should dynamically increase the subsidy on markets they're more likely to get back".

Continuous markets could have much larger subsidies and let traders win much larger amounts of money for good predictions, because the house would more often get their money back in case of a partial resolution.

• A 50th percentile prediction should approximately cost the subsidizers M$0. This means "resolving at a percentage near where the subsidy was added".

• An especially bad prediction should actually make the subsidizers money.

• A very good prediction should cost the subsidizers money.

• If a market closes after the resolution is known, then liquidity siphoners cost the subsidizers money. This means they have to offer less liquidity in general, to account for this risk. So "resolving as of a date in the past" should allow the central bank to create bigger markets for you to trade in.

Do consider whether you actually want higher marginal leverage, or if you just feel like the payouts are less because Manifold central bank is printing less money. (And therefore, the central bank could be subsidizing my markets 10x as much since they're safer to subsidize!)

@Mira Manifold devs historically haven't cared about money printing very much. But I think they actually do care, and they're just too stupid to see the consequences.

You constantly see them trying to institute taxes ( /SG/should-manifold-charge-a-fee-on-mar ) ( /SG/will-manifold-announce-a-tax-on-uni ) and fining people like Catnee for "bad loans". So obviously they are thinking about the money supply a lot.

But they don't have the predictive skill to understand the obvious consequences of their economical policies, so they react by creating random blunt changes that are poor fits for the actual issue.

So even though it seems "they don't care", users and traders are being punished when the consequences eventually catch up and make the problems obvious even to very stupid and unobservant site admins. So you should care about being friendlier to the central bank and AMM liquidity even if Manifold devs don't appear to.

@Mira For example, on a market like /SG/will-a-democrat-win-the-2024-us-pre , it's very likely that it will trade in the range 45%-60% all year.

If Manifold closed the market a few weeks in advance, they could probably subsidize the market M1 million and get most of it back while offering people the chance to make extremely large bets.

If everybody made markets that allowed for partial resolutions in the common case, they could be funded with much larger subsidies. And people might actually enjoy the massive liquidity and predicting more than the ability to squeeze every drop out of every market with near 100% certainty.

My linear interpolation markets do allow the same possibility(if Mistral is released with exactly 100B parameters and there's a 100B option), but since it also often is expected to partially resolve it should support a 2x larger subsidy than an equivalent binary. Larger buckets mean less precision but support a larger subsidy.

The idea is to reduce the impact of noise around boundaries and reduce leverage.

It's not quite "reducing leverage". If a tiny difference in interpretation causes a large change in payout, you can think of that as leverage. But it's also "what are you as market creator incentivizing people to predict?"

A market like "Will Mistral-large have 100 billion parameters?" arises from people wanting an estimation. Maybe they want to predict the growth of VRAM demand for large models so they can budget for buying vs. renting GPUs. Whether it's 99 billion or 100 billion doesn't really matter.

But a binary option market would be appropriate if you actually cared about the threshold. For example, maybe your GPU has 24GB VRAM, and the model either loads or doesn't. If it doesn't, you can try to quantize or remove layers, but it's going to be more annoying that if it loaded outright. So somebody asking "Will Mistral-large have <NNB parameters?", where NNB was calculated to correspond to 24GB or 48GB, would be a good question where edge cases can be resolved by trying to load it in PyTorch. If I were running a market on the exact # of parameters like that, I wouldn't specify the resolution in terms of announced parameters but rather "If I rent a specific Nvidia GPU and load the model using Mistral's released scripts or llama.cpp, will I get an error?"

The market format does let you shape the payout curve: If you really do want more precision around an important boundary, use smaller buckets around it. If you want less precision, use larger buckets. In the extreme case, you could have 1 bucket for every possible number(with a UI for specifying ranges or normal distributions that buys into them). And that would have even more "marginal leverage" if that's what you want to maximize. So if you think you're not getting enough payout on my markets, classic binary options are still not anywhere near optimal and you should just be asking for finer buckets. And most people creating binary option markets aren't putting that much thought into their boundaries anyways.

But I think it's not correct to take an "estimate question" like "how many parameters will Mistral have?" and turn it into a very precise boundary. "100B" would just be a nice-sounding round number, and not anything deserving of precision. The question is approximate, so approximate answers should also be rewarded.

People think they like the "easy to interpret numbers", but then they're unhappy about how the last 5 DAUs are counted, or "what about the embeddings. Mistral rounded the numbers", or "there's 13 bots - should those be counted too?". Because when it's close to the boundary, a small interpretation difference creates a massive swing in payouts.

If the resolution is continuous with respect to data, then small changes to the interpretation have small changes to everyone's payouts.

One unfortunate consequence of less dramatic markets is that they attract less money: If person A thinks an edge case counts and person B doesn't, they will pour unbounded amounts of money in because they each think they're getting a great deal. Then market makers move in, it shows up on trending, soon there are paid actors in the comments arguing each side, and eventually moderators start holding polls on whether to override the resolution. If you skip all the drama, there's less money and less to talk about, because the small difference doesn't really matter either way. If your market closes after the result is known, it makes the edge case problem even worse, because people will buy it up to 99.9% thinking it's free money and then argue how you'd be hurting them if you resolve NO.

The average Manifolder is too stupid to know they want continuous markets, because their tiny minds can't see the bad consequences of discontinuity a couple months down the road, so it is up to us enlightened individuals to ignore their preferences and make the markets continuous despite their objections.

I also believe that "displayed probabilities are prices, not probabilities", so objections of the form "It makes it hard to read the actual probability" are rejected as meaningless since there are no actual probabilities(However: if you make a market about a dice roll or mined blockchain hash, I allow interpretation as a probability). I also think people that say that are stupid and poor traders.

If you want to convince people I'd suggest adding a worked example of effects on leverage to your description.

I'm generally not a huge fan of things that make it so you can't read the market probability as an actual probability. It probably complicates things enough for most traders that doing it isn't a good idea, but I'd have to think about it more to decide if it would be good with better UI/liquidity tweaks.

@jskf I agree with this, in that I think anything that makes it likely that a person can read the description in reasonably good faith and miss a detail that strongly changes how they should interpret the market probability is asking for a bad time, even if it makes mathematical sense to do so (and I do think there's a good argument for it, it's just not a good UX).