All answer submissions must be a declarative statement about this market itself, for example, "This market will have more than 10 options," or "The percentage of this option is between 5% and 10%." Any answer that is not phrased as a declarative sentence or isn't about this market will not pay out (when I say "pay out", I mean that I will resolve partially to that option). You can, however, include something in addition to the declarative sentence as a tag, e.g., "ABC: This option is higher than 5%", for the purpose of referencing it with other options (e.g, "ABC has a higher probability than DEF."). But don't duplicate someone else's tag - otherwise, your option won't pay out, as a punishment for confusing traders.
I will resolve equally to all options that meet the above criteria, as well as the following:
They are true at close.
I either know that they are true, or can easily verify it. This means that options like "This option's percentage has the same parity as the eleventh Dedekind number," will not pay out, unless I can find some proof that they are true.
They weren't guaranteed to be true when they were submitted. So no, "The probability of this option is between 0% and 100%, inclusive."
The option does not reference the number of traders or the number of trades on the market.
The option only references events that occur before close, or simultaneously to it. This means that, "At least five answers pay out," is not a valid option, since payouts don't occur until after close. However, "At least five answers are true," is valid (more on that later).
The truth of the option is not a matter of significant controversy among well-informed people, a subjective opinion, or a private detail of someone's life.
The option is not horribly offensive in some way.
No user may submit more than five options. If you do, any options you submit aside from the first five will not pay out. If I can't figure out which ones are the first five, I'll use my best judgement.
In the case of ambiguous options, I will either resolve according to what I think is the most straightforward interpretation of the sentence, or, if I think it is so ambiguous that there is no straightforward interpretation, that option will not pay out unless all interpretations that I think are reasonable candidates for the straightforward meaning are true.
Misspellings and grammatical mistakes are okay, as long as it's obvious what they mean.
The option doesn't violate Manifold's rules, such as encouraging spam, nor does it have a significant chance of encouraging behavior that is harmful or illegal in the U.S.
Options that refer to truth will be dealt with using Tarski's truth hierarchy. This is a solution to linguistic paradoxes like the liar's paradox that notes that semantic terms like "true" are inherently ambiguous when used to refer to sentences that are allowed to include semantic terms themselves. This ambiguity is what leads to the seeming contradiction in "This sentence is false," and the indeterminacy of "This sentence is true," and it results from the fact that no completely precise language can include a truth predicate that applies to all sentences in the language, including sentences that contain the truth predicate itself. To get around this, Tarski proposed defining a hierarchy of truth predicates. The first predicate, true1, applies only to object-level sentences, that is, sentences that do not themselves include semantic terms like truth values. So, for example, "Snow is white," is true1, but "'Snow is white' is true1" is not true1. To describe the truth of meta-sentences that include semantic predicates like true1 and false1, we use sentences on the next level of the hierarchy, true2 and false2. So "'Snow is white' is true1" is true2. "Snow is white," itself is also true2. This can continue indefinitely, where the predicate true-α can describe the truth of any sentence that contains only truth predicates of order less than α.
To utilize Tarski's truth hierarchy, I will assume that, unless otherwise specified, any option that uses words like "true" and "false" is referring to true1 or false1. So an option stating, "This option is not true" would count as being true2, since it is indeed not true1 (since true1 doesn't apply to it). However, that particular example wouldn't pay out anyway, since it is guaranteed to be true2. Similarly, "This option is false" is false2, since the predicate false1 doesn't apply to it, so it would not pay out either. But an option like, "At least five options are true" can pay out, as long as five options that don't contain a truth predicate are indeed true.
(This next bit is technical and almost certainly won't matter to you unless you are trying to find a way to break this market.) Note that the Tarskian hierarchies also apply to other semantic properties, if necessary. For example, if someone tries to break the truth hierarchy by submitting "At least one option is true-n, where n is one higher than the largest order of a truth predicate in any option", then I will not include any truth predicates whose order is predicated on the orders of the whole collection of truth predicates when determining the value of n.
Oh, and for the sake of following my own rules, any time the word "true" is used in this description without qualification, it refers to true-ω₁. If you have no idea what that means, don't worry about it. It will only matter to people who know enough about set theory to try to break the criteria I've put in place.
There is one additional caveat that I need to mention when dealing with words like "true". I will restrict their scope to only include options that are valid responses and fit the bullet points above, unless otherwise stated. So for example, if someone submitted an option like, "This option's percentage has the same parity as the eleventh Dedekind number", the truth of that option would not affect whether "At most ten options are true" pays out. This is to avoid options like the latter being penalized as "can't be verified" just because of other bad options.
If none of the options are valid and true at close (somehow), I will resolve the market to Other. That is the only situation in which Other pays out.
Please note that I have the final say on how this market resolves. I will do my best to follow the rules above, but if some game-breaking exploit is found (something that would make it impossible to resolve correctly in a reasonable amount of time), I may add further rules or clarify the existing rules to counter it. You can, however, abuse loopholes in the rules that don't break the game. I have intentionally left some open.
Credit to @SophiaLaird for creating the market that inspired this and to @Joshua for originally coming up with a list of rules to make a version with more precise resolution criteria that wouldn't lead to paradoxes. I have kept or modified some of Joshua's rules and added a bunch of rules of my own to prevent game-breaking exploits that were possible even under his rule set.
Related questions
Okay, we now have 5 users who admitted to adding an invalid option and not reading the description carefully.
Also, I somehow forgot to mention, "This option will resolve at less than 4%," last time. I'm interpreting that to actually mean, "This option will close at less than 4%."
Okay, I'm looking at the options, and a few things I've noticed:
The only single-letter label that hasn't been used yet is (W), so (Z) will pay out as long as someone uses that one.
(U) and (Ñ) aren't self-resolving, so they can't pay out.
A fake version of (A) has been created, "(A) This market will have > 80 unique traders." That means that, "This answer resolves true if someone creates a lettered option that's a duplicate of a different lettered option (I.G: there are two option (B))," will pay out. The real version of (A) is, "This option does not have highest probability."
"At the time of close, if (N) is true then the number of responses is no more than 50," is now equivalent to "not (N)", since the consequent is false.
It could be argued that (X) is subjective, but I'm going to allow it, because if the visual errors really are obvious, they should be obvious to everyone and so wouldn't be subjective. However, there are currently no obvious visual errors.
I have no idea how to verify, "At close there is a finite-state automaton with less than P states which accepts all true options and rejects all other options, where P is the highest percentage of a single option," so that won't pay out unless I find some way to determine its truth. The option is also ambiguous: What exactly is the Turing machine supposed to accept: the position of the option in the ordering that appears in the market, the number assigned to each option (the order submitted), or a binary encoding of the text of each option?
I think, "At least 5 users will admit to adding an invalid option to this option and not reading the rules carefully in the comments and are telling the truth," will probably end up being true, because more than five people have submitted invalid options. At least two have already admitted to doing so in the comments (me and Bohaska), and I think some others have as well, but I'm not sure how many. Currently some of the comments are missing. To make this easier to resolve, I would appreciate if some people responded to this comment admitting that they accidentally submitted an invalid option (only if you're telling the truth).
I took more than 10 minutes looking over the answers to write this comments, so "@JosephNoonan will use 10 minutes or longer to determine the resolution of this market," will pay out. (I said it was invalid before, but that was because I wasn't thinking of the possibility of using ten minutes before the market closes, and you can see my reply to Floris below that I would consider that valid.)
@JosephNoonan I also said that I mistakenly added an invalid option because I didn't read the rules carefully.
@JosephNoonan Here's a fun one for you; I submitted my response 'test' to see if I could buy it and make a profit on buying NO against it (but this market loads so slow for me that I was sniped), AND I did not read the section on Tarski's truth hierarchy in the market description carefully. So "At least 5 users will admit to adding an invalid option to this option and not reading the rules carefully in the comments and are telling the truth" does apply to me, b/c it uses 'and' not 'and so'. (Also, I am telling the truth). I think I count towards resolving that option YES.
@JosephNoonan Assuming my previous comment ("Eeek, didn't read the rules carefully enough. Nuts.") somehow did not qualify, let it be said that I admit that added the QED option.
Here is a visual graph error, that hopefully becomes obvious once I point it out (and a similar error probably still exists at close). The screenshot below suggest that option (C) has been constant at 11% for the last 24-48 hours. This is false: this option hasn't been above 6% for the last 36 hours. Proof: The second screenshot shows my limit order on this option that is (as of writing this comment) not yet completely filled nor canceled.
The last part of a graph often shows a bunch of constant lines (lately), which are clear errors in the graph.
@FlorisvanDoorn I'm not sure it counts as obvious when you have to use a specific user's unfilled limit order to prove that its an error. My interpretation is that you can just look at the graph and immediately tell that there's something wrong with it.
@JosephNoonan The graph is now showing that no trades have significantly changed the value of any of the options in the last two days... If that's not an obvious error, that seems like a really high bar to me.
And also: you can just look at the graph (at the current moment) and at what the top option is, and see that they don't match. I just wanted to give extra proof that the graph was not just wrong now but consistently and significantly wrong for >24 hours.
@FlorisvanDoorn Yeah, I agree that having it flatline like that is an obvious visual error, so I think I will have X pay out if it stays like that.
I just made five bets on, "This answer has 5 bets on it," to ensure that it comes up true.
@JosephNoonan but if someone already bet on it then it would be false
@JosephNoonan Doesn't it violate "The option does not reference the number of traders or the number of trades on the market"?
@lag I'm interpreting it to mean "at least 5", not "exactly 5".
@roma Hm, actually I forgot that I also had a rule against mentioning the number of trades. The main point of that rule was to avoid options that encouraged people to spam the market with trades. I'm going to say that, since this one technically didn't violate the rule (it referenced the number of trades on one option, not the market as a whole), and the number of trades required was small, thus preventing people from spamming, I'll allow it. But if someone submits a similar option with a large number of required trades, that would be considered invalid because it violates Manifold's rules by encouraging spam. Also, options like this could be very hard to verify the truth of even if they do have only a small number, so they might end up invalid on that basis.
is (Å) there are at least 30 options submitted considered as confusing traders
@StevenEhrbar (QED) can't pay out because it was guaranteed to be true when it was submitted.
@bohaska The option "@JosephNoonan will use 10 minutes or longer to determine the resolution of this market", while pretty much guaranteed to be true, is invalid because it references events that will happen after close.
@JosephNoonan Is it also invalid if you spend 10 minutes of time to determine the solution of this market after this option was made and before the market closes? (e.g. by updating the spreadsheet you posted before)?
@FlorisvanDoorn That would be valid, since it references only events that happen before the market closes, and as long as I make that fact public, it won't be a private detail (going by the standard below to also allow Duncn's answer).
