(A) This option does not have highest probability

(B) This option does not have lowest probability

(C) This option has greater probability than at least one newer option (A and B are the only well-posed older options)

'b':15 'c':1 'greater':5 'least':9 'newer':11 'older':22 'one':10 'option':3,12,23 'pose':21 'probabl':6 'well':20 'well-pos':19

'five':3 'least':2 'option':4 'true':7 'true-ω':6 'ω':8

(D) The percentage of this option is a prime number

'd':1 'number':10 'option':6 'percentag':3 'prime':9

(E) Option A has the highest probability and Option B has the lowest probability.

'b':10 'e':1 'highest':6 'lowest':13 'option':2,9 'probabl':7,14

(F) Of Options A-E, fewer than four options are true AND fewer than four options are false.

'a-e':4 'e':6 'f':1 'fals':19 'fewer':7,14 'four':9,16 'option':3,10,17 'true':12

(G) At least four options form an integer sequence of probabilities that differ by one; e.g. 3% 4% 5% 6%

'3':17 '4':18 '5':19 '6':20 'differ':13 'e.g':16 'form':6 'four':4 'g':1 'integ':8 'least':3 'one':15 'option':5 'probabl':11 'sequenc':9

(H) Options A-H are arranged in alphabetical order (ascending and descending both count)

'a-h':3 'alphabet':9 'arrang':7 'ascend':11 'count':15 'descend':13 'h':1,5 'option':2 'order':10

(I) This market has at least 25 unique traders

'25':7 'least':6 'market':3 'trader':9 'uniqu':8

(J) B does not have the highest probability

This market has more than 15 answer options.

The number of options is the nth r-gonal pyramidal number for any n,r≥3.

'3':17 'gonal':10 'n':15 'nth':7 'number':2,12 'option':4 'pyramid':11 'r':9,16 'r-gonal':8

(K) The probability, in percent, of B is greater than the amount of options on the market at close

'amount':12 'b':7 'close':19 'greater':9 'k':1 'market':17 'option':14 'percent':5 'probabl':3

(Z) There are options with single-letter tags for every letter of the alphabet (possibly including other characters in the tag, like parentheses)

'alphabet':15 'charact':19 'everi':11 'includ':17 'letter':8,12 'like':23 'option':4 'parenthes':24 'possibl':16 'singl':7 'single-lett':6 'tag':9,22 'z':1

Answer Other is among the first half or exactly in the middle by probability.

'among':4 'answer':1 'exact':9 'first':6 'half':7 'middl':12 'probabl':14

there are at least 4 ordinals α with 1 ≤ α < ω₁ such that an answer to this market is true-(α+1) but not true-α

'+1':22 '1':9 '4':5 'answer':15 'least':4 'market':18 'ordin':6 'true':20,26 'true-α':25 'α':7,10,21,27 'ω':11

At time of close,  Plasma Ballin' intends to resolve this in good faith.

'ballin':6 'close':4 'faith':13 'good':12 'intend':7 'plasma':5 'resolv':9 'time':2

At least one question in this market has a probability lower than 0.5% at close.

'0.5':13 'close':15 'least':2 'lower':11 'market':7 'one':3 'probabl':10 'question':4

(M) The final sequence of options at close will have emergently produced at least one Scrabble word from the first letter of each option.

'close':8 'emerg':11 'final':3 'first':20 'least':14 'letter':21 'm':1 'one':15 'option':6,24 'produc':12 'scrabbl':16 'sequenc':4 'word':17

(N) The final sequence of options at close will NOT have emergently produced at least one Scrabble word from the first letter of each option.

'close':8 'emerg':12 'final':3 'first':21 'least':15 'letter':22 'n':1 'one':16 'option':6,25 'produc':13 'scrabbl':17 'sequenc':4 'word':18

(O) The displayed probability of this option is ≤ 99.9%

'99.9':9 'display':3 'o':1 'option':7 'probabl':4

(P) The displayed probability of answer (L) is the same as its truth7 value (0.0% or 0% if false7, 100.0% or 100% if true7)

'0':17 '0.0':15 '100':22 '100.0':20 'answer':6 'display':3 'false7':19 'l':7 'p':1 'probabl':4 'true7':24 'truth7':13 'valu':14

(Q) there are more answers with label than without

(Å) there are at least 30 options submitted 

'30':6 'least':5 'option':7 'submit':8 'å':1

$99999999999999999999999999999999999999999999999999999 mana

'99999999999999999999999999999999999999999999999999999':1 'mana':2

(AA) The top option with the median character length will be higher than at 10% of these options.

'10':15 'aa':1 'charact':8 'higher':12 'length':9 'median':7 'option':4,18 'top':3

A majority of the answers in this market will be priced <1% when the market resolves.

'1':12 'answer':5 'major':2 'market':8,15 'price':11 'resolv':16

At market close at least one market will be priced above 1/N, where N is the number of answers that are true as of close.

'1/n':12 'answer':19 'close':3,25 'least':5 'market':2,7 'n':14 'number':17 'one':6 'price':10 'true':22

(R) At least 69 options have the word "rationalussy" in them.

'69':4 'least':3 'option':5 'r':1 'rationalussi':9 'word':8

the number of true-N options is greater than sqrt(N), where N is the number of responses.

'greater':9 'n':6,12,14 'number':2,17 'option':7 'respons':19 'sqrt':11 'true':5 'true-n':4

(S) Options A, B, C, D, E, F, G, H all have displayed probability > 0.5

'0.5':15 'b':4 'c':5 'd':6 'display':13 'e':7 'f':8 'g':9 'h':10 'option':2 'probabl':14

(T) the sum of probabilities of options A, B, C, D, E, F, G, H is <  their product

'b':9 'c':10 'd':11 'e':12 'f':13 'g':14 'h':15 'option':7 'probabl':5 'product':18 'sum':3

(BLUE) this option will be some shade of blue in the market's graph at close time

'blue':1,9 'close':16 'graph':14 'market':12 'option':3 'shade':7 'time':17

At the time of close, if (N) is true then the number of responses is no more than 50 

'50':19 'close':5 'n':7 'number':12 'respons':14 'time':3 'true':9

The displayed probability of this answer is less than 0.42069. 

'0.42069':10 'answer':6 'display':2 'less':8 'probabl':3

This is a statement that will be true when this market resolves. As for now it is now

'market':11 'resolv':12 'statement':4 'true':8

The people who bet on this answer like bannanas

'answer':7 'bannana':9 'bet':4 'like':8 'peopl':2

(Ñ) At the day of closing, it was sunny in most of Spain

'close':6 'day':4 'spain':13 'sunni':9 'ñ':1

) The sum of market probabilities for answers starting with the character "(" is greater than 50%.

'50':15 'answer':7 'charact':11 'greater':13 'market':4 'probabl':5 'start':8 'sum':2

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))

'answer':2 'b':25 'creat':7 'differ':17 'duplic':14 'i.g':20 'letter':9,18 'option':10,19,24 'resolv':3 'someon':6 'true':4 'two':23

(A) This market will have > 80 unique traders

@JosephNoonan will use 10 minutes or longer to determine the resolution of this market. 

'10':4 'determin':9 'josephnoonan':1 'longer':7 'market':14 'minut':5 'resolut':11 'use':3

The price of the Dow Jones Industrial Index on this market's closing time will be higher than the price of the Nasdaq on this market's closing time multiplied by 2.5

'2.5':32 'close':13,28 'dow':5 'higher':17 'index':8 'industri':7 'jone':6 'market':11,26 'multipli':30 'nasdaq':23 'price':2,20 'time':14,29

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.

'5':3 'ad':8 'admit':6 'care':20 'comment':23 'invalid':10 'least':2 'option':11,14 'read':17 'rule':19 'tell':26 'truth':28 'user':4

(Y) At the day of closing, the New York Times headline will start with the same letter as the first letter in the current highest-ranked answer (including letters inside parentheses, such as "Y" for this answer).

'answer':28,38 'close':6 'current':24 'day':4 'first':20 'headlin':11 'highest':26 'highest-rank':25 'includ':29 'insid':31 'letter':17,21,30 'new':8 'parenthes':32 'rank':27 'start':13 'time':10 'y':1,35 'york':9

(U) The market creator is in top 15 in the Master League leaderboard

'15':8 'creator':4 'leaderboard':13 'leagu':12 'market':3 'master':11 'top':7 'u':1

(X) The graph of this market has obvious visual errors

'error':10 'graph':3 'market':6 'obvious':8 'visual':9 'x':1

At close this market will be liked (the ❤️ button) by me (@roma)

'button':9 'close':2 'like':7 'market':4 'roma':12

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

'accept':16 'automaton':9 'close':2 'finit':7 'finite-st':6 'highest':29 'less':11 'option':19,24,34 'p':13,26 'percentag':30 'reject':21 'singl':33 'state':8,14 'true':18

This option will resolve at less than 4%.

At least 5 options in this market include accidental spelling or grammar problems, and are acknowledged and fixed by the writers of the options

'5':3 'accident':9 'acknowledg':16 'fix':18 'grammar':12 'includ':8 'least':2 'market':7 'option':4,24 'problem':13 'spell':10 'writer':21

(W) This option isn't considered to have been "guaranteed to true when [it was] submitted".

'consid':6 'guarante':10 'isn':4 'option':3 'submit':16 'true':12 'w':1

(α) For every α<ω₁, the majority of the true-α answers are true-1.

'-1':16 'answer':13 'everi':3 'major':7 'true':11,15 'true-α':10 'α':1,4,12 'ω':5

There is an answer that is true2 but not true1 that has a displayed probability of at least 2%.

'2':19 'answer':4 'display':14 'least':18 'probabl':15 'true1':10 'true2':7

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:

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-

. 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.

 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.