To be resolved via poll at close time
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@JosephNoonan i think it can be argued it's the right way to define it as a function RxN->R (ie in polynomials)
To elaborate: since you can define 0^0 in different ways to get different answers, the actual answer is (by definition) undefined. There's a wikipedia page on this https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero which says "The choice whether to define 0^0 is based on convenience, not on correctness. If we refrain from defining 0^0, then certain assertions become unnecessarily awkward... The consensus is to use the definition 0^0 = 1, although there are textbooks that refrain from defining 0^0."
I take that to mean that 0^0 is obviously undefined, but it's useful to pretend that it has a value of 1. The article also says that some mathematicians go further and say that "0^0 has to be 1", but I regard that as obvious nonsense. It may be a useful fiction to pretend that it has a value of 1, but the actual value is clearly undefined.
@DanielParker there isn't some objectively correct answer as to whether 0^0 is defined, unless you have some established framework for continuing a partially-defined function. but any such framework is, to some extent, an arbitrary choice.
@April Understood, thanks. I’m just offering a thought to support the answer of “1”.
Also, it’s not explicitly specified here, but am I correct that the poll which will determine this resolution is:
https://manifold.markets/JosephNoonan/what-is-00
And that a resolution of “1” there will resolve this market as “YES”, while a resolution of “0”, “Other”, or “Undefined” there will resolve this market as “NO”?
@April i can imagine three possible resolution methods here:
"Does 1 have a plurality in that poll?"
"Does 1 have > 50% in that poll?"
Run a separate poll
Would anyone like to express an opinion on which of these is best?
@April I'm not sure I understand what your original intention was - with the description here of "To be resolved via poll at close time" did you plan to start a new poll at the time this market would close? I'm sure it's obvious, but because that other poll had been created an hour before you created this market, I assumed they were related. I'm guessing some other people who have commented here assumed the same because they made similar comments about the mathematics on that other poll also.
Anyway, I don't have a strong opinion either way, as I think my wager here is not really impacted by what you choose to do. My suggestion is to just use the existing poll created by @JosephNoonan for this market, and with the specifics I mentioned above: a resolution of “1” there will resolve this market as “YES”, while a resolution of “0”, “Other”, or “Undefined” there will resolve this market as “NO”. I think that would be fair if anyone who already wagered on this market made the same assumption I did that this was already the case. Either way, I'm fine with any decision you make as this is your market. :-)
@JaredBJonas It's possible that my poll will resolve to 1 even while 1 only has a plurality (it currently has an outright majority, but it's not that big). If this market does resolve based on my poll, I think it would be more in line with the stated criteria of this market to resolve YES if 1 gets an outright majority, and NO if it gets a minority (even if that minority is a plurality). And I guess 50% if it gets exactly 50% of the votes? Mainly because this market didn't say the poll would have multiple options, so it was implied that it would just be a yes or no poll on whether 0^0=1.
@JosephNoonan Though even then, it's probably more in line with the criteria for the creator to just make a yes/no poll at close.
@JosephNoonan i simply did not realize someone else made a poll when i made the market is the issue; the plan was for a yes/no at close, so maybe i'll just do that? open to arguments to resolve based on the already existing poll though.
@April I had the same assumption as Floris. The poll I made wasn't meant to be connected to this market, I made it in response to a comment on a different market.
@JosephNoonan okay looks like most people expected a new poll so i'll plan to do that unless i get multiple objections
@April It sounds like your original plan is the most agreeable to everyone. Like I said, it wouldn’t change any bets I made here anyway. Thanks!