How bad is it to resolve a market as N/A?
I claim that resolving N/A is bad, that it's usually worth the effort to untangle ambiguities and hash out what's fairest. That can be exhausting, invidious work and it's understandable if you're not up for it, but at least consider it a last resort to resolve N/A. And if traders are lobbying for an N/A resolution, that might be all the more reason not to do it!
But this is easier said than done. Sometimes you pose an innocent-seeming question and traders make different assumptions and bet accordingly. Later, the unanticipated ambiguities come to light and all possible resolutions feel grievously unfair to one set of traders or another. And it's possible that N/A is indeed what's least unfair. But here's a collection of reasons to resist it:
1. It's anticlimactic and throws away people's work
This one seems obvious and relatively minor. Resolving N/A unwinds everyone's trades as if they never happened. Less obviously, that includes clawing back profits of those who correctly predicted a price movement and then cashed out. This invariably surprises people.
2. It spoils incentives
This is kind of a corollary to reason #1 but is also a counterargument to a pro-N/A argument. Namely, that the real value of a prediction market is to see the market probability evolve. The final resolution, or lack thereof, doesn't undo that value. That's true but resolving N/A sets a bad precedent, making people less motivated to do the work to make market probabilities accurate in the first place if they think N/A is at all likely.
3. It can be a way to cheat
Here's an extreme example to illustrate how bad this can be. Imagine creating a "Will aliens arrive by Christmas?" market. You dump all your money on YES. If aliens show up, resolve to YES, win big. If aliens don't show up, you start stirring up fairness concerns. It wasn't specified whether you meant extraterrestrial aliens. Etc. Get the debate going and then suggest that maybe the fairest thing is to resolve N/A. Everyone gets their money back, no harm no foul. But it was totally rigged! You made a big bet on YES and then found a way to weasel out of paying up when you were proven wrong.
It's not normally so blatant but it's worth having that in mind. "Just give everyone their money back, no harm no foul" can be extremely incorrect. Totally harm, totally a foul. Be very skeptical of anyone suggesting that resolving N/A is what's fairest.
Rule of thumb: if the ambiguities that arose were no more likely to arise for any of the ways the underlying question might've played out, then N/A may be what's least unfair. It can be a judgment call.
4. It can distort market probabilities in decision markets
Say you want to know whether, if you buy Apple's VR headset, you'll actually use it enough that you'll be happy you bought it. So you make a market asking exactly that. You might naturally commit to resolving N/A if the market convinces you you'd regret the purchase. No purchase, no way to resolve the market. The problem is that this can spoil the incentives for traders and leave the market quite biased towards YES.
Imagine I'm pretty sure you'd regret getting the VR headset. If I drive the price to my true estimate of, say, 10% that you'll like it, my upside is cut off. If I'm wrong and the price goes back up and you buy the thing and have no regrets, I lose money. If I'm right then you defer to the wisdom of the market, don't buy the thing, and resolve N/A. I'd be paying up if I'm wrong and getting no payout if I'm right. Thus I won't drive the price down enough to convince you not to do the thing. I might not bet NO at all, in case others drive the price down that far.
What should you do instead? Maybe resolve to the market price in the case that you don't buy the headset. That does risk market manipulation. Driving the price to 1% is guaranteed profit if I think I have enough money to keep the price there. At that price I know you won't buy the headset and thus you'll resolve to the market's estimate of a 1% chance of headset happiness. Ka-ching. But my own meta-prediction is that that's too risky to try to exploit in practice. Especially if you don't commit to a particular threshold for doing vs not doing the thing. Any would-be manipulator has to worry that you might buy the headset despite the market seeming 99% sure you'll regret it. If you do, and don't in fact regret it, the manipulators lose their shirts.
5. Ambiguous outcomes are often better resolved to a probability
Did the thing being predicted kinda/partially/ambiguously happen? You don't have to endlessly debate YES vs NO and give up and resolve N/A when neither side can claim a decisive victory. Instead the creator can make a judgment call like "this counts as 75% YES" and just resolve to that. Resolve-to-PROB, it's called. It may seem weird but is pretty exquisitely fair if that 75% is the best reflection of the weird reality that ended up happening.
Exceptions
A. Questions that are fundamentally nonpredictive, like "Is Trump good?".
B. When the resolution criteria explicitly stipulate an N/A resolution if such-and-such happens. Like "Will Biden beat Trump? Resolves N/A if either of them dies before the election."
C. When an error was made in specifying the resolution criteria -- such as changing the criteria after some people already bet -- such that any possible resolution would be truly unfair to some subset of traders.
(I originally said some of this in a "will DALL-E be able to draw blue grass and a green sky?" market and a "will I regret bleaching my hair?" market. It was in the latter that user @Conflux pointed out the potential for market distortion in a "will I regret XYZ?" market. For more on trickinesses with decision markets, see Prediction Market Does Not Imply Causation.)