BLANDCorporatio wrote:If I get your argument right, drachefly, you're saying that the various alternative hypotheses about caster popping are less information costly because of Signamancy and similar effects (possibly) dictating or indicating something deeper that controls not just caster selection, but various other aspects of a side. ... (ie, while it looks like random u.i.d. deserves the bigger slice of the pie, it's actually not the case).
They are less information costly than they would be if we didn't have this background information and were basing things off the real world. If, for instance, signamancy was not known or largely not understood (e.g. we were discussing this before the discussion of signamancy in book 2), the hypothesis that the (non-magical) makeup and clothing that a ruler wears could have bearing on whether casters pop and what type they are would be horrendously unlikely, simply from how much detail you'd have to include to specify what you were talking about.
Essentially, the possibility of such a connection has been brought to our awareness at the start of this investigation, through other things we know about Erfworld.
With all of the factors that could reasonably be contributing, and all of the combinations of them that could be applying, even before we begin measuring evidence specific to this case
(sets of casters on each side), though the null hypothesis still has the largest individual probability of any of the rules, it is already a minority of overall weight of the hypotheses.
A bit like with a gas - even at room temperature, the most occupied microstate for the air in your room is for it all to be lying on the floor almost motionless, but there are so many
states in a 'normal' macrostate, and they are not that much less likely individually, that you're not going to find the air in your room doing that in the projected lifetime of the universe.
We're not in the thermodynamic limit with the casters, obviously.
BLANDCorporatio wrote:My question is how can one go about actually assigning numbers to such things, be it in this or some simpler example that may illustrate the process better.
That is the trick, isn't it?
We have some experience with Erf mechanics. Without specifying which one we're talking about, how likely is it that something out of conscious control... involves natural signamancy? Natural thinkamancy? Fate? Non-independent, biased towards anticorrelation (like drawing cards)? Biased towards correlation? Is terrain-based? is based on something nothing else is based on?
If we had enough such mechanics we could estimate the chances of it involving multiple different factors. For now, independent probabilities seem a reasonable starting point. Thus, the prior probability of our u.i.d. 'null hypothesis' will be the product of the probabilities of each of those not being the case.
Putting numbers to it...
the u.i.d null is: "luckamancy is the only thing at work determining this, and the probabilities are even"
Signamancy, luckamancy and fate are pervasive in these kinds of effects concerning how things out of your control work out, but fate could be overrepresented due to our seeing the narrative. Let's call it 1/5 on signamancy, 1/10 on fate. Let's drill down into luckamancy with correlations and anticorrelations (if it's neutral, that's the u.i.d null right there)
Anticorrellations - luckamancy involve shuffling numbers around in a way that seems rather more like a deck of cards than dice. If that's a global effect in some way, it would naturally work out non-u.i.d. even without it being a mechanic specific to this subject
. Let's call it 1/6.
Correlations... well, luckamancy could go the other way too, but we haven't seen it. Let's call it 1/200.
natural thinkamancy - what you really want, subconsciously... we haven't seen this at work, but there's an obvious mechanism in related matters like overlord's awareness of side status, build orders, etc. Let's say 1/5.
terrain - unit types poppable totally depend where you are. I would put that really high, somewhere around 1/4
Novel, specific factors - we've run into new things behind the scenes many times - around 1/6.
So... the prior probability of u.i.d. is, by this measure: 4/5 * 9/10 * 5/6 * 199/200 * 4/5 * 3/4 * 5/6 = 30%