Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Subscripts for Probabilities, published by niplav on April 13, 2023 on LessWrong.
cross-posted from niplav.github.io
Gwern has wondered about a use-case for subscripts in hypertext. While they have settled on a specific use-case, namely years for citations, I propose a different one: reporting explicit probabilities.
Explicitely giving for probabilities in day-to-day English text is usually quite clunky: "I assign 35% to North Korea testing an intercontinental ballistic missile until the end of this year" reads far less smoothly than "I don't think North Korea will test an intercontinental ballistic missile this year".
And since subscripts are a solution in need of a problem, one can wonder how well those two fit together: Quite well, I claim.
In short, I propose to append probabilities in subscript after a statement using standard HTML subscript notation (or LATEX as a fallback if it's available), with the probability possibly also being a link to a relevant forecasting platform with the same question:
I think Donald Trump is going to be incarcerated before 203065%.
This is almost as readable as the sentence without the probability.
There are some complications with negations in sentences or multiple statements. For the most part, I'll simply avoid such cases ("Doctor, it hurts when I do this!" "Don't do that, then."), but if I had to, I'd solve the first problem by declaring that the probability applies to the literal meaning of the previous sentence, including all negations; the problem with multiple statements is solved by delimiters.
As an example for the different kinds of negation: "The train won't come more than 5 minutes late90%" would (arguendo) mean the same thing as "I don't think the train will come more than 5 minutes late90%" means the same as "The train will take more than 5 minutes to arrive10%" equivalent to "I assign 90% probability to the train arriving within the next 5 minutes".
With multiple statements, my favorite way of delimiting is currently half brackets: "I think ⸤it'll rain tomorrow⸥55%, but
⸤Tuesday is going to be sunny⸥80%, but I don't think
⸤your uncle is going to be happy about that⸥15%."
The probabilities in this context aren't quite
evidentials, but neither are they veridicals nor
miratives, I propose the world
"credal" for this category.
Enumerating Possible Notations
The exact place of insertion is subtle: In sentences with a single central statement, there are multiple locations one could place the probability.
After the verb related to belief: "I think55% it'll rain tomorrow."
Advantage: Close to the word relating to the belief (which could reflect the strength of belief in itself, using "guess"/"wager"/"think"/"believe").
Disadvantages:
Conflicts with assigning probabilities to multiple statements.
Puts visual clutter before the statement in question.
At the end of the statement: "I think it'll rain tomorrow55%."
Advantage: Allows assigning probabilities to simple statements ("It'll rain tomorrow55%") and to multiple statements (see below).
Disadvantage: If the probability is intended to contextualise the statement, this context is weaker if it is introduced after the statement in question.
At the subject of the sentence: "I55% think it'll rain tomorrow."
Advantage: This can be used to distinguish the beliefs of different people. "I55% think it'll rain tomorrow, but Cú Chulainn22% is skeptical about it."
Disadvantage: Putting the probability before the statement the probability is about feels quite unnatural.
This becomes trickier in sentences with multiple statements.
Probabilities after each subclaim: "I think it'll rain tomorrow55%, but Tuesday is going to be sunny80%, but I don't think your uncle is going to be happy about that15%.
Adding in delimiters to denote a specific subclaim the probability is about. I wonder whethe...