Many of you readers may instinctively know that this is wrong. If you flip a coin (50% chance) twice, you are not guaranteed to get heads. The probability of getting a heads is 75%. However you may be surprised to learn that there is some truth to this statement; modifying...
Summary: A text watermark is some edit to a piece of text that makes its creator easy to identify. The main use for this would be to watermark Large Language Model outputs. This post explores how effective any text watermark could be in general. It does this by analyzing the...
I appreciate people playing along :)
All the responses to this post made my week. Thanks!
Appreciate it a lot. Thanks!
Yeah, I suppose we agree then.
Sure:
For a monogamous partner, finding a successful partner has a value of 1
Finding 2 successful partners also has a value of 1, because in a monogamous relationship, you only need one partner.
The same holds for 3, 4, etc partners. All those outcomes also have a value of 1.
So first, let's find the probability of getting a value of 0. Then let's calculate the probability of getting a value of 1.
The probability of getting a value of 0 (not finding a partner):
There is one other mutually exclusive alternative: Finding at least one partner (which has a value of 1)
So we have a 34.9% chance of getting a value of 0 and a 65.1%... (read more)
Ah, shoot. You're right. Probably not good to use "odds" and "probability" interchangeably for percentages like I did. Should be fixed now.
95% is a lower bound. It's more than 95% for all numbers and approaches 95% as n gets bigger. If n=2 (E.G. a coin flip), then you actually have a 98.4% chance of at least one success after 3n (which is 6) attempts.
I mentioned this in the "What I'm not saying" section, but this limit converges rather quickly. I would consider any to be "close enough"
I think what Justin is saying is that finding a single monogamous partner is not significantly different from finding two, three, etc. For some things you only care about succeeding once. So a 63% chance of success (any number of times) means a .63 expected value (because all successes after the first have a value of 0).
Meanwhile for other things, such as polyamorous partners, 2 partners is meaningfully better than one, so the expected value truly is 1, because you will get one partner on average. (Though this assumes 2 partners is twice as good as one, we can complicate this even more if we assume that 2 partners is better, but not twice as good)
It's a great idea. I ended up bolding the one line that states my conclusion to make it easier to spot.
Many of you readers may instinctively know that this is wrong. If you flip a coin (50% chance) twice, you are not guaranteed to get heads. The probability of getting a heads is 75%. However you may be surprised to learn that there is some truth to this statement; modifying the statement just slightly will yield not just a true statement, but a useful and interesting one.
It's a spoiler, though. If you want to figure this out as you read this article yourself, you should skip this and then come back. Ok, ready? Here it is:
It's a chance and I did it times, so the probability should be... .
Almost always.
Suppose you're flipping a coin... (read 515 more words →)
A text watermark is some edit to a piece of text that makes its creator easy to identify. The main use for this would be to watermark Large Language Model outputs. This post explores how effective any text watermark could be in general. It does this by analyzing the smallest amount of text that a watermark could fit inside of. It is addressed to anyone working on watermarks, or interested in how feasible they could be. It provides a formula for testing watermark effectiveness and concludes that certain qualities that we would want from a watermark, especially robustness, significantly and negatively impact a watermark’s efficiency.
Ideally we want a watermark to meet three... (read 2951 more words →)
Yes! That's a good point that I didn't mention.