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Comment by Recursing | Hacker News Reader

Reminds me of https://markxu.com/strong-evidence

«One time, someone asked me what my name was. I said, “Mark Xu.” Afterward, they probably believed my name was “Mark Xu.” I’m guessing they would have happily accepted a bet at 20:1 odds that my driver’s license would say “Mark Xu” on it.

The prior odds that someone’s name is “Mark Xu” are generously 1:1,000,000. Posterior odds of 20:1 implies that the odds ratio of me saying “Mark Xu” is 20,000,000:1, or roughly 24 bits of evidence. That’s a lot of evidence.»

«Extraordinary claims require extraordinary evidence, but extraordinary evidence might be more common than you think.»

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Someone offering that bet though would also alter the odds though. Because why would someone offer such a ridiculous bet after you've told your name, unless they had special information about your name? Although it being a possible YouTube prank channel would make it also possible that you actually have a chance to win for the reactions.

This is part of a very important principle: if someone approaches you about something, you should be far more suspicious than if you had randomly picked someone off the street.

The most well known application of this is teaching kids to ask a random shopkeeper for help if they get lost, but to not get in a stranger's car when offered a lift.

> One of these days in your travels, a guy is going to show you a brand-new deck of cards on which the seal is not yet broken. Then this guy is going to offer to bet you that he can make the jack of spades jump out of this brand-new deck of cards and squirt cider in your ear. But, son, do not accept this bet, because as sure as you stand there, you're going to wind up with an ear full of cider.

(Guys and Dolls)

Also good advice for dating!

If an attractive lady walks up to me at a party, first thing I'm doing is asking for references.

My dude…

This must come up a lot.

About as often as you'd expect.

This also applies to self defense. If someone has targeted you, the odds of you beating them in a fight is different than the odds you can take on a random person, or a random thief even

Better or worse odds for you?

I would put the odds of Mark Xu’s license having that name on it at about 15%. Because Mark is probably an anglicised asian name.

Not to mention that many Chinese immigrants will give their children European names.

In that case the license will match?

The question is are you using the name on your drivers license, which is probably the one on your birth certificate.

The OP covers this a bit as well:

> 20 coin tosses (by me) all coming up Tails. YES

> If you tossed the coins then the first answer would be NO, unless I'm very confident you lack the ability to fool me …

This article seems to twist the definition of “extraordinary” to something clearly not intended by the original quote about claims and evidence.

Mark is a very common first name. Xu is a Chinese surname shared by over ten million people (according to Wikipedia). It’s entirely ordinary that someone would have this combination of names.

Don't ask me why, but I had to urge to look up the number of Chinese surnames: About 2000 are currently in use, half the Han Chinese population uses just 19 surnames. Quite low compared to the 850 THOUSAND (another source has more than a million) surnames used in Germany, twice as much as in Spain bespite it have a tradition of double-names. I guess Germany being such a central state with many migration waves over the last 600~800 years since family names have become common.

It's even more concentrated in Vietnam. A very large chunk of the country is called Nguyen. Korea has similar with Kim/Park/Lee.

Someone, yes. The person in front of you? Unlikely.

Analogy: someone has a winning lottery ticket. Is it the one in your hand? Probably not.

That’s a good analogy for my point, because just having a lottery ticket isn’t extraordinary even though all of the tickets are unique.

If somebody claims they are holding a winning lottery ticket and will sell it to me for a 50% discount because they are leaving the country in two hours and don’t have time to cash it out, that’s an extraordinary claim and I would need extraordinary evidence to take the deal.

If someone says their name is Mark Wu, it’s like saying they are holding a non-winning lottery ticket with serial number 12345654321. It’s at best a curiosity.

Why is the 20 multiplied by the million? Why not 0.95 multiplied by million?

Using the same argument I would accept infinite odds that my username is quickthrower2 so there is infinite information?

It's important to understand that when they said "bits" they didn't mean information in the Shannon entropy sense, but rather in the log-odds evidence sense.

Gaining a Shannon entropy bit means learning the answer to a yes-no question that had 1:1 odds.

Gaining a log-odds evidence bit means doubling your best-guess odds on a question you are uncertain about, from X:Y to (2X):Y.

One Shannon bit is worth arbitrarily many evidence bits, because a Shannon bit takes you from 1:1 odds to UNBOUNDEDLYHUGE:1 odds. So... yeah, actually, reading your username is worth infinite bits of log-odds evidence on what your username is! (Ignoring practical issues like the small chance of computer malfunctions, of course.)

And to answer your initial question: the 20 just came from the assertion they'd bet 20:1. That was arbitrary.

This isn't how the mathematics of odds works, as the GP correctly pointed out. An event which is 20:1 on is not 20 times more likely than certainty.

Going from 1:4 to 1:2 means that the event has become twice as likely. But going from 2:1 to 4:1 does not: it means that the complementary event has become half as likely.

Based on this, we can't do math with odds treating them identically to ratios.

If you do the math correctly, the two types of information measure are basically the same thing.

A log-odds of b bits means an odds of 2^b : 1 which means a probability of p = 2^b / (2^b + 1).

In the original comment, the evidence update was stated as going from 20:1 to 1:1000000 and it was claimed this was approximately 24 bits of evidence. The update is from 2^4.3:1 to 2^-19.9:1. Subtracting the exponents you get 4.3 - -19.9 = 24.2 which is approximately 24 as claimed. The "20" in 20:1 is correctly accounted for by the ~4 additional bits of evidence on top of updating from 1:1000000 to 1:1.

Clearly evidence bits behave very differently from entropy bits. Acquiring a single entropy bit is an update from 1:1 to 0:1 which is 2^0:1 to 2^-infinity:1. It's worth an unbounded number of evidence bits. It's important not to mix these two things up.

Yes, you are doing math with odds as though they are fractions or ratios, which is deeply incorrect. 20:1 is not the reciprocal of 1:20 but the complement. Odds ratios and similar calculations do not work like this. You can do this type of calculation using X:1 odds or 1:X odds but not both in the same calculation.

Or perhaps you can provide a reference to a justification of this type of calculation?

Search "decibels" in https://www.yudkowsky.net/rational/bayes for the explanation.

I think you're just wrong about needing everything to be in the form X:1 or 1:X. When I compute the ratio of 1000000:1 divided by 1:20 it gives 1000000:(1/20) then scaling both sides by the same factor gives 20000000:1.

Your reference definitely doesn't show a calculation of the type you are trying to do. Likelihood ratios are not the same as odds ratios; they do not have the problem I described.

I would be very surprised if you can find any reference at all to the number you describe as 'evidence bits', or anything equivalent, made by anyone who can show an understanding of basic probability, statistics, or information theory.

I understand how you get 20,000,000 as the answer to the calculation you carry out. My point is that that number is not meaningful in any way.

When you apply a statistical test, the various outcomes cause Bayesian updates that correspond to adding or subtracting fixed bits of evidence. When you repeat the test (and the repetitions are independent), the amount of bits of evidence you add or subtract remain the same. In other words, focusing on bits of evidence shows Bayesian updates behave like a biased random walk under repetition of a test and allow you to compute the properties of that walk.

For example, suppose you are trying to estimate how much rounding errors in a pseudo random number generator betray that it is not a true exact representation of the random process. One way to quantify this is to compute the expected bits of evidence revealed per call to the RNG.

There's something so wrong with that logic. Imagine it as:

Mark: "I've thought of a number between one and a billion and written it down. The number I wrote down was 6,822,172"

Recursing (you): "ok"

Mark: "ohh you believe me? Then let's take a bet, if I did write down 6,822,172 then you win. If I wrote down any other number between one and a billion then I win".

Would you take that bet? I think you'd be suspicious.

Mark: "I predict that Recursing would take that bet, happily, because why wouldn't they believe me? Therefore them taking the bet is very strong evidence that I actually did write down 6,822,172".

You can't use your prediction about someone else's behaviour as evidence!

24 bits seems about right for the information content of six Latin characters arranged in a pronounceable English orthography (the ‘X’ has pretty high information value though).

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