Quick puzzle about utility functions under affine transformations

6 Liron 16 July 2016 05:11PM

Here's a puzzle based on something I used to be confused about:

It is known that utility functions are equivalent (i.e. produce the same preferences over actions) up to a positive affine transformation: u'(x) = au(x) + b where a is positive.

Suppose I have u(vanilla) = 3, u(chocolate) = 8. I prefer an action that yields a 50% chance of chocolate over an action that yields a 100% chance of vanilla, because 0.5(8) > 1.0(3).

Under the positive affine transformation a = 1, b = 4; we get that u'(vanilla) = 7 and u'(chocolate) = 12. Therefore I now prefer the action that yields a 100% chance of vanilla, because 1.0(7) > 0.5(12).

How to resolve the contradiction?

 

You Are A Brain - Intro to LW/Rationality Concepts [Video & Slides]

13 Liron 16 August 2015 05:51AM

Here's a 32-minute presentation I made to provide an introduction to some of the core LessWrong concepts for a general audience:

You Are A Brain [YouTube]

You Are a Brain [Google Slides] - public domain

I already posted this here in 2009 and some commenters asked for a video, so I immediately recorded one six years later. This time the audience isn't teens from my former youth group, it's employees who work at my software company where we have a seminar series on Thursday afternoons.

Wisdom for Smart Teens - my talk at SPARC 2014

15 Liron 09 February 2015 06:58PM

I recently had the privilege of a 1-hour speaking slot at SPARC, a yearly two-week camp for top high school math students.

Here's the video: Wisdom for Smart Teens

Instead of picking a single topic, I indulged in a bunch of mini-topics that I feel passionate about:

  1. Original Sight
  2. "Emperor has no clothes" moments
  3. Epistemology is cool
  4. Think quantitatively
  5. Be specific / use examples
  6. Organizations are inefficient
  7. How I use Bayesianism
  8. Be empathizable
  9. Communication
  10. Simplify
  11. Startups
  12. What you want
I think the LW crowd will get a kick out of it.

 

 

 

 

A proposed inefficiency in the Bitcoin markets

3 Liron 27 December 2013 03:48AM
Salviati: Simplicio, do you think the Bitcoin markets are efficient?

Simplicio: If you'd asked me two years ago, I would have said yes. I know hindsight is 20/20, but even at the time, I think the fact that relatively few people were trading it would have risen to prominence in my analysis.

Salviati: And what about today?

Simplicio: Today, it seems like there's no shortage of trading volume. The hedge funds of the world have heard of Bitcoin, and had their quants do their fancy analyses on it, and they actively trade it.

Salviati: Well, I'm certainly not a quant, but I think I've spotted a systematic market inefficiency. Would you like to hear it?

Simplicio: Nah, I'm good.

Salviati: Did you hear what I said? I think I've spotted an exploitable pattern of price movements in a $10 Billion market. If I'm right, it could make us a lot of money.

Simplicio: Sure, but you won't convince me that whatever pattern you're thinking of is a "reliable" one.

Salviati: Come on, you don't even know what my argument is.

Simplicio: But I know how your argument is going to be structured. First you're going to identify some property of Bitcoin prices in past data. Then you'll explain some causal model you have which supposedly accounts for why prices have had that property in the past. Then you'll say that your model will continue to account for that same property in future Bitcoin prices.

Salviati: Yeah, so? What's wrong with that?

Simplicio: The problem is that you are not a trained quant, and therefore, your brain is not capable of bringing a worthwhile property of Bitcoin prices to your attention.

Salviati: Dude, I just want to let you know because this happens often and no one else is ever going to say anything: you're being a dick.

Simplicio: Look, quants are good at their job. To a first approximation, quants are like perfect Bayesian reasoners who maintain a probability distribution over the "reliability" of every single property of Bitcoin prices that you and I are capable of formulating. So this argument you're going to make to me, a quant has already made to another quant, and the other quant has incorporated it into his hedge fund's trading algorithms.

Salviati: Fine, but so what if quants have already figured out my argument for themselves? We can make money on it too.

Simplicio: No, we can't. I told you I'm pretty confident that the market is efficient, i.e. anti-inductive, meaning the quants of the world haven't left behind any reliable patterns that an armchair investor like you can detect and profit from.

Salviati: Would you just shut up and let me say my argument?

Simplicio: Whatever, knock yourself out.

Salviati: Ok, here goes. Everyone knows Bitcoin prices are volatile, right?

Simplicio: Yeah, highly volatile. But at any given moment, you don't know if the volatility is going to move the price up or down next. From your state of knowledge, it looks like a random walk. If today's Bitcoin price is $1000, then tomorrow's price is as likely to be $900 as it is to be $1100.

Salviati: I agree that the Random Walk Hypothesis provides a good model of prices in efficient markets, and that the size of a each step in a random walk provides a good model of price volatility in efficient markets.

Simplicio: See, I told you you wouldn't convince me.

Salviati: Ah, but my empirical observation of Bitcoin prices is inconsistent with the Random Walk hypothesis. So the only thing I'm led to conclude is that the Bitcoin market is not efficient.

Simplicio: What do you mean "inconsistent"?

Salviati: I mean Bitcoin's past prices don't look much like a random walk. They look more like a random walk on a log scale. If today's price is $1000, then tomorrow's price is equally likely to be $900 or $1111. So if I buy $1000 of Bitcoin today, I expect to have 0.5($900) + 0.5($1111) = $1005.50 tomorrow.

Simplicio: How do you know that? Did you write a script to loop through Bitcoin's daily closing price on Mt. Gox and simulate the behavior of a Bayesian reasoner with a variable-step-size random-walk prior and a second Bayesian reasoner with a variable-step-size log-random-walk prior, and thus calculate a much higher Bayesian Score for the log-random-walk model?

Salviati: Yeah, I did.

Simplicio: That's very virtuous of you.

[This is a fictional dialogue. The truth is, I was too lazy to do that. Can someone please do that? I would much appreciate it. --Liron.]

Salviati: So, have I convinced you that the market is anti-inductive now?

Simplicio: Well, you've empirically demonstrated that the log Random Walk Hypothesis was a good model for predicting Bitcoin prices in the past. But that's just a historical pattern. My original point was that you're not qualified to evaluate which historical patterns are *reliable* patterns. The Bitcoin markets are full of pattern-annihilating forces, and you're not qualified to evaluate which past-data-fitting models are eligible for future-data-fitting.

Salviati: Ok, I'm not saying you have to believe that the future accuracy of log-Random-Walk will probably be higher than the future accuracy of linear Random Walk. I'm just saying you should perform a Bayesian update in the direction of that conclusion.

Simplicio: Ok, but the only reason the update has nonzero strength is because I assigned an a-priori chance of 10% to the set of possible worlds wherein Bitcoin markets were inefficient, and that set of possible worlds gives a higher probability that a model like your log-Random-Walk model would fit the price data well. So I update my beliefs to promote the hypothesis that Bitcoin is inefficient, and in particular that it is inefficient in a log-Random-Walk way.

Salviati: Thanks. And hey, guess what: I think I've traced the source of the log-Random-Walk regularity.

Simplicio: I'm surprised you waited this long to mention that.

Salviati: I figured that if I mentioned it earlier, you'd snap back about how efficient markets sever the causal connection between would-be price-regularity-causing dynamics, and actual prices.

Simplicio: Fair enough.

Salviati: Anyway, the reason Bitcoin prices follow a log-Random-Walk is because they reflect the long-term Expected Value of Bitcoin's actual utility.

Simplicio: Bitcoin has no real utility.

Salviati: It does. It's liquid in novel, qualitatively different ways. It's kind of anonymous. It's a more stable unit of account than the official currencies of some countries.

Simplicio: Come on, how much utility is all that really worth in expectation?

Salviati: I don't know. The Bitcoin economy could be anywhere from hundreds of millions of dollars, to trillions of dollars. Our belief about the long-term future value of a single BTC is spread out across a range whose 90% confidence interval is something like [$10, $100,000] for 1BTC.

Simplicio: Are you saying it's spread out over the interval [$10, $100,000] in a uniform distribution?

Salviati: Nope, it's closer to a bell curve centered at $1000 on a log scale. It gives equal probability of ~10% both to the $10-100 range and to the $10,000-100,000 range.

Simplicio: How do you know that everyone's beliefs are shaped like that?

Salviati: Because everyone has a causal model in their head with a node for "order of magnitude of Bitcoin's value", and that node varies in the characteristically linear fashion of a Bayes net.

Simplicio: I don't feel confident in that explanation.

Salviati: Then take whatever explanation you give yourself to explain the effectiveness of Fermi estimates. Those output a bell curve on a log scale too, and seems like estimating Bitcoin's future value should have a lot of methodology in common with doing back-of-the-envelope calculations about the blast radius of a nuclear bomb.

Simplicio: Alright.

Salviati: So the causality of Bitcoin prices roughly looks like this:

[Beliefs about order of magnitude of Bitcoin's future value] --> [Beliefs about Bitcoin's future price] --> [Trading decisions]

Simplicio: Okay, I see how the first node can fluctuate a lot in reaction to daily news events, and that would have a disproportionately high effect on the last node. But how can an efficient market avoid that kind of log-scale fluctuation? Efficient markets always reflect a consensus estimate of an asset's price, and it's rational to arrive at an estimate that fluctuates on a log scale!

Salviati: Actually, I think a truly efficient market shouldn't just skip around across orders of magnitudes, just because expectations of future prices do. I think truly efficient markets show some degree of "drag", which should be invisible in typical cases like publicly-traded stocks, but become noticeable in cases of order-of-magnitude value-uncertainty like Bitcoin.

Simplicio: So you think you're the only one smart enough to notice that it's worth trading Bitcoin so as to create drag on Bitcoin's log-scale random walk?

Salviati: Yeah, I think maybe I am.


Salviati is claiming that his empirical observations show a lack of drag on Bitcoin price shifts, which would be actionable evidence of inefficiency. Discuss.

Atkins Diet - How Should I Update?

2 Liron 11 June 2012 09:40PM

This seems like an authoritative 25-year research project that the Atkins diet is pretty bad:

http://www.nutritionj.com/content/11/1/40/abstract

 

Right now my belief is that the Atkins diet is good. It's backed by anecdotal evidence of trying a low-carb diet for 18 months following a 12-month low-fat diet and seemingly getting better results with the low-carb diet.

I'm counting on LWers to tell me how to update my belief in light of this study. Thanks.

Quixey Challenge - Fix a bug in 1 minute, win $100. Refer a winner, win $50.

6 Liron 19 January 2012 07:39PM

Hiring is so hard that we spent a man-month creating a sub-startup to do it. The product is the Quixey Challenge which is running today until 7pm PST (GMT-8).

Benefits of playing:

  • You can learn something from our craftsmanship of the algorithms (we work hard on them)
  • The 1-minute challenge is a rush
  • You can make money
  • If you do well you can interview at Quixey
Even if you have zero engineering skills, you can get $50 for referring someone who wins.

 

Quixey is hiring a writer

10 Liron 05 January 2012 06:22AM

We've posted about jobs at Quixey before:

Quixey - startup applying LW-style rationality - hiring engineers

Since then we've hired LessWrong user cata. And it occurred to us that the LessWrong community is not only full of software engineers, it's also full of unusually strong writers.

continue reading »

Quixey - startup applying LW-style rationality - hiring engineers

27 Liron 28 September 2011 04:50AM

Quixey is a 2-year-old startup with a lot of ties to the rationalist community. Our product is an all-platform "functional search" engine for apps. Our main engineering task is to build the most accurate possible map of all software on all platforms (the "functional web"), and write search algorithms that let users find apps to do what they need.

We're hiring top-notch engineers for full time positions in our Palo Alto, CA office. If your overall engineering skill level is "Google+", we have a lot to offer:

 

continue reading »

Quixey Engineering Screening Questions

2 Liron 09 October 2010 10:33AM

My startup, Quixey, is looking to hire a couple top-notch software engineers. Quixey is an early-stage stealth startup founded in October 2009. We are launching our beta product this month: An all-platform app directory and "functional search" engine that lets users query for software by answering the question: What do you want to do?

We are confident that Quixey's functional search will be qualitatively better than all existing solutions for finding web apps, mobile phone apps, desktop apps, browser extensions, etc. Our prototype returns significantly more relevant search results in head-to-head comparisons with all the iPhone and Android app search solutions that currently exist(!)

Our office is on University Ave in Palo Alto. If you live in the Bay Area and want to join a hot tech startup extremely early (employee #1, high-equity compensation package), and you're better than the average Google engineer, then please try our screening questions. If you're the kind of person we're looking for, the questions shouldn't take you more than a few minutes each.

Questions

1. Write a Python function findInSorted(arr, x). It’s supposed to return the smallest index of a value x in an array arr which, as a precondition, must be sorted from least to greatest. Or, if arr doesn’t contain an element equal to x, the function returns -1. Make the code as beautiful as possible (without sacrificing asymptotically optimal performance characteristics).

2. Write a JavaScript function countTo(n) that counts from 1 to n and pops up an alert for each number (i.e. alert(1), alert(2), ..., alert(n)). Easy, right? Except you're not allowed to use while- or for-loops. (And you're not allowed to trick the interpreter using "eval", or dynamically generated <script> elements appended to the DOM tree, or anything like that.)

For problem 2, the time and space requirements of your function should be as good as those of the asymptotically optimal algorithm, even without tail call optimization.

Email your answers to liron@quixey.com and I'll get back to you right away. Please don't post your answers in this thread because that will make my filter really noisy. If you do well on the screening questions, we will want to bring you in for an interview.

Bloggingheads: Robert Wright and Eliezer Yudkowsky

6 Liron 07 August 2010 06:09AM

View more: Next