= 27d567bc2d48d9f40e9ccc20ea370b15)
For the sake of clarity, my criticism of Josh's book was developed within the context of Josh promoting his book in a LW thread titled "The Best Textbooks on Every Subject."
Help with a (potentially Bayesian) statistics / set theory problem?
Update: as it turns out, this is a voting system problem, which is a difficult but well-studied topic. Potential solutions include Ranked Pairs (complicated) and BestThing (simpler). Thanks to everyone for helping me think this through out loud, and for reminding me to kill flies with flyswatters instead of bazookas.
I'm working on a problem that I believe involves Bayes, I'm new to Bayes and a bit rusty on statistics, and I'm having a hard time figuring out where to start. (EDIT: it looks like set theory may also be involved.) Your help would be greatly appreciated.
Here's the problem: assume a set of 7 different objects. Two of these objects are presented at random to a participant, who selects whichever one of the two objects they prefer. (There is no "indifferent" option.) The order of these combinations is not important, and repeated combinations are not allowed.
Basic combination theory says there are 21 different possible combinations: (7!) / ( (2!) * (7-2)! ) = 21.
Now, assume the researcher wants to know which single option has the highest probability of being the "most preferred" to a new participant based on the responses of all previous participants. To complicate matters, each participant can leave at any time, without completing the entire set of 21 responses. Their responses should still factor into the final result, even if they only respond to a single combination.
At the beginning of the study, there are no priors. (CORRECTION via dlthomas: "There are necessarily priors... we start with no information about rankings... and so assume a 1:1 chance of either object being preferred.) If a participant selects B from {A,B}, the probability of B being the "most preferred" object should go up, and A should go down, if I'm understanding correctly.
NOTE: Direct ranking of objects 1-7 (instead of pairwise comparison) isn't ideal because it takes longer, which may encourage the participant to rationalize. The "pick-one-of-two" approach is designed to be fast, which is better for gut reactions when comparing simple objects like words, photos, etc.
The ideal output looks like this: "Based on ___ total responses, participants prefer Object A. Object A is preferred __% more than Object B (the second most preferred), and ___% more than Object C (the third most preferred)."
Questions:
1. Is Bayes actually the most straightforward way of calculating the "most preferred"? (If not, what is? I don't want to be Maslow's "man with a hammer" here.)
2. If so, can you please walk me through the beginning of how this calculation is done, assuming 10 participants?
Thanks in advance!
Useful clarification. In that case, you should know that the book is currently being used by several undergraduate and graduate business programs as an introductory business textbook.
The book is designed to be a business primer ("an elementary textbook that serves as an introduction to a subject of study"), and business is a very important area of study that rewards rationality. At the time of my original post, no one had recommended a general business text. That's why I mentioned the book in this thread.
I appreciate your distaste for perceived self-promotion: as a long-time LW lurker, my intent was to contribute a resource LW readers might find valuable, nothing more.
If you're interested in the general topic and want a more academic treatment, you may enjoy Bevelin's Seeking Wisdom. I found it a bit disorganized and overly investment-focused, but you may find it's more to your liking.
This book, or, to be accurate, the 20 or so pages I read, are terrible. For someone who prefers dense and thorough examinations of topics, The Personal MBA is cotton candy. It is viscerally pleasing, but it offers little to no sustenance. My advice: don't get an MBA or read this book.
The mistake I made was considering the author's appearance in this thread as strong evidence that his book would offer value to a rationalist. In fact, the author is a really good marketer whose book has little value to offer. Congratulations to him, however, since he got me to buy a brand-new copy of a book, something I rarely do.
Wow, Duke - that's a bit harsh.
It's true that the book is not densely written or overly technical - it was created for readers who are relatively new to business, and want to understand what's important as quickly as possible.
Not everyone wants what you want, and not everyone values what you value. For most readers, this is the first book they've ever read about how businesses actually operate. The worst thing I could possibly do is write in a way that sounds and feels like a textbook or academic journal.
I don't know you personally, but from the tone of your comment, it sounds like you're trying to signal that you're too sophisticated for the material. That may be true. Even so, categorical and unqualified statements like "terrible" / "cotton candy" / and "little value to offer" do a disservice to people who are in a better position to learn from this material than you are.
That said, I'll repeat my earlier comment: if you've read another solid, comprehensive primer on general business practice, I'd love to hear about it.
In response to
How to Beat Procrastination
del
Personally, I use PICS: Positive, Immediate, Concrete, and Specific. Huge improvement when you actually use it to plan real goals.
Rather phenomenal Amazon reviews you have, sir.
Thanks - glad people are finding it useful.
In response to
The Best Textbooks on Every Subject
Business: The Personal MBA: Master the Art of Business by Josh Kaufman.
I'm the author, so feel free to discount appropriately. However, the entire reason I wrote this book is because I spent years searching for a comprehensive introductory primer on business practice, and I couldn't find one - so I created it.
Business is a critically important subject for rationalists to learn, but most business books are either overly-narrow, shallow in useful content, or overly self-promotional. I've read thousands of them over the past six years, including textbooks.
Business schools typically fragment the topic into several disciplines, with little attempt to integrate them, so textbooks are usually worse than mainstream business books. It's possible to read business books for years (or graduate from business school) without ever forming a clear understanding of what businesses fundamentally are, or how they actually work.
If you're familiar with Charlie Munger's "mental model" approach to learning, you'll recognize the approach of The Personal MBA - identify and master the set of business-related mental models that will actually help you operate a real business successfully.
Because making good decisions requires rationality, and businesses are created by people, the book spend just as much time on evolutionary psychology, decision-making in the face of uncertainty, and anti-akrasia as it does on traditional business topics like marketing, sales, finance, etc.
Peter Bevelin's Seeking Wisdom is comparable, but extremely dry and overly focused on investment vs. actually running a business. The Munger biography Poor Charlie's Almanack contains some helpful details about Munger's philosophy and approach, but is not comprehensive.
If anyone has read another solid, comprehensive primer on general business practice, I'd love to know.
View more: Prev
= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
= f037147d6e6c911a85753b9abdedda8d){kind=logo}
If we allow inconsistency, i.e. if you plan on using this in the real world, then you could get the response B>A, A>C, C>B. That is, there may not be any such thing as a most preferred object, and thus no such thing as the "probability of being the 'most preferred' object."
A workaround would be to ask a related question: "if object 1 is A, and object 2 is unknown, what is the probability that A>2?" The most preferred object would just be the object with the highest answer to this question.
The alternate path would be to assume that there is a preference ordering from 1 to 7, with some sort of noise applied. This feels clunky to me, though.
Good point about inconsistency... I was thinking that individual responses may be inconsistent, but the aggregated responses of the group might reveal a significant preference.
My first crack at this was to use a simple voting system, where B from {A,B} means +1 votes for B, 0 for A, largest score when all participant votes are tallied wins. What messes that up is participants leaving without completing the entire set, which introduces selection bias, even if the sets are served at random.
Preference ordering / ranking isn't ideal because it takes longer, which may encourage the participant to rationalize. The "pick-one" approach is designed to be fast, which is better for gut reactions when comparing words, photos, etc.