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December 11, 2017

Random walking

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BAGEL SHOP IDEA

I was sitting in a bagel shop on Saturday with my 9 year old daughter. We had brought along hexagonal graph paper and a six sided die. We decided that we would choose a hexagon in the middle of the page and then roll the die to determine a direction:

1 up (North)
2 diagonal to the upper right (Northeast)
3 diagonal to the lower right (Southeast)
4 down (South)
5 diagonal to the lower left (Southwest)
6 diagonal to the upper left (Northwest)

Our first roll was a six so we drew a line to the hexagon northwest of where we started. That was the first “step.”

After a few rolls we found ourselves coming back along a path we had gone down before. We decided to draw a second line close to the first in those cases.

We did this about 50 times. The results are pictured above, along with kid hands for scale.

I sent the picture to my friend and serial co-author Jake Hofman because he likes a good kid’s science project and has a mental association for everything in applied math. He wrote “time for some Brownian motion?” and sent a talk he’d given a decade ago at a high school which taught me all kind of stuff I didn’t realize connecting random walks to Brownian motion, Einstein, the existence of atoms and binomial pricing trees in finance. (I was especially embarrassed not to have mentally connected random walks to binomial pricing because I had a slide on that in my job talk years ago and because it is the method we used in an early distribution builder paper.)

Back at home Jake did some simulations on random walks in one dimension (in which you just go forward or backward with equal probability) and sent them to me. Next, I did the same with hexagonal random walks (code at the end of this post). Here’s an image of one random walk on a hexagonal field.

I simulated 5000 random walks of 250 steps, starting at the point 0,0. The average X and Y position is 0 at each step, as shown here.

This might seem strange at first. But think about many walks of just one step. The number of one-step journeys in which your X position is increased a certain amount will be matched, in expectation, by an equal number of one-step journeys in which your X position is decreased by the same amount. Your average X position is thus 0 at the first step. Same is true for Y. The logic scales when you take two or more steps and that’s why we see the flat lines we do.

If you think about this wrongheadedly you’d think you weren’t getting anywhere. But of course you are. Let’s look at your average distance from the starting point at each step (below).

The longer you walk, the more distant from the starting point you tend to be. Because distances are positive, the average of those distances is positive. We say you “tend to” move away from the origin at each step, because that is what happens on average over many trips. At any given step on any given trip, you could move towards or away from the starting point with equal probability. This is deep stuff.

Speaking of deep stuff, you might notice that the relationship is pretty. Let’s zoom in.

The dashed line is the square root of the number of steps. It’s interesting to note that this square root relationship happens in a one-dimensional random walk as well. There’s a good explanation of it in this document. As Jake put it, it’s as if the average walk is covered by a circular plate whose area grows linearly with the number of steps. (Why linearly? Because area of a circle is proportional to its radius squared. Since the radius grows as the square root of the number of steps, the radius squared is linear in the number of steps)

(*) As a sidenote, I was at first seeing something that grew more slowly than the square root and couldn’t figure out what the relationship was. It turns out that the square root relationship holds for the root mean squared distance (the mean of the squared distances) and I had been looking at the mean Euclidean distance. It’s a useful reminder that the term “average” has quite a few definitions. “Average” is a useful term for getting the gist across, but can lead to some confusion.

Speaking of gists, here’s the R code. Thanks to @hadleywickham for creating the tidyverse and making everything awesome.

RCODE

December 8, 2017

BDRM 2018 call for papers

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BDRM SUBMISSION DEADLINE DECEMBER 29, 2017

What: Behavioral Decision Research in Management (BDRM) Conference
When: June 7-9, 2018
Where: Harvard Business School, Harvard University
Submission Deadline: December 29, 2017

CONFERENCE CO-CHAIRS:

Max Bazerman, Alison Wood Brooks, Ryan Buell, Francesca Gino, Leslie John, Elizabeth Keenan, Anat Keinan, Julia Minson, Mike Norton, Todd Rogers, and Shelle Santana

We invite submissions of papers for the 16th biennial conference on Behavioral Decision Research in Management, to be held at Harvard Business School, Boston, MA, on June 7-9, 2018.

BDRM is the leading conference for behavioral research with business and organizational implications. We encourage submissions of original work in all areas of behavioral research including, but not limited to, the areas of decision-making, consumer behavior, experimental and behavioral economics, decision analysis, behavioral finance, organizational behavior, negotiation, behavioral strategy, behavioral operations research, behavioral accounting, and medical and legal decision making.

We are happy to announce the following keynote speakers:

  • Teresa Amabile, Baker Foundation Professor and Edsel Bryant Ford Professor of Business Administration, Emerita at Harvard Business School
  • Paul Rozin, Professor of Psychology at the University of Pennsylvania

SUBMISSION INFORMATION AND DEADLINES FOR THE BDRM CONFERENCE

Submissions for the BDRM conference are due by December 29, 2017. Notification of acceptances will be sent in late March 2018.

Abstracts should include a brief description of the research problem, the key methodology and assumptions, and a summary of major results and implications. Abstracts will be selected for oral presentation by blind review (no author names or affiliations should appear on the abstracts).

Abstracts should not exceed three (3) pages double-spaced, Times New Roman, font size 12, and can be submitted in Word or .pdf format. No math symbols should be used and tables and diagrams should be minimal.

Each participant may present only one paper. When submitting papers to this conference, you must agree to be available at any time on June 8 and June 9, 2018 to give your presentation. If you will not be available on one of these days, please arrange for a co-author to give the presentation. We will not consider date/time change requests for presentations.

We will be grouping competitive papers into 75-minute sessions, containing four papers each. Each author will have approximately 15 minutes to present their work. The last 15 minutes will be dedicated to questions.

Papers accepted by the reviewers will be conditionally accepted until at least one author registers for the conference.

You may submit your paper here

The conference website provides additional information about the conference, including accommodations

November 29, 2017

Postdoc positions in Computational Social Science at Microsoft Research in New York City

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APPLICATION DEADLINE JANUARY 1, 2018

Microsoft Research New York City investigates computational social science, algorithmic economics and prediction markets, machine learning, and information retrieval. We do cutting-edge, multidisciplinary research, both theoretical and applied, with access to an extraordinary diversity of big and small data sources, an open publications policy, and close links to top academic institutions around the world.

We are looking for postdoctoral researchers in the area of computational social science with strong quantitative and programming skills. Postdocs are typically hired for a two-year term appointment following the academic calendar, starting in July 2018. Applicants must have completed the requirements for a PhD, including final submission of their dissertation, prior to joining Microsoft Research. Applicants with tenure-track offers from other institutions will be considered, provided they are able to defer their start date to accept our position.

Basic qualifications:

  • PhD in computer science, statistics, math or a related quantitative social science field
  • Strong mathematical and programming skills

Preferred qualifications:

  • Awareness of the theoretical and experimental social science literature
  • Advanced knowledge of statistics, econometrics, and experimental design

HOW TO APPLY
If you meet the basic and preferably preferred qualifications above, please visit:

https://www.microsoft.com/en-us/research/opportunity/postdoctoral-researcher-css/

for information on applying.

November 22, 2017

29 groups analyzed the same data set, apparently in many different ways

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CROWDSOURCING RESEARCH

We have been meaning to post, for quite some time, about this very interesting report from Nature entitled Crowdsourced research: Many hands make tight work. In it, the authors describe how a finding of theirs didn’t hold up when re-analyzed by the Uri Simonsohn. Instead of digging in their heels, they admitted Uri was right and realized there’s wisdom in having other people take a run at analyzing a data set as they might discover better ways of doing things.

They wondered if, in a wisdom-of-the-crowds fashion, whether aggregating multiple, independent analyses might lead to better conclusions. (We at Decision Science News would expect such an effect would be enhanced when working with a selected crowd of analysts.)

The authors recruited 29 groups of researchers to analyze a single data set concerning soccer penalties and the race of players. The figure at the top of this post shows how the different groups arrived at many different estimates (with different confidences) but about 70% of teams found a significant, positive relationship.

It’s fascinating stuff. The comment is here and the paper by the 29 groups of researchers is here.

November 15, 2017

OBHDP Special Issue on Nudges and Choice Architecture in Organizations

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OUR FIELD’S MOST RECENT NOBEL LAUREATE THALER AMONG EDITORS

Organizational Behavior and Human Decision Processes (OBHDP) is Announcing a Special Issue on Nudges and Choice Architecture in Organizations

GUEST EDITORS

Katherine L. Milkman, University of Pennsylvania (Managing Guest Editor)
Gretchen Chapman, Rutgers University
David Rand, Yale University
Todd Rogers, Harvard University
Richard H. Thaler, University of Chicago

WHY IS THIS SPECIAL ISSUE IMPORTANT?

The 2008 publication of the best-selling book Nudge: Improving Decisions about Health, Wealth and Happiness by Richard Thaler and Cass Sunstein sparked enormous interest in how choice architecture and nudges can be used to improve outcomes in organizations. Policymakers inside and outside of government are scrambling to master new nudging strategies to improve the decisions of citizens, employees and customers. At least 51 countries now boast “centrally directed policy initiatives” influenced by behavioral science, or so-called “nudge-units,” and many Fortune 500 companies are opening similar divisions. A recent review article highlighted the extraordinary cost-effectiveness of nudges relative to other levers of influence (e.g., incentives, rules, educational campaigns) that are typically used by policymakers inside and outside of organizations to influence behavior (Benartzi et al., 2017). However, in spite of the growing applied interest in using nudging as a policy too!
l, far more field research is needed on what nudges and choice architecture strategies work best to change behavior in organizations. This special issue is meant to (a) publish (future) seminal papers testing the efficacy of nudges and choice architecture through field experiments in organizations and (b) substantially accelerate and shape the direction of academic research in this area.

SCOPE OF SPECIAL ISSUE

Appropriate papers should present field experiments (alone or in combination with laboratory experiments) that explore the efficacy of nudging and choice architecture in organizations. By “field experiment”, we mean a study with random assignment of participants to conditions and participants who engaged in the tasks under study in an environment where they naturally undertake these tasks. We are most interested in experiments (a) whose outcomes are measures of actual behavior (rather than self-report), (b) that include participants who are not MTurk workers, undergraduates in a laboratory, or survey panelists from services like Qualtrics and ClearVoice, and (c) that were conducted in real-world organizational settings. We adopt the following definition of a nudge: nudges “aim to change ‘people’s behavior in a predictable way without forbidding any options or significantly changing their economic incentives. To count as a mere nudge, [an]…intervention must be easy and cheap to avoid. Nudges are not mandates’ (Thaler & Sunstein, 2008). Nudges do not impose material costs but instead alter the underlying ‘choice architecture,’ for example by changing the default option to take advantage of people’s tendency to accept defaults passively. Nudges stand in contrast to traditional policy tools, which change behavior with mandates or bans or through economic incentives (including significant subsidies or fines).” (Benartzi et al., 2017)

We particularly seek manuscripts that have several of the following features: introduce new tools of choice architecture, shed light on important ongoing debates in the literature, yield important new empirical or theoretical insights about previously-studied nudges, are of policy importance, or open up promising directions for future research.

An illustrative, but not exhaustive list of topics that fall within the scope of this special issue is provided below:

1. Field validation and testing of nudges or choice architecture techniques in organizations that have previously only been tested in the laboratory or in limited field contexts.
2. Field validation and testing of novel, untested nudges or choice architecture techniques in organizations.
3. Comparisons of effect sizes or cost effectiveness of multiple nudges and/or economic levers related to managerially relevant outcomes.
4. Field results that shed light on novel mechanisms underlying nudges or choice architecture

To learn more or submit a manuscript, visit http://tinyurl.com/obhdp-nudge

November 8, 2017

Prague Conference on Behavioral Sciences 2018

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CASS SUNSTEIN KEYNOTE SPEAKER

The 2nd edition of Prague Conference on Behavioral Sciences 2018 which takes place in Prague on May 4-5, 2018 and aims to discuss new developments and applications of current trends in behavioral sciences.

The keynote speaker is professor Cass R. Sunstein from Harvard Law School who will receive the Allais Memorial Prize in Behavioral Sciences 2018.

The call for abstracts is now open. Please visit the conference’s website http://www.pcbs.cz to find out more details.

Note that the super early-bird fee period (reduction up to 50%) ends December 31, 2017.

To register visit http://cebex.org/events/pcbs/

#PCBS2018 is organized under the auspices of the city of Prague.

November 1, 2017

The SJDM Newsletter is ready for download

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SOCIETY FOR JUDGMENT AND DECISION MAKING NEWSLETTER

The quarterly Society For Judgment and Decision Making newsletter is ready for download:

http://sjdm.org/newsletters/

This one has the 2017 Program in it, so you have that going for you, which is nice.

The journal Judgment and Decision Making preliminarily ranks 9 out of 104 journals in replicability

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JDM IS TOO LEGIT TO CEASE IN ITS REPLICABILITY

The R-Index blog was created by Ulrich Schimmack and aims to increase the replicability of published results in psychological science. Recently, the blog created rankings of 104 psychology journals in terms of replicability and published preliminary results. More detail can be found here.

We were pleased to see that the journal Judgment and Decision Making landed in the top 10 of these 104 journals where replicability is concerned.

Jon Baron does a great job with the journal. In other news, we previously reported that Judgment and Decision Making also leads in open data.

October 25, 2017

How long do you need to flip a coin to see a streak?

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STREAK RESULTS FOR LIKELY (>50%) and HIGHLY LIKELY (>99%)


Click to enlarge

From research on the hot hand to the observation that people don’t create enough streaks when instructed to create pseudo random data, the decision science community is pretty interested in the perception of streaks.

One day we got to wonder, how long would you have to flip a coin for it to be more likely than not you would see a streak of length 10? And in this thought experiment, we mean a fair coin and that the streak could be one of heads or one of tails, and finally that more likely than not means greater than 50% likely.

We found a nice Markov chain solution to the problem and figured out the answer for streaks from length 2 to 16. The above graph has the first 10. The answer is that you need to flip 712 times to exceed a 50% chance of observing a streak of length 10.

Next we wanted to see how the number of flips would grow if we wanted to be highly likely of seeing a streak, where highly likely means greater than 99%.


Click to enlarge

Lastly, we took the results out to 16 flips and plotted the result on a log axis.


Click to enlarge

Here’s R code to mess around with. The Markov chain but could be sped up a lot by starting the search closer to the likely crossover point.

October 19, 2017

WHEN THE REVOLUTION CAME FOR AMY CUDDY

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COMPELLING WRITING

The New York Times just came out with an article called “When the Revolution Came for Amy Cuddy” which is about the science behind an extremely popular TED Talk, and is also about the replication crisis more generally.

As Decision Science News readers, we are confident you will find much to agree within it and much to disagree within it.

You may know many of the people interviewed.

You will probably be talking about it at the upcoming Society for Judgment and Decision-Making conference.

It is compelling writing. Compelling as all get out. We could not put it down.

ADDENDUM

Andrew Gelman has written a reply

There is a lot of debate going on about this article over on this facebook group.