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Categorization and coordination

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Vessela Daskalova provides a methodology to determine whether decision-makers may benefit from employing fewer categories, even without exogenous costs.

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The paper titled "Categorization and Coordination," co-authored by the speaker and Nick Green from Queen Mary University of London, explores how individuals utilize mental categories to make predictions based on past experiences. It examines the trade-offs between coarse and fine categorization and investigates when each may be beneficial. Examples include employers categorizing applicants and equity researchers categorizing firms.

The authors argue that categorization is a decision-making process influenced by previous encounters, and individuals can employ either coarse or fine categories, impacting their predictions based on the category averages. The study emphasizes that while fine categorization may minimize bias in deterministic environments, coarse categorization can be advantageous in stochastic environments, where noise and sample size play significant roles.

Key findings reveal that coarse categorization may help in minimizing prediction errors when coordinating with others, especially in noisy contexts. The paper discusses three scenarios: individual prediction, coordination of predictions, and a combination of both, employing a model that incorporates game theory and statistical analysis. Through a bias-variance decomposition, the authors identify factors influencing the effectiveness of categorization and highlight the importance of the environment's characteristics.

Ultimately, the paper suggests that while coarse categorization has been linked to biases, it can also arise rationally in certain contexts and may provide valuable insights into decision-making biases in various fields.

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X-TIMESTAMP-MAP:LOCAL=00:00:00.000,MPEGTS=900000

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The paper that I'm going to talk about is called,

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categorization and Coordination

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and it's joint work,

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with my co-author Nick Green from Queen Mary

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University of London.

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So, what we do in this paper is we are interested in the

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use of mental categories to make predictions.

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And so you could think of many examples

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of people using mental categories.

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So it could be employers categorizing applicants based

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on their field of study where they went to university,

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perhaps their gender, race and so on.

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Or you could think of equity researchers,

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categorizing firms, based on the sector

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that they operate in based on their size,

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and other characteristics.

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Likewise, customers categorizing hotels.

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So there are multiple examples

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of people categorizing out there,

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and that's why we are interested in categorization.

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But, well, what does it mean to categorize?

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So, categorization is a form

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of decision making on the pa on the basis

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of past experiences.

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So the idea is,

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an individual will have accumulated a set

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of past experiences and they store them into categories.

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And, when encountering a new situation

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that resembles this past experiences based on its observable

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characteristics, they make a prediction based on the

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category average for this category.

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So this is what categorization is.

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Um, what we look at this at in this paper is the idea

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that in any situation there will be many different possible

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ways to categorize.

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Um, and what we focus on in particular is the idea

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that individuals may be using a few course categories.

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So basically putting their past experiences in

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just a few categories.

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And this will mean that they will be,

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possibly many experiences in each one of these categories

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or individuals could sort their past experiences

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into many fine categories.

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And this means that there would be,

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possibly fewer experiences in each category.

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So the way the individual categorizes matters,

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because they're using the category average

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to make predictions.

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And that's why we are interested in the question,

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when is course categorization actually good for individuals?

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Can it be ever good beneficial for them

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to categorize coursely?

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Can they make better predictions if they

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categorize coursely?

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Uh, this is the key question of the paper.

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And, we,

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answered this question using a simple model.

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Combining game theory and statistics.

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There's abundant literature in psychology showing

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that people use categories in various contexts.

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And more recently there's a literature in economics

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that links course categorization

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to various biases in decision making.

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And so, this, they range

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from discrimination against minorities to over

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and, underpricing of assets

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and financial markets to customers reacting

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to advertising in various ways.

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So in many different contexts,

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course categorization has been linked

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to biases in decision making.

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And so from, inspired by this, we, we are kind

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of interested in the question

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where if course categorization link is linked

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or can lead to biases

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and decision making, why do people categorize coursely?

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Uh, is it one could think that it's due to some sort

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of cognitive limitations?

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So when an innate limitation on the number

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of categories we can use,

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or, basically it could be

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that there are computational costs of using more categories,

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even if we could have many available in our brains.

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But so what we show in this paper is

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that it's not necessarily the case, that,

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that basically course categorization has to be due

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to cognitive limitations.

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So course categorization can arise

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rationally under some environments.

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This is the point of probably the main message of the paper.

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So this is the main message.

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And, in showing this, we are inspired

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by literature from different fields, from cognitive science,

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from, machine learning,

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from econometrics in particular,

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there's the literature on the bias variance,

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the composition of expected prediction error,

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and this what we draw on.

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But the way,

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what our paper focuses on is taking this kind of intuition

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that, there can be this different components

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of expected prediction error to a strategic context, so

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to a, a game theoretical context where individuals want

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to coordinate their predictions with each other.

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And that's how it differs from a lot of this literature,

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which is focusing on individual decision making.

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We have a model of an individual

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who categorizes their past experiences, in order

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to make predictions about a new situation

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that they will encounter.

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Um, so the individual will observe

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some observable characteristics of this past experiences

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and places the past experiences in categories based

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on the observables.

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Um, and then what the individual is trying

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to do is they're trying to predict some unobserved value,

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of the situation, let's say the, suitability

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of an applicant for a particular job.

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And they're trying to predict this based on observable

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characteristics such as where, where the applicant went

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to university, or, their race and gender and so on.

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Um, and so the individual places this past experience into a

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category and makes a prediction based

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on the category average.

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Um, and as I mentioned before,

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because there are many different possible ways

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to categorize, and

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because the individual is making a prediction in the

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category average, this will,

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this will influence their prediction.

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So whether the individual categorizes coarsely

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or whether the individual categorizes finally has an impact

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on the prediction that the individual makes.

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The key focus of the paper is to look at the question,

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when is it good for this individual to categorize coarsely?

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And, in particular,

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we take an X under perspective on this.

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So in this model, we kind of think

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of this category averages as sets of estimators

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that the individual uses to make predictions.

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And we look,

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and we assume the objective of the individual is

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to minimize their expected prediction error

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on the next object.

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Um, and the question is

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what determines which categories are issues?

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The minimize expected prediction error, if it's course

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or fine categorizations,

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we do some comparative statics on that.

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So the three types of cases,

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that we consider in this research is individual prediction,

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coordination of predictions and individual prediction

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and coordination of predictions together.

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So what do I mean by that? Um, individual predictions.

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A prediction means that we have an individual

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who is interested in predicting the true value

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of the next situation that they encounter correctly.

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Um, and, so basically their objective is

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to minimize expected prediction error in

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individual prediction.

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This is what we are assuming this is the first case.

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Now the second benchmark case that we consider

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is two individuals who are matched to play a type

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of coordination game with each other.

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And their objective is to try to

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minimize their expected prediction error,

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from the other person.

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So they no longer in this case, in this particular case,

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they no longer care about predicting the true value

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of the object correctly,

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they just care about coordinating their

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prediction with the other person.

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And so if they only care about coordinating their prediction

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with the other person, what we,

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what we assume is their objective is

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to minimize their expected prediction error

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from coordination.

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Um, and, and this is the second case we consider.

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And then the third case we consider is naturally in many

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situations, they will care both about correct individual

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prediction and coordination of predictions.

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And so basically they placed some weight on individual

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prediction and some weight on coordination of predictions.

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Now, the key thing is, in all of these three cases,

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what we do is we do a bias variance decomposition

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of expected prediction error.

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And this will give us a trade off

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of when it's good to categorize.

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Finally, versus when it's good to categorize coursely.

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Basically there will be a couple of key factors

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that determine, when course categorization is beneficial

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or when fine categorization is beneficial for an individual

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who wants to make predictions

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or coordinate predictions with others.

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But let me start by distinguishing the factors.

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So the factors,

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or among the factors we consider are the sample size

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of past experiences that the individual has accumulated,

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and, the noise of the environment.

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So whether the environment is deterministic or stochastic.

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So this what type

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of environment the individual is operating in is

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very important here.

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So what is additional realistic environment?

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What is a stochastic environment?

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A deterministic environment is an environment in which,

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the observable characteristics fully determine the

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unobserved value of the object.

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So basically, whether where I went to school,

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what, a type of, what field of study I had,

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my gender, my race fully determined, my ability

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or my suitability for a particular job.

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Uh, and everyone who has the same

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characteristics would have the same ability

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or suitability for a job.

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Now, of course, this is not realistic, right?

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So this is just kind of a benchmark case in which everyone

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who looks the same has the same value,

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has the same mobility, suitability,

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whatever it is we are trying to predict.

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Uh, the more interesting case

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and the more realistic case is really a

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stochastic environment.

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A stochastic environment is an environment in which

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observables do not,

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fully determine on individual's, unobserved value

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or an individual's suitability.

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Um, and so these are the environments

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that we very much focus on stochastic environments.

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And now back to my three cases.

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So an individual prediction, what happens is

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that if an individual is just trying

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to predict the true value of the object correctly,

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and they're operating in a deterministic environment,

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so basically observe both fully determined value, then

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the best thing the individual could do is

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to use the finest possible categorization.

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So have a separate category for each object type.

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So splitting their experiences into many categories.

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Now, this is if the environment is deterministic, if

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noise over sample size increases.

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So if the environment becomes stpa stochastic

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and the individual has a limited number of experiences

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or the environment is changing, then

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basically the finest possible categorization

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may no longer be the best.

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So it may become rational for an individual

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to use a coarser categorization

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because this type

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of categorization might now minimize expected prediction error.

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Now, what is the reason for this?

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Well, the reason is this bias variance trade off.

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So, in a deterministic environment, there's no variance.

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So that's why the finest possible categorization was best

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because it minimizes the bias.

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But in a stochastic environment, the noisiness

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of the environment starts to play a role.

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And what the individual can do in order to

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minimize the effect of this noisy past experiences on their

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new prediction is

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to lump their experiences in one big category.

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So this means that there will be a higher sample size per

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category, more experiences per category,

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and this is what helps to decrease the variance component,

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of the expected prediction error.

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So there's this trade off between bias

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and variance components.

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This is the case for individual prediction.

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Now, the focus of this paper is really on the case

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of coordination and predictions.

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Uh, and so there two individuals are, matched,

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to play a one-shot simultaneous move game

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where each individual chooses what categorization

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to use in order to make a prediction.

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And we analyze this type of setting.

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They're trying to minimize their expected prediction error

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from each other, from just coordinating their predictions,

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and we can, derive, equilibrium existence,

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equilibrium efficiency and so on.

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But I'll just focus on the main results here.

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And so the main results are

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that if the environment it is deterministic

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and the individual just cares about coordinating

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with the other person, then the best thing that they can do,

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is use the same categorization as the other, just kind

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of like use the same model for making predictions.

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Uh, but it does not really matter which exact model they're

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using as long as they're using the other in a deterministic

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environment if they want to coordinate predictions.

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Now, this is basically saying

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that it doesn't matter if they use a finer

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or a cosar categorization in a deterministic environment,

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in a stochastic environment,

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however, it matters greatly.

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So as noise increases relative to sample size,

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finer, categorization profiles, may no longer

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be equilibrium.

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Uh, and also for any kind of stochastic environment,

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forer categorization profiles will help,

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will be more efficient, will,

14:39.405 --> 14:43.445
will always help agents always lead to lower

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expected prediction errors.

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So courses, symmetric categorization profiles.

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So this is kind of saying, well, if the individual wants

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to minimize their expected prediction error from

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coordination from the other person's prediction,

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then they're better off categorizing coarsely if there is,

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any noise in the environment.

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Um, and, as I said,

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it's the various equilibrium efficiency,

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equilibrium existence arguments, but this is the key point.

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What's the intuition of why, agents

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would be better off categorizing coursely if they want

15:19.245 --> 15:21.005
to coordinate their prediction with each other?

15:21.875 --> 15:25.525
Well, this has to do with the variance component

15:25.525 --> 15:27.005
of the expected prediction error.

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As I said before, this expected prediction error can be

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decomposed into bias, into variance component.

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Now, course categorization, leads to, leads to a bias.

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Uh, but what it helps to do is it helps

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to minimize the variance component

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because if individuals lump their experiences

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into fewer categories,

15:48.735 --> 15:51.485
there are more experiences per category.

15:51.865 --> 15:53.965
And what this means is

15:54.315 --> 15:56.885
that the idiosyncratic noise

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of each individual's past experience will be minimized,

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or, by using a courser categorization.

16:05.665 --> 16:09.845
So that's the intuition briefly of why it may be better off

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to categorize coursely if individuals want to,

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coordinate their predictions with each other.

16:15.145 --> 16:16.285
And this whole intuition

16:16.285 --> 16:18.365
that I've developed here carries over

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to the individual prediction and coordination case as well.

16:21.865 --> 16:25.605
The key message of this paper, again, is

16:25.635 --> 16:29.525
that course categorization can be beneficial,

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both in an individual prediction environment.

16:32.785 --> 16:35.485
Uh, but what we focus on mostly is this environment

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where individuals want to coordinate with others.

16:38.305 --> 16:41.525
So course categorization, can be beneficial

16:41.665 --> 16:42.965
for individuals who want

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to coordinate their predictions with others.

16:45.105 --> 16:48.045
And this is of course, under some assumptions,

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they sample independently from each other and so on.

16:51.265 --> 16:53.565
So now why does this matter?

16:54.065 --> 16:57.365
Uh, why does it matter that course categorization,

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can be good in stochastic environments

17:00.215 --> 17:02.765
where individuals have limited past experiences

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where there are many such environments out there.

17:06.105 --> 17:10.605
And the previous literature has linked various biases in

17:10.805 --> 17:14.445
decision making, to, course categorization.

17:14.825 --> 17:16.845
So we think this is kind of a step

17:16.905 --> 17:20.405
to understanding why course categorization may

17:20.405 --> 17:21.565
arise, nevertheless.

17:21.945 --> 17:24.645
So why do people still categorize coursely,

17:24.645 --> 17:26.805
even if this leads to some sort of biases,

17:27.365 --> 17:28.685
mistakes in decision making?

17:29.225 --> 17:32.645
Um, and also, the findings

17:32.645 --> 17:34.245
of the paper are really quite nuanced.

17:34.245 --> 17:36.005
So it kind of says,

17:36.195 --> 17:39.725
that in some environments we may expect,

17:39.795 --> 17:41.605
only minor categorization

17:41.665 --> 17:43.925
to be present In some environments,

17:44.025 --> 17:47.045
we may expect worse categorization to be present.

17:47.305 --> 17:48.725
And in some environments we may

17:48.725 --> 17:51.445
Expect categorizations at different levels, of course.

17:51.905 --> 17:54.845
So this is consistent, with what we observe,

17:55.105 --> 17:56.165
out there really.

17:56.585 --> 17:58.765
Um, so the key point is,

17:58.875 --> 18:01.365
that worst categorization can be beneficial,

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and this is shown using a bias variance straight off.

00:00 - The paper that I'm going to talk about is called, categorization and Coordination and it's joint work, with my co-author Nick Green from Queen Mary University of London. So, what we do in this paper is we are interested in the

00:16 - use of mental categories to make predictions. And so you could think of many examples of people using mental categories. So it could be employers categorizing applicants based on their field of study where they went to university, perhaps their gender, race and so on. Or you could think of equity researchers, categorizing firms, based on the sector that they operate in based on their size, and other characteristics.

00:51 - Likewise, customers categorizing hotels. So there are multiple examples of people categorizing out there, and that's why we are interested in categorization. But, well, what does it mean to categorize? So, categorization is a form of decision making on the pa on the basis of past experiences. So the idea is, an individual will have accumulated a set

01:18 - of past experiences and they store them into categories. And, when encountering a new situation that resembles this past experiences based on its observable characteristics, they make a prediction based on the category average for this category. So this is what categorization is. what we look at this at in this paper is the idea that in any situation there will be many different possible ways to categorize. and what we focus on in particular is the idea

01:53 - that individuals may be using a few course categories. So basically putting their past experiences in just a few categories. And this will mean that they will be, possibly many experiences in each one of these categories or individuals could sort their past experiences into many fine categories. And this means that there would be, possibly fewer experiences in each category. So the way the individual categorizes matters,

02:25 - because they're using the category average to make predictions. And that's why we are interested in the question, when is course categorization actually good for individuals? Can it be ever good beneficial for them to categorize coursely? Can they make better predictions if they categorize coursely? this is the key question of the paper. And, we,

02:49 - answered this question using a simple model. Combining game theory and statistics. There's abundant literature in psychology showing that people use categories in various contexts. And more recently there's a literature in economics that links course categorization to various biases in decision making. And so, this, they range from discrimination against minorities to over and, underpricing of assets

03:23 - and financial markets to customers reacting to advertising in various ways. So in many different contexts, course categorization has been linked to biases in decision making. And so from, inspired by this, we, we are kind of interested in the question where if course categorization link is linked or can lead to biases and decision making, why do people categorize coursely?

03:48 - is it one could think that it's due to some sort of cognitive limitations? So when an innate limitation on the number of categories we can use, or, basically it could be that there are computational costs of using more categories, even if we could have many available in our brains. But so what we show in this paper is that it's not necessarily the case, that, that basically course categorization has to be due

04:19 - to cognitive limitations. So course categorization can arise rationally under some environments. This is the point of probably the main message of the paper. So this is the main message. And, in showing this, we are inspired by literature from different fields, from cognitive science, from, machine learning, from econometrics in particular, there's the literature on the bias variance,

04:46 - the composition of expected prediction error, and this what we draw on. But the way, what our paper focuses on is taking this kind of intuition that, there can be this different components of expected prediction error to a strategic context, so to a, a game theoretical context where individuals want to coordinate their predictions with each other. And that's how it differs from a lot of this literature, which is focusing on individual decision making.

05:17 - We have a model of an individual who categorizes their past experiences, in order to make predictions about a new situation that they will encounter. so the individual will observe some observable characteristics of this past experiences and places the past experiences in categories based on the observables. and then what the individual is trying to do is they're trying to predict some unobserved value,

05:46 - of the situation, let's say the, suitability of an applicant for a particular job. And they're trying to predict this based on observable characteristics such as where, where the applicant went to university, or, their race and gender and so on. and so the individual places this past experience into a category and makes a prediction based on the category average. and as I mentioned before, because there are many different possible ways

06:16 - to categorize, and because the individual is making a prediction in the category average, this will, this will influence their prediction. So whether the individual categorizes coarsely or whether the individual categorizes finally has an impact on the prediction that the individual makes. The key focus of the paper is to look at the question, when is it good for this individual to categorize coarsely? And, in particular,

06:41 - we take an X under perspective on this. So in this model, we kind of think of this category averages as sets of estimators that the individual uses to make predictions. And we look, and we assume the objective of the individual is to minimize their expected prediction error on the next object. and the question is what determines which categories are issues?

07:06 - The minimize expected prediction error, if it's course or fine categorizations, we do some comparative statics on that. So the three types of cases, that we consider in this research is individual prediction, coordination of predictions and individual prediction and coordination of predictions together. So what do I mean by that? individual predictions. A prediction means that we have an individual who is interested in predicting the true value

07:38 - of the next situation that they encounter correctly. and, so basically their objective is to minimize expected prediction error in individual prediction. This is what we are assuming this is the first case. Now the second benchmark case that we consider is two individuals who are matched to play a type of coordination game with each other. And their objective is to try to minimize their expected prediction error,

08:08 - from the other person. So they no longer in this case, in this particular case, they no longer care about predicting the true value of the object correctly, they just care about coordinating their prediction with the other person. And so if they only care about coordinating their prediction with the other person, what we, what we assume is their objective is to minimize their expected prediction error

08:31 - from coordination. and, and this is the second case we consider. And then the third case we consider is naturally in many situations, they will care both about correct individual prediction and coordination of predictions. And so basically they placed some weight on individual prediction and some weight on coordination of predictions. Now, the key thing is, in all of these three cases, what we do is we do a bias variance decomposition of expected prediction error.

09:02 - And this will give us a trade off of when it's good to categorize. Finally, versus when it's good to categorize coursely. Basically there will be a couple of key factors that determine, when course categorization is beneficial or when fine categorization is beneficial for an individual who wants to make predictions or coordinate predictions with others. But let me start by distinguishing the factors. So the factors,

09:27 - or among the factors we consider are the sample size of past experiences that the individual has accumulated, and, the noise of the environment. So whether the environment is deterministic or stochastic. So this what type of environment the individual is operating in is very important here. So what is additional realistic environment? What is a stochastic environment? A deterministic environment is an environment in which,

09:58 - the observable characteristics fully determine the unobserved value of the object. So basically, whether where I went to school, what, a type of, what field of study I had, my gender, my race fully determined, my ability or my suitability for a particular job. and everyone who has the same characteristics would have the same ability or suitability for a job. Now, of course, this is not realistic, right?

10:28 - So this is just kind of a benchmark case in which everyone who looks the same has the same value, has the same mobility, suitability, whatever it is we are trying to predict. the more interesting case and the more realistic case is really a stochastic environment. A stochastic environment is an environment in which observables do not, fully determine on individual's, unobserved value

10:56 - or an individual's suitability. and so these are the environments that we very much focus on stochastic environments. And now back to my three cases. So an individual prediction, what happens is that if an individual is just trying to predict the true value of the object correctly, and they're operating in a deterministic environment, so basically observe both fully determined value, then the best thing the individual could do is

11:26 - to use the finest possible categorization. So have a separate category for each object type. So splitting their experiences into many categories. Now, this is if the environment is deterministic, if noise over sample size increases. So if the environment becomes stpa stochastic and the individual has a limited number of experiences or the environment is changing, then basically the finest possible categorization may no longer be the best.

11:58 - So it may become rational for an individual to use a coarser categorization because this type of categorization might now minimize expected prediction error. Now, what is the reason for this? Well, the reason is this bias variance trade off. So, in a deterministic environment, there's no variance. So that's why the finest possible categorization was best because it minimizes the bias. But in a stochastic environment, the noisiness

12:26 - of the environment starts to play a role. And what the individual can do in order to minimize the effect of this noisy past experiences on their new prediction is to lump their experiences in one big category. So this means that there will be a higher sample size per category, more experiences per category, and this is what helps to decrease the variance component, of the expected prediction error. So there's this trade off between bias

12:56 - and variance components. This is the case for individual prediction. Now, the focus of this paper is really on the case of coordination and predictions. and so there two individuals are, matched, to play a one-shot simultaneous move game where each individual chooses what categorization to use in order to make a prediction. And we analyze this type of setting. They're trying to minimize their expected prediction error

13:25 - from each other, from just coordinating their predictions, and we can, derive, equilibrium existence, equilibrium efficiency and so on. But I'll just focus on the main results here. And so the main results are that if the environment it is deterministic and the individual just cares about coordinating with the other person, then the best thing that they can do, is use the same categorization as the other, just kind of like use the same model for making predictions.

13:54 - but it does not really matter which exact model they're using as long as they're using the other in a deterministic environment if they want to coordinate predictions. Now, this is basically saying that it doesn't matter if they use a finer or a cosar categorization in a deterministic environment, in a stochastic environment, however, it matters greatly. So as noise increases relative to sample size, finer, categorization profiles, may no longer

14:28 - be equilibrium. and also for any kind of stochastic environment, forer categorization profiles will help, will be more efficient, will, will always help agents always lead to lower expected prediction errors. So courses, symmetric categorization profiles. So this is kind of saying, well, if the individual wants to minimize their expected prediction error from coordination from the other person's prediction,

14:57 - then they're better off categorizing coarsely if there is, any noise in the environment. and, as I said, it's the various equilibrium efficiency, equilibrium existence arguments, but this is the key point. What's the intuition of why, agents would be better off categorizing coursely if they want to coordinate their prediction with each other? Well, this has to do with the variance component of the expected prediction error.

15:27 - As I said before, this expected prediction error can be decomposed into bias, into variance component. Now, course categorization, leads to, leads to a bias. but what it helps to do is it helps to minimize the variance component because if individuals lump their experiences into fewer categories, there are more experiences per category. And what this means is that the idiosyncratic noise

15:57 - of each individual's past experience will be minimized, or, by using a courser categorization. So that's the intuition briefly of why it may be better off to categorize coursely if individuals want to, coordinate their predictions with each other. And this whole intuition that I've developed here carries over to the individual prediction and coordination case as well. The key message of this paper, again, is that course categorization can be beneficial,

16:29 - both in an individual prediction environment. but what we focus on mostly is this environment where individuals want to coordinate with others. So course categorization, can be beneficial for individuals who want to coordinate their predictions with others. And this is of course, under some assumptions, they sample independently from each other and so on. So now why does this matter? why does it matter that course categorization,

16:57 - can be good in stochastic environments where individuals have limited past experiences where there are many such environments out there. And the previous literature has linked various biases in decision making, to, course categorization. So we think this is kind of a step to understanding why course categorization may arise, nevertheless. So why do people still categorize coursely, even if this leads to some sort of biases,

17:27 - mistakes in decision making? and also, the findings of the paper are really quite nuanced. So it kind of says, that in some environments we may expect, only minor categorization to be present In some environments, we may expect worse categorization to be present. And in some environments we may Expect categorizations at different levels, of course.

17:51 - So this is consistent, with what we observe, out there really. so the key point is, that worst categorization can be beneficial, and this is shown using a bias variance straight off.

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