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A Way to Detect Bias

paulgraham.com

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Re: A Way to Detect Bias

#191

Post by yummyfajitas »

Tarrosion wrote: post #178
yummyfajitas wrote: post #33

People, most of whom clearly are not that good at math, are being really harsh on Paul Graham. Graham is mostly right, but slightly incorrect. In particular, suppose group A has the distribution f(x) and B has the distribution g(x). If f(x) and g(x) are shaped significantly differently past the cutoff , then mean(H(x-C)f(x)) and mean(H(x-c)g(x)) might not agree even though there is no bias by construction. (Here H(x)…

In a grandchild comment, you note that how close the min of each group is to the cutoff depends on sample size. This is true, but I think it's deal-breakingly true. Suppose we have to input groups, A and B. Members of each group are distributed as Exp(1), ie same underlying distribution. Our selection procedure is totally fair as well: we take everyone without question. However, there are 9x as many people in group A…

First of all, making a group 9x larger doesn't change the shape of the distribution. The distribution would look like 9 exp(|x|), not exp(9|x|).

Secondly, I calculate a p-value for this test here:

https://news.ycombinator.com/item?id=10484309

It's proportional to the smaller of the sample sizes. I'll have a more detailed writeup soon. Also, this test is non-parametric, so you don't actually need to know either C or the distributions f and g - all you need is a certain level of uniform regularity in f and g.

Re: A Way to Detect Bias

#192

Post by mdonahoe »

compbio wrote: post #128
pg wrote: post #91

Earlier quoted context omitted.

It's true that this test assumes groups of applicants are roughly equal in (distribution of) ability. That is the default assumption in most conversations I've been involved in about bias, and particularly the example I used, but I'll add something making that explicit.

If feel the addition: "C" the applicants you're looking at have roughly equal distribution of ability. makes the reasoning more tautological/weak. If we take two dart boards (one for female -, one for male founders) as a visual, where hitting near the bull's eye counts as "startup success". If we take "C" to be true, then the darts would be thrown at random. Now we draw a circle around the bull's eye. Anything landin…

Doesn't this logic assume that there are the same number of darts thrown total at both boards?

The issue with founder funding is there are fewer female applicants than male applicants, and the applications aren't published.

Re: A Way to Detect Bias

#193

Post by radioactivist »

yummyfajitas wrote: post #191
Tarrosion wrote: post #178

Earlier quoted context omitted.

In a grandchild comment, you note that how close the min of each group is to the cutoff depends on sample size. This is true, but I think it's deal-breakingly true. Suppose we have to input groups, A and B. Members of each group are distributed as Exp(1), ie same underlying distribution. Our selection procedure is totally fair as well: we take everyone without question. However, there are 9x as many people in group A…

First of all, making a group 9x larger doesn't change the shape of the distribution. The distribution would look like 9 exp(|x|), not exp(9|x|). Secondly, I calculate a p-value for this test here: https://news.ycombinator.com/item?id=10484309 It's proportional to the smaller of the sample sizes. I'll have a more detailed writeup soon. Also, this test is non-parametric, so you don't actually need to know either C or t…

A note: The original post is correct in what it says. It is saying if one draws N independent samples from an exp(1) distribution then the minimum is distributed as exp(N). This is true. Because of this, for any finite sample there is a systematic 'bias' by your metric if the sample size differs between the two groups. However, you are correct in that this difference vanishes as N becomes large and further that one can make controlled statements about the expected size of this difference, given the distribution.

Re: A Way to Detect Bias

#194

Post by somberi »

This how I understand this:

Look back at decisions you have made under various lenses and learn about your decisions and what biases they have, so that you can avoid them or amplify them (if positive) in future.

Re: A Way to Detect Bias

#195

Post by learnstats2 »

WildUtah wrote: post #20

On a simple mathematical basis, this is false. Consider two groups of candidates for a scholarship, A and B. We want to select all candidates that have an 80% or better chance of graduation. Group A comes from a population where the chance of graduation is distributed uniformly from 0% to 100% and group B is from one where the chance is distributed uniformly from 10% to 90%, with the same average but less variation i…

Your premise discriminates between two groups.

It's not clear how you can assign a candidate a 90% chance of graduation. That probability must be a subjective assessment that has come from some (biased) source. In truth, an individual will either graduate or not.

In your example, you can assign 0% and 100% probabilities in group A, but you can't in group B. The most plausible mathematical explanation for that is that you collected insufficient relevant information about candidates in group B.

Re: A Way to Detect Bias

#196

Post by yummyfajitas »

devalier wrote: post #151
tedsanders wrote: post #131

Earlier quoted context omitted.

A charitable interpretation of what he or she said is this: don't evaluate bias by looking at outcomes of the average applicant, look at the outcomes of the borderline applicants. Even if there is no perfect way to define or measure the minimum acceptable applicant, I think it is reasonable to identify whether applicants were borderline or not.

A charitable interpretation of what he or she said is this: don't evaluate bias by looking at outcomes of the average applicant, look at the outcomes of the borderline applicants. That is fine, that is what he was saying. The point is that his solution is completely impractical for the original goal of finding an objective, statistically valid way of measuring whether bias exists. "Borderline" cannot be measured obje…

PG and I are assuming a measurable outcome, which the selection process is explicitly supposed to predict.

I made no claims about practicality - right now all I have is a little bit of measure theory showing that pg's algo is, in principle, fixable. I fully agree that the first round capital data he cites is inadequate (and also wrong, due to the unjustified exclusion of uber, which they explicitly note would alter the results).

My concrete claim: PGs idea for a statistical test is solid, I can (and shortly will) prove a toy version works, and given enough work one can probably cook up a practical version for some problems.

"Your idea isn't 100% perfect right out of the gate" is a very unfair criticism. Are we supposed to nurture every idea in complete secrecy until it is perfect?

Re: A Way to Detect Bias

#197

Post by nl »

lexcorvus wrote: post #112
rewqfdsa wrote: post #107

Earlier quoted context omitted.

Favoring fair outcome over having fair rules is against everything I believe. We should not strive for a participation trophy culture.

Indeed. The problem is that people frequently infer unfair rules from unequal outcomes, without taking into account the possibility of systematic group differences. Alan: I believe in equality of opportunity, not equality of outcome. Bob: How do you know there isn't equality of opportunity? Alan: Well, just look at how unequal the outcomes are! At this point, Bob would be wise to change the subject, because if he pre…

Bob: Can you give me an example?

nl: Sure.

To overcome possible biases in hiring, most orchestras revised their audition policies in the 1970s and 1980s. A major change involved the use of blind' auditions with a screen' to conceal the identity of the candidate from the jury. Female musicians in the top five symphony orchestras in the United States were less than 5% of all players in 1970 but are 25% today. We ask whether women were more likely to be advanced and/or hired with the use of blind' auditions. Using data from actual auditions in an individual fixed-effects framework, we find that the screen increases by 50% the probability a woman will be advanced out of certain preliminary rounds.[1]

Bob: What? But that doesn't count because...

[1] http://gap.hks.harvard.edu/orchestrating-impartiality-impact...

Re: A Way to Detect Bias

#198

Post by yummyfajitas »

radioactivist wrote: post #193
yummyfajitas wrote: post #191

Earlier quoted context omitted.

First of all, making a group 9x larger doesn't change the shape of the distribution. The distribution would look like 9 exp(|x|), not exp(9|x|). Secondly, I calculate a p-value for this test here: https://news.ycombinator.com/item?id=10484309 It's proportional to the smaller of the sample sizes. I'll have a more detailed writeup soon. Also, this test is non-parametric, so you don't actually need to know either C or t…

A note: The original post is correct in what it says. It is saying if one draws N independent samples from an exp(1) distribution then the minimum is distributed as exp(N). This is true. Because of this, for any finite sample there is a systematic 'bias' by your metric if the sample size differs between the two groups. However, you are correct in that this difference vanishes as N becomes large and further that one c…

Oops - I did misread what he wrote. He was discussing the distribution of the min of the sample, not the distribution itself.

Also, there may be a bias in the true p-value, but there is none in the p-value bound based on h(d) and min(N1, N2).

Re: A Way to Detect Bias

#199

Post by morgante »

SamReidHughes wrote: post #108
yummyfajitas wrote: post #33

People, most of whom clearly are not that good at math, are being really harsh on Paul Graham. Graham is mostly right, but slightly incorrect. In particular, suppose group A has the distribution f(x) and B has the distribution g(x). If f(x) and g(x) are shaped significantly differently past the cutoff , then mean(H(x-C)f(x)) and mean(H(x-c)g(x)) might not agree even though there is no bias by construction. (Here H(x)…

> In practice, measure the weakest male and weakest female to be accepted in your sample set, or some similar approximation. In practice, where do you get these definitive unbiased measurements of the expected return of investing in an individual (or graduation probability or some other score)?

This test can be used after the fact, so you're not measuring expected return but actual return.

It's pretty easy to measure actual return (or actual graduation rate, or actual GPA, etc.).

Re: A Way to Detect Bias

#200

Post by lexcorvus »

nl wrote: post #197
lexcorvus wrote: post #112

Earlier quoted context omitted.

Indeed. The problem is that people frequently infer unfair rules from unequal outcomes, without taking into account the possibility of systematic group differences. Alan: I believe in equality of opportunity, not equality of outcome. Bob: How do you know there isn't equality of opportunity? Alan: Well, just look at how unequal the outcomes are! At this point, Bob would be wise to change the subject, because if he pre…

Bob: Can you give me an example? nl: Sure. To overcome possible biases in hiring, most orchestras revised their audition policies in the 1970s and 1980s. A major change involved the use of blind' auditions with a screen' to conceal the identity of the candidate from the jury. Female musicians in the top five symphony orchestras in the United States were less than 5% of all players in 1970 but are 25% today. We ask wh…

I didn't say there are no valid examples of bias, just that many people assume unequal outcomes must result from unequal opportunity, ignoring the possibility of real group differences. Surely you know many real-life Alans who see bias every time a particular Group X is underrepresented in Field Y. Moreover, the values of X aren't random; you'll almost never hear complaints of bias regarding, say, trash haulers, or NFL cornerbacks. (But NFL quarterbacks—ah, plenty of bias there!)
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