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A Way to Detect Bias

paulgraham.com

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Re: A Way to Detect Bias

#211

Post by morgante »

SamReidHughes wrote: post #210
morgante wrote: post #199

Earlier quoted context omitted.

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.).

What test? We're talking about computing the minimum of what before-the-fact EV should be (based on what set of information?) here, not computing what the mean EV should be (for which you can add up the outcomes and divide by N).

> What test?

The test for bias proposed by pg and modified by yummyfajitas.

> before-the-fact EV

Why are you bringing in before-the-fact EV at all? That's not a component.

The test is based on comparing the minimums, yes. So, for example, what is GPA of the worst female and male students. What part of that requires expectations?

Re: A Way to Detect Bias

#212

Post by mrwilliamchang »

Nimitz14 wrote: post #124
mrwilliamchang wrote: post #104

I think I have a simpler counterexample to disprove pg's hypothesis than any other counterexample I've read in the comments. Suppose our goal is to admit the top 5 applicants with the following performances: A - 30,000 A - 10,000 A - 9,000 B - 7,000 B - 5,000 # Cutoff point below this line A - 4 B - 3 B - 2 Even though admitting the top 5 by score is perfectly fair, the applicants from group A perform better.

I don't see what you're getting at. Group A is better and there are more of them. What's the problem?

pg's argument is that if the average performance of one admitted group is better than the other the admission process has a bias. This example shows that you can have an unbiased process, but the average performance of the groups differs.

Re: A Way to Detect Bias

#213

Post by SamReidHughes »

morgante wrote: post #211
SamReidHughes wrote: post #210

Earlier quoted context omitted.

What test? We're talking about computing the minimum of what before-the-fact EV should be (based on what set of information?) here, not computing what the mean EV should be (for which you can add up the outcomes and divide by N).

> What test? The test for bias proposed by pg and modified by yummyfajitas. > before-the-fact EV Why are you bringing in before-the-fact EV at all? That's not a component. The test is based on comparing the minimums, yes. So, for example, what is GPA of the worst female and male students. What part of that requires expectations?

Before-the-fact EV is what the entire question of bias is about. In the case of investments, your minimum outcome is that you shut down the company. Comparing this for male/female sets is useless. Also, looking at other aspects of the distribution (e.g. how many $10M exits, $100M exits) isn't useful because for investing, you want to maximize mean return, and it's not like looking at 20-80%tile outcomes numerically tells you much about that -- are these people saving dead companies or are they derisking $10B companies?

With students there is more of a connection between before-the-fact EV and outcomes, and much more information exposed (grades and course registrations on a semester-by-semester basis). Without that information (if you just looked at who graduated, who didn't) you can't really say as much. (You could run a Netflix-like competition to see who has the best graduation prediction engine and use its estimates as your definitive answer to what an unbiased EV predictor would say about college applicants.) With GPA information, let's say you look at the 10th percentile GPA's in each set and below, for boys it's 0.1-1.1 and for girls it's 0.1-1.5. What does that tell you about before-the-fact EV cutoffs? It doesn't tell you much, because one set of students, when they fail, could be more likely to fail harder than the other. It takes a lot more work than just that.

Re: A Way to Detect Bias

#214

Post by pygy_ »

rewqfdsa wrote: post #175
pygy_ wrote: post #168

Earlier quoted context omitted.

You're beating a straw man. He said in some circumstances .

Yet he didn't list any or describe any criteria for evaluating them. The "in some circumstances" bit was just a way to weasel out of potential objections.

I thought the example was pretty obvious.

Re: A Way to Detect Bias

#215

Post by nkurz »

mrwilliamchang wrote: post #212
Nimitz14 wrote: post #124

Earlier quoted context omitted.

I don't see what you're getting at. Group A is better and there are more of them. What's the problem?

pg's argument is that if the average performance of one admitted group is better than the other the admission process has a bias. This example shows that you can have an unbiased process, but the average performance of the groups differs.

It's likely that the two of you are talking across each other because you read slightly different articles. Paul added an assumption to his article, possibly after William read it, which is intended to rule out his posited distribution: "(c) the groups of applicants you're comparing have roughly equal distribution of ability".

This strikes me as a "heroic assumption", but it's true that if you make it most of the flaws in his argument go away. Add in the unspoken assumption that the groups are both are large enough that sampling variation does not matter, and I think he's probably logically correct.

On the other hand, once you make these assumptions, the rest of his argument seems unnecessary, since all you need to know is the ratio of males and females funded. If male and female founders are exchangeable, the process is biased if one group is funded more often than they are represented in the applicants.

You don't even need to look at outcome, since we've already assumed the founders are of equal ability. I think that Paul is aiming at the case where we don't know the ratio of applicants. I think his argument can be useful in this case, but only if you have already accepted his assumptions.

Re: A Way to Detect Bias

#216

Post by yummyfajitas »

devalier wrote: post #206
yummyfajitas wrote: post #196

Earlier quoted context omitted.

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 t…

OK I missed that you meant "easily fixed" in the strictly mathematical sense, not in the practical, real-world application sense. With statistics on human affairs, 99% of the hard part is not the math, it is applying that math to a complicated, heterogenous, and difficult to measure underlying phenomena. And in most cases, statistics alone will never give you a straight answer, the best they can do is supplement and…

And because human affairs are hard, we should criticize anyone who dares to voice an idea they haven't fully figured out yet.

This idea that statistics can only confirm and supplement "qualitative observations" (I.e. my priors) is completely unscientific and anti-intellectual. If that's true, forget stats - lets just write down the one permitted belief on a piece of paper and not waste resources on science. Science is really boring when only one answer is possible.

Re: A Way to Detect Bias

#217

Post by devalier »

yummyfajitas wrote: post #216
devalier wrote: post #206

Earlier quoted context omitted.

OK I missed that you meant "easily fixed" in the strictly mathematical sense, not in the practical, real-world application sense. With statistics on human affairs, 99% of the hard part is not the math, it is applying that math to a complicated, heterogenous, and difficult to measure underlying phenomena. And in most cases, statistics alone will never give you a straight answer, the best they can do is supplement and…

And because human affairs are hard, we should criticize anyone who dares to voice an idea they haven't fully figured out yet. This idea that statistics can only confirm and supplement "qualitative observations" (I.e. my priors) is completely unscientific and anti-intellectual. If that's true, forget stats - lets just write down the one permitted belief on a piece of paper and not waste resources on science. Science i…

This idea that statistics can only confirm and supplement "qualitative observations" (I.e. my priors) is completely unscientific and anti-intellectual.

Since when is investing in startups a science? What is anti-intellectual, what is anti-science is to use the wrong tool for the job. Human affairs are not a science in the way that physics is a science. Statistics are far, far more fraught because there are so many variables in play, phenomena are hard to quantify, each case is so heterogenous, etc. You cannot use statistics in human affairs without also having a very good observational understanding of what is actually going on, otherwise you will end up in all sorts of trouble.

Re: A Way to Detect Bias

#218

Post by fanzhang »

The test pg suggests was also proposed by the economist Gary Becker [1]. Like many people here noticed, the catch is that the test only works if you compare marginal performance and not average performance. Economists call this the inframarginality problem [2]. There are a number of solutions to this problem to restore pg's result:

- As pg himself says, if we assume certain statistical distributions of ability and selection rules, the inframarginality problem goes away.

- We'd also solve the inframarginality problem if we can tell roughly who the marginal applicants were. If pg could ask the VC firm, see who almost got rejected, and compare these two groups, he'd be set. pg is well-positioned to test this on the YC dataset.

Likewise, he could solve this problem if he can observe another variable that reveals who the marginal applicants likely were (for example, the startups that had the fewest co-investors).

- There's also an entire literature out there that tries to solve the problem using other ways. For example if a system follows the "KPT" sufficient conditions then the inframarginality problem also goes away.

[1] One prominent approach ... is the “outcome test,” which originated in Gary S. Becker (1957). In the context of motor vehicle searches, the outcome test is based on the following intuitive notion: if troopers are profiling minority motorists due to racial prejudice, they will search minorities even when the returns from searching them, i.e., the probabilities of successful searches against minorities, are smaller than those from searching whites. More precisely, if racial prejudice is the reason for racial profiling, then the success rate against the marginal minority motorist (i.e., the last minority motorist deemed suspicious enough to be searched) will be lower than the success rate against the marginal white motorist. (From [3])

[2] "While this idea has been well understood, it is problematic in empirical applications because researchers will never be able to directly observe search success rates against marginal motorists. This is due to the fact that we cannot identify the marginal motorist, since accomplishing this would require having complete information on all of the variables that troopers use in determining the suspicion level of motorists. Because of this omitted-variables problem, we can observe only the average success rate of searches against white and minority motorists, and not the marginal success rate. Since the equality of marginal search success rates does not imply, and is not implied by, the equality of the average search success rates, we cannot determine the relationship between the marginal search success rates of white and minority motorists by looking at average success rates. In past literature, this has been referred to as the “infra-marginality” problem. (From [3]).

[3] Anwar, Shamena, and Hanming Fang, "An Alternative Test of Racial Prejudice in Motor Vehicle Searches: Theory and Evidence." American Economic Review. (2006)

http://economics.sas.upenn.edu/~hfang/publication/racial-pro...

Re: A Way to Detect Bias

#219

Post by mrwilliamchang »

nkurz wrote: post #215
mrwilliamchang wrote: post #212

Earlier quoted context omitted.

pg's argument is that if the average performance of one admitted group is better than the other the admission process has a bias. This example shows that you can have an unbiased process, but the average performance of the groups differs.

It's likely that the two of you are talking across each other because you read slightly different articles. Paul added an assumption to his article, possibly after William read it, which is intended to rule out his posited distribution: "(c) the groups of applicants you're comparing have roughly equal distribution of ability". This strikes me as a "heroic assumption", but it's true that if you make it most of the fla…

> "Paul added an assumption to his article, possibly after William read it, which is intended to rule out his posited distribution"

Yeah. That is what happened.

Re: A Way to Detect Bias

#220

Post by [deleted] »

rewqfdsa wrote: post #130
superuser2 wrote: post #125

Earlier quoted context omitted.

Apply Occam's Razor to these supposed group differences. Which do you think is a more plausible reality? A. Interviewers prefer candidates who are like themselves, interviewers are mostly white men, therefore most hires are white men. B. The uterus and melanin both inhibit programming ability, interviewers are perfect judges of programming ability, therefore most hires are white men. To look at the present (incomplet…

Which is more plausible? a) the action of natural selection, sexual selection, and the hormone environment magically stop at the blood-brain barrier, or b) there are real group differences between human populations? We've already eliminated all overt discrimination. If you continue to cry discrimination, you're essentially postulating a giant unconscious conspiracy. I find the idea wildly implausible. It's much simpl…

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