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The Mathematics of Paul Graham's Bias Test

chrisstucchio.com

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Re: The Mathematics of Paul Graham's Bias Test

#51

Post by eru »

igonvalue wrote: post #44

It's since been dressed up with some mathiness, but this idea was originally proposed in the comment threads of pg's original article. [0] See the responses there for a few reasons why it just won't work. To be concrete, assuming "performance" is measured as return on investment, min(performance) will always go to to -100% (i.e., bankruptcy) with a large enough sample size. [0] https://news.ycombinator.com/item?id=10…

With a large enough sample size, someone might find a way to break the -100% barrier.

Re: The Mathematics of Paul Graham's Bias Test

#52

Post by oskarth »

I think this is the first post that's a DH5 on pg's How to disagree scale (http://paulgraham.com/disagree.html). Not only that, the OP is charitable enough to explicit state why it's not a DH6:

Paul Graham wrote an article about an idea. The idea is generally correct - bias in a decision process will be visible in post-decision distributions, due to the existence of marginal candidates in one group but not the other. But the math was wrong. // That's ok! Very few ideas are perfect when they are first developed.

I'm not good enough at statistics to check that OP's math is sound, but this is the mindset of a scientist. OP reasons rigorously, finds a way to salvage the core insight and improves on it. As readers can see, it took quite a lot of work and prior knowledge to do.

If I were pg I would consider putting a link to this post on both the disagree.html and bias.html as a note for posterity.

Re: The Mathematics of Paul Graham's Bias Test

#53

Post by notahacker »

agarden wrote: post #31
lukev wrote: post #10

One other thing which both this and PG's original theory get wrong: Their basic premise is wrong, if bias continues to exist after the selection event in question. For example, if YC had (hypothetically) a real bias against black or women entrepreneurs, it is almost certain that future funding rounds, as well as all possible exit scenarios, would exhibit very much of the same bias. In which case, the future "performa…

Let's assume that bias does persist past selection through the duration of the program. Does that change the interpretation when you look at First Round Capital's data that shows its female founders outperforming the males by 63%? I don't think it does. The test may not be sufficient to prove that you have no bias, but it may be good enough to prove that you do. When it does indicate bias, it seems likely to be corre…

The interpretation is still somewhat unreliable as in many cases there's still another hypothesis, which is that $UNDERREPRESENTED_MINORITY actually overperforms due to favourable treatment after the selection process

Of course favourable treatment can't make people into superstar startup founders or baseball players (and I'm sure any special treatment afforded to black baseball players in the 1940s was the complete opposite of favourable). But more generally it can make an organisation with fair selection processes look like it sets a higher bar for $MINORITY because it addresses low numbers by being very keen to promote and very reluctant to fire/deselect members of said minority, so these kind of studies still have to be considered with care.

(Of course even if an organisation is proactively treating a minority group favourably after selection doesn't mean that conscious or unconscious biases don't exist in the selection process.)

Re: The Mathematics of Paul Graham's Bias Test

#54

Post by leni536 »

oskarth wrote: post #52

I think this is the first post that's a DH5 on pg's How to disagree scale ( http://paulgraham.com/disagree.html ). Not only that, the OP is charitable enough to explicit state why it's not a DH6: Paul Graham wrote an article about an idea. The idea is generally correct - bias in a decision process will be visible in post-decision distributions, due to the existence of marginal candidates in one group but not the othe…

To be fair pg's scale isn't perfect. DH1-DH5 is something you can improve if you want to refute a given argument. DH6 is about choosing the "main" argument you want to refute. There is nothing to improve between DH5 and DH6, especially if you agree with the main argument but you disagree with some minor argument.

Re: The Mathematics of Paul Graham's Bias Test

#55

Post by yummyfajitas »

danieltillett wrote: post #2

Very nicely done Chris, but the basic problem with Paul’s analysis is not the mathematics (this can be fixed as you have shown), but the underlying data. Any data set you could get to measure bias in the start-up world is too small and messy to tell you anything useful. No matter how sophisticated your analysis, if the data is garbage then all you will end up with is garbage. This does even consider the problem of da…

Yeah, a minima-ish statistic (even one less sensitive to noise) is probably not going to work for VC. Noise isn't the only issue - in VC the minima will always be zero unless a VC only picks winners.

A test in this general direction (but which handles noise) is much better suited for answering questions like "are colleges biased against Asians". In that case you have a pretty clear output (college GPA) which very rarely reaches zero.

Re: The Mathematics of Paul Graham's Bias Test

#56

Post by yummyfajitas »

ceph_ wrote: post #24
bsder wrote: post #13

The fact that they have to exclude Uber for no good a priori reason should have been raising red flags all over the place. "But Uber skews the results!" So what? You don't get to just throw out data points you don't like without good reason. If your "test" is that sensitive to individual outliers, then perhaps it isn't really a good test after all.

Dropping outliers is common in statistical analysis.

It's still BS. Outliers are a signal that you don't have a simple, nicely decaying distribution.

The right way to deal with outliers is to use a method that acknowledges their existence, not to ignore them. For example, if outliers destroy your OLS linear regression, it's because your error is not normal. That means you need to do Bayesian linear regression with a non-normal error term, not just throw them away.

Re: The Mathematics of Paul Graham's Bias Test

#57

Post by skj »

lukev wrote: post #10

One other thing which both this and PG's original theory get wrong: Their basic premise is wrong, if bias continues to exist after the selection event in question. For example, if YC had (hypothetically) a real bias against black or women entrepreneurs, it is almost certain that future funding rounds, as well as all possible exit scenarios, would exhibit very much of the same bias. In which case, the future "performa…

As uncomfortable as it may be too say, that means that it isn't bias on YC's part; it's an accurate predictor of future success.

I would argue that social responsibility requires YC to take the hit, but bias is the wrong word if they don't.

Re: The Mathematics of Paul Graham's Bias Test

#59

Post by yummyfajitas »

lukev wrote: post #10

One other thing which both this and PG's original theory get wrong: Their basic premise is wrong, if bias continues to exist after the selection event in question. For example, if YC had (hypothetically) a real bias against black or women entrepreneurs, it is almost certain that future funding rounds, as well as all possible exit scenarios, would exhibit very much of the same bias. In which case, the future "performa…

This isn't actually a flaw in the theory. The theory is designed to measure whether the selection process is inaccurately predicting outcomes. So an unbiased selection process will account for post-selection factors - including the fact that VCs might not like a person.

It's also worth noting that an unbiased prediction is not necessarily "fair" in the colloquial sense. For example, I've seen data suggesting that an unbiased prediction of college outcomes would actually penalize black applicants, since black applicants underperform relative to their SATs and college grades. (The person who had this data was very careful not to draw this conclusion in the publication - career limiting move, as they say.)

So a fair selection process which looks only at high school grades/SAT/etc might actually be biased as a statistical decision procedure.

Re: The Mathematics of Paul Graham's Bias Test

#60

Post by makomk »

haberman wrote: post #28

> So rather than comparing mean performance, we'll compare minimum performance. If I'm understanding correctly, the new test is based on a single data point from each group, rather than an aggregate statistic (like mean). I'm no statistician, but it seems like this data would have far too much variance and noise for this to be a useful test. The minimum performer could be someone who had a sudden personal crisis. Or…

If I'm following his argument correctly, he assumes that there is a hard cut-off at some unknown point in the performance metric being measured, below which no-one is selected and above which all or most people are, and tests whether that hard cut-off point is the same for the two groups. It's going to be an accurate test in that scenario, but that's not a good model of reality. This is especially true when the performance metric being used is noisy and measured after the people are selected - which is exactly the scenario we're actually interested in!
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