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Does Diversity Trump Ability? An Example of the Misuse of Mathematics [pdf]

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Re: Does Diversity Trump Ability? An Example of the Misuse of Mathematics [pdf]

#41

Post by scythe »

DanBC wrote: post #38
kenjackson wrote: post #7

Earlier quoted context omitted.

It also seems to defy common sense. How many top ACM programming teams randomly pick programmers from the college? How many great bball teams are randomly picked from players? There are few activities, where excellence is easily measured, where randomly picking participants results in superior results.

Moneyball shows us that all that knowledge and experience used to pick a baseball team was wrong and that people should ignore their "common sense" (which is usually just another word for "cognitive bias") and should use hard data. In the absence of hard data just picking a team randomly froma pool of qualifying players seems to me like it would be as good as pickping players based on the team-picker's experience of…

>Moneyball shows us that all that knowledge and experience used to pick a baseball team was wrong and that people should ignore their "common sense" (which is usually just another word for "cognitive bias") and should use hard data.

Nothing of the sort. Moneyball showed that an actuarial method was better than other methods in picking a baseball team. This does not mean that the previous methods were no better than random chance. In the case of baseball there was a large corpus of data which had good correlations to players' future performance. That's a rather unique situation.

In this case assuming that whatever previous methods are immediately wrong was on a much weaker basis: just the dataset from one particular toy challenge. A comparison with Moneyball is misleading.

Re: Does Diversity Trump Ability? An Example of the Misuse of Mathematics [pdf]

#42

Post by calibraxis »

bobthechef wrote: post #37
johnbender wrote: post #14

Earlier quoted context omitted.

It's important to realize that common sense is never a replacement for a proof or emperical result. That is, common sense is not sufficient to refute the claims made by the original paper. The power of science is that it often defies reasoning and in so doing provides new insights into how things work.

Are you being intentionally facetious? How could science defy "reasoning"? Is science some mystery cult that is shrouded in obscurantism and lack of intelligibility? Or poor choice of word perhaps? Science is most definitely about reasoning and reasoning properly. You must realize that proof and empirical result are never a replacement for common or good sense. The very attitude that proof is self-sustaining is as si…

To be fair, science does gain its (narrow, but useful) power from defying common sense.

(For instance, people like Aristotle IIRC explained why things fall to the ground: they go back to their natural places. Ok, that's common sense; it makes sense to enough people until they let themselves get puzzled by it. Galileo's one person who explored the weirdnesses it entails; and Newton couldn't really accept gravity's occult non-mechanical properties that the evidence pointed at.)

But I agree that's one thing, and the geek-culture's uncritical fascination with the scientific enterprise is yet another. (Which probably has a bad effect on who gets to become scientists.) Thanks for pointing out Duhem's book; will try to look at it.

Re: Does Diversity Trump Ability? An Example of the Misuse of Mathematics [pdf]

#44

Post by amathstudent »

im3w1l wrote: post #43

Has there been any attempt at quantifying the "wishful thinking bias" in social science?

Here's something you might find interesting: http://vserver1.cscs.lsa.umich.edu/~crshalizi/weblog/698.htm...

There have are also loads of replication projects, some currently ongoing, of both experimental and statistical papers, with generally dismal results.

Re: Does Diversity Trump Ability? An Example of the Misuse of Mathematics [pdf]

#45

Post by kitsune_ »

amathstudent wrote: post #2

As someone who knows it intimately, I would like to say that this kind of thing is endemic across the social science literature. What is frustrating is that only very few people seem to have the ability to understand why it is not sound.

Because I didn't have any money after high school I decided to get a degree where I could work part time. I had been programming for quite some years but had an interest in media and politics. So I started to study media sciences at the largest university here in Switzerland. After a month I realized that I had made a huge mistake. There was a class called 'statistics in social sciences' and the assistants had trouble with basic stuff like calculating the mean, median, avg etc. They even celebrated their mathematical illiteracy to a certain degree. On top of that, much of the writing in the standard text books could be reduced to meaningless tautologies once you deconstructed the complex phrases a bit. I dropped out very quickly after that. The whole experience left a very sour taste in my mouth.

Re: Does Diversity Trump Ability? An Example of the Misuse of Mathematics [pdf]

#46

Post by rlvesco7 »

There is one positive aspect to all this that I would like to point out.

Most social science does not use math, so it makes it hard to argue against ill-defined concepts and ideas. So the fact that these mistakes were found is actually a positive thing and shows one reason why math is useful. That's not to say math cannot be used to obscure arguments and assumptions, it can, but words can do that too.

Re: Does Diversity Trump Ability? An Example of the Misuse of Mathematics [pdf]

#47

Post by kenjackson »

DanBC wrote: post #38
kenjackson wrote: post #7

Earlier quoted context omitted.

It also seems to defy common sense. How many top ACM programming teams randomly pick programmers from the college? How many great bball teams are randomly picked from players? There are few activities, where excellence is easily measured, where randomly picking participants results in superior results.

Moneyball shows us that all that knowledge and experience used to pick a baseball team was wrong and that people should ignore their "common sense" (which is usually just another word for "cognitive bias") and should use hard data. In the absence of hard data just picking a team randomly froma pool of qualifying players seems to me like it would be as good as pickping players based on the team-picker's experience of…

Moneyball is a totally different matter. Moneyball is simply saying the metrics used in the past were wrong.

Let me ask you this. Who do you think would win a chess match. The top 5 rated players in the world on one team, our five random adults chosen from the population who knows the game of chess?

Furthermore I'm dating their theory need not be tested with a poor computational model. You can easily test it with real people with problems to solve.

Lastly you add the caveat of "with no hard data". The paper makes the EXACT opposite claim, which is, if you HAVE hard data you should NOT pick the top performing individuals but rather sample randomly to create a team.

Re: Does Diversity Trump Ability? An Example of the Misuse of Mathematics [pdf]

#48

Post by [deleted] »

DanBC wrote: post #38
kenjackson wrote: post #7

Earlier quoted context omitted.

It also seems to defy common sense. How many top ACM programming teams randomly pick programmers from the college? How many great bball teams are randomly picked from players? There are few activities, where excellence is easily measured, where randomly picking participants results in superior results.

Moneyball shows us that all that knowledge and experience used to pick a baseball team was wrong and that people should ignore their "common sense" (which is usually just another word for "cognitive bias") and should use hard data. In the absence of hard data just picking a team randomly froma pool of qualifying players seems to me like it would be as good as pickping players based on the team-picker's experience of…

[deleted]

Re: Does Diversity Trump Ability? An Example of the Misuse of Mathematics [pdf]

#49

Post by QuantumChaos »

4bpp wrote: post #40

The response paper seems to harp a lot on how the circumstance that typically, N_1 and N >> k, precludes any realistic applicability of the original theorem -- but it admits a fairly self-consistent and altogether much more sinister interpretation if you call the different \Phi "groups" (or "races" for maximum creepiness). The assumptions then say something to the effect of "every group's approach to problem solving…

Your post captures the problem much better than the linked article.

I would summarize the problem as being that the result is tautological, but the gloss of mathematics gives it the appearance of not being tautological.

If people said "diverse teams are better because people from different backgrounds are good at solving different kids of problems" then that would be accurate, but leave room for debate about whether then assumption is true. If they say "diverse teams are mathematically proven to be better", this would be inaccurate, but give great ammunition to argue that science supports progressive views.

Re: Does Diversity Trump Ability? An Example of the Misuse of Mathematics [pdf]

#50

Post by roguecoder »

tbrownaw wrote: post #16
johnbender wrote: post #14

Earlier quoted context omitted.

It's important to realize that common sense is never a replacement for a proof or emperical result. That is, common sense is not sufficient to refute the claims made by the original paper. The power of science is that it often defies reasoning and in so doing provides new insights into how things work.

But a clearly absurd or nonsensical result should be enough reason to double-check that the proof and results are actually valid. Common sense may have a somewhat low weight for evaluating how probable some scientific result is, but it doesn't have zero weight. And neither does the possibility of experimental error.

You have it exactly backwards: all results should be double-checked and independently verified, especially the ones that confirm to common sense due to the pressure of confirmation bias.
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