# Congratulations! Your All Male Panel is Statistically Unlikely

The issue of conferences in which all the invited speakers are male is probably well known to blog readers, and is the target of campaigns such as the Gendered Conference Campaign and the hilarious Tumblr Congrats, You Have An All Male Panel. Recently, Greg Martin, a mathematician at UBC, gave an interview with the Atlantic with a nice mathematical argument showing that most all-male panels are in fact statistically quite unlikely. This nicely undercuts an all-too-common response among conference organizers that their all-male panel “just happened” or was simply the result of chance.

If conference speakers were being chosen by a system that treated gender fairly (which is to say, gender was never a factor at all), then in any conference with over 10 speakers, say, it would be extremely rare to have no female speakers at all—less than 5 percent chance, depending on one’s assumption about the percentage of women in mathematics as a whole.

Turning that statement around, we conclude that any such conference without any female speakers must have come into being in a system that does not treat gender fairly.

Martin’s interview also links to a Conference Diversity Calculator that lets you play around with calculating the likelihoods of various demographic distributions among conference speakers, given their representation among the pool of available speakers.

## 7 thoughts on “Congratulations! Your All Male Panel is Statistically Unlikely”

1. David Wallace says:

Something is wrong here. The statistics here are very elementary – there’s no need to be a professional mathematician to calculate them. If 20% of research-active philosophers are female (I’ve pulled that number from memory and for illustration) then the probability of N randomly selected research-active philosophers all being male is (0.8)^N. If N=10, that’s about 10%.

So, if you’ve organised a 10-person conference and you’ve invited only men, that’s a wake-up call: there’s only (setting aside specialisation-specific factors) a 10% chance that would have happened if you’d organised it fairly. So think hard about whether you *have* been fair. Your all-male lineup is reasonable, albeit defeasible, evidence that you haven’t been.

But if you just *come across* a 10-person conference with no women, that conclusion probably isn’t warranted. There are lots of conferences, after all. Even in a system that does treat gender fairly, all-male 10-person conferences would often crop up, just because 10% of a large number is still a reasonably large number. GCC calls out way less than 10% of conferences.

Come to think of it, GCC has called out conferences with 4 speakers before. 0.8^4 is 40%. Nearly half of all four-speaker conferences would be all-male even in a perfectly fair selection environment.

I’m in favour, on balance, of the Gendered Conference Campaign (I think I’m a signatory to one of the I-support-this petitions from a couple of years back). But I’m in favour because I think trying to ensure gender representation on as many conferences as possible is a good, if crude, way to filter out the bias that probably is there, and because it’s a good way to provide role models – not because any given occurrence of an all-male line-up is clear evidence of bias. Small-number statistics just don’t work that way. (And the – very sensible – GCC FAQ seems perfectly aware of this: it conspicuously does not claim that the problem with all-male conferences is that they must have come about through bias.)

(Martin uses 5% rather than 10%, because he’s considering a larger panel and because maths has a different gender ratio than philosophy. But the basic conclusion isn’t affected. I find his comment, quoted above, very odd. Analogously, one might say: “if dice were fair, then any time you roll two dice it would be extremely rare – less than 4% – to get two sixes. Turning that statement around, we conclude that any dice throw that generates two sixes must have come into being because the dice aren’t fair.” But I’ve rolled plenty of double sixes on fair dice, because I’ve rolled dice many times.)

2. Joe says:

Agreed that each conference organizer should think it pretty unlikely that they’re somehow the odd one out. That said, this calculator does predict that if selection is completely fair, 11% of your average 8-person philosophy conferences will have no women (assuming that 24% of eligible speakers are female). So, question: should we really be “calling out” every conference that doesn’t have a female speaker? Doesn’t this guarantee that we will wrongly blame a great many organizers? Or should our aims be more “longitudinal”, i.e., calling out recurring, annual conferences with bad records?

3. Audrey says:

I don’t think that the issue here really is whether any individual conference was organized in a biased fashion or not, though I do see why the Martin quote could be interpreted as calling out individual conferences. I liked it because it seemed to me to be pointing at systemic issues to explain why all male lineups seem to happen much more than chance would dictate, but perhaps that’s just because I read it in the context of the longer interview.

Regardless (especially given that we’re generally quite bad at knowing when our decisions are in fact biased), I agree that don’t think that it’s productive to speculate about the extent to which any individual conference was organized fairly. But I do think that processes showcasing just how common it is to have conferences with unlikely gender balances are a useful reminder to conference organizers that bias in speaker selection is still quite a problem.

4. A non-statistician says:

Audrey, on the one hand, you now say: “I don’t think that the issue here really is whether any individual conference was organized in a biased fashion or not.”

But, in your original post, you said: “This nicely undercuts an all-too-common response among conference organizers that their all-male panel “just happened” or was simply the result of chance.”

Isn’t there some tension between these statements, or do you still fully stand by the second one? Since we are typically in no position to know or even to have a justified belief as to whether any given all-male lineup was the result of chance, how does the observation that all-male lineups are statistically pretty unlikely undercut the organizers’ reply that theirs just happened/was the result of chance? Unless there’s some independent evidence that all-male lineups occur significantly more often than they would if the participants were randomly selected, there’s no reason to doubt that every one of the organizers who says theirs was the result of chance is right.

I do agree with this:

“But I do think that processes showcasing just how common it is to have conferences with unlikely gender balances are a useful reminder to conference organizers that bias in speaker selection is still quite a problem.”

However, are there any such processes? As far as I’ve been able to determine, 100% of the conferences featured in the GCC posts have been all-male. These posts don’t tell us anything about how common such conferences are. Have there been any attempts to show that all-male lineups are, in the actual world, more common than they would be if the speakers were randomly chosen?

5. Ralph Heargrave says:

So what is the issue here, Audrey? Maximising the number of invitations to women?

6. David Wallace says:

Speaking personally, I never interpreted the GCC as based on the fact that women are underrepresented at conferences relative to their representation among research-active philosophers (although, as it happens, I suspect they probably are – or at least were prior to the GCC!) I took it to be saying that since women are 20%-25% of the research active philosophy population, making sure there are women at a conference is a non-onerous requirement and is good for providing role models for junior people and grad students. If in fact it counters an underrepresentation as well, that’s a bonus. (And I took it as a strong *defeasible* requirement to have women present – not as something that in no circumstances can be overridden for academic reasons, especially in very small meetings.)

7. A non-statistician says:

David Wallace,

Just to clarify: I never interpreted the GCC that way either. I was just asking if there had been any attempts to show that women were underrepresented at conferences relative to their representation among research-active philosophers. Audrey’s comment seemed to presuppose that there had been. (I only mentioned that the GCC attempts no such thing because I’ve sometimes heard it misinterpreted, in off-line conversations, in just the way you describe.)