gender inclusivity in communication models

I submitted a paper to ISIT in which I tried something different. It’s about communication models with a jammer, so there are three parties: Alice, Bob, and the jammer. Alice wants to send a message to Bob. The jammer wants to prevent it from being reliably received.

We always use Alice for the encoder/transmitter. Knowing nothing more than the name, I would use the pronouns she/her/hers to refer to Alice.

We always use Bob for the encoder/transmitter. Knowing nothing more than the name, I would use the pronouns he/him/his to refer to Bob.

What about the jammer? In previous papers (and in our research discussions) we called the jammer various names: Calvin (to get the C) or James (for the J). We ended up also using he/him/his for the jammer too.

This time I proposed we use Jamie for the jammer. Knowing nothing more than the name, I suggested they/them/their as the most appropriate. In my mind, Jamie may be gender nonconforming, right?

At this point many readers (if there are any) would say I’m being a bit on the nose. Why make James into Jamie and why deliberately change the pronouns? Won’t it just confuse people?

There are so many responses to this.

First, just on pragmatics. This makes pronouns which are uniquely decodable to the parties in the communication model. What can be clearer?

Second, if pronouns create a problem for a mathematically-minded reader, then they are far too obsessed with (gendered) Alice/Bob metaphor. It’s a mathematical engineering paper, not a kid’s story.

But finally, and most importantly, even though all the authors of this paper may be cis-gendered, writing the stories in our papers in a more inclusive way is the right thing to do. Why Alice and Bob? Why not Aarti and Bhaskar, Anting and Bolei, Avital and Binyamin, or Arash and Babak? I’ve heard arguments that we should be more ecumenical in the national origin of our communicating parties. Can we be more inclusive by gender as well?

We can and should!

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What signals sent by author lists

I recently had a conversation about ordering of author lists for papers. Of course, each field has its own conventions but as people start publishing in multiple communities’ venues things can get a bit murky. There are pros and cons and different people have different values, etc.

This is all standard and has been hashed to death.

But what happens when you merge two papers with different author lists? Alphabetical makes things very easy, but if you go a different route, then the primary authors have to slug it out to see who gets first author credit. To split the difference, you could put a footnote saying that authors are in alphabetical order. In the conversation, it came up that putting the footnote implies that there was some tension between the two author groups and so this was the compromise solution after a debate. That was new to me: is this the correct inference to make in most cases?

Condorcet Paradoxes and dice

NB: don’t take this as a sign that I’ve brought the blog back to life for real. I’ve made too many unfulfilled promises on that front…

There was a talk at UChicago in the fall (I’m still on the seminar mailing lists) given by Jan Hązła based, I think, on a paper titled “The Probability of Intransitivity in Dice and Close Elections” with Elchanan Mossel, Nathan Ross, and Guangqu Zheng. The abstract was quite interesting and led to a discussion with my colleagues Emina Soljanin and Roy Yates in which I realized I didn’t quite get the result so I promised to come back after reading it more carefully. Fast forward several months and now I am in Berkeley (on a pre-tenure sabbatical) and they are back east so I figured I could at least blog about it.

The problem is about intransitive dice, which was a new term for me. Consider an n-sided die with numbers \mathbf{a} = (a_1, a_2, a_n) and call \sum_{i=1}^{n} a_i the face sum. The die is fair, so the expected face value is \frac{1}{n} \sum_{i=1}^{n} a_i. We can define an ordering on dice by saying $\mathbf{a} \succ \mathbf{b}$ if a uniformly chosen face of \mathbf{a} is larger than a uniformly chosen face of \mathbf{b}. That is, if you roll both dice then on average \mathbf{a} would beat \mathbf{a}.

A collection of dice is intransitive if the relation \succ based on dice beating each other cannot be extended to a linear order. The connection to elections is in ranked voting — an election in which voters rank candidates may exhibit a Condorcet paradox in which people’s pairwise preferences form a cycle: A beats B, B beats C, but C beats A in pairwise contests. (As an aside, in election data we looked at in my paper on instant runoff voting we actually rarely (maybe never?) saw a Condorcet cycle).

Suppose we generate a die randomly with face values drawn from the uniform distribution on [-1,1] and condition on the face sum being equal to 0. Then as the number of faces n \to \infty, three such independently generated dice will become intransitive with high probability (see the Polymath project).

However, it turns out that this is very special to the uniform distribution. What this paper shows (among other things) is that if you generate the faces from any other distribution (but still condition the face sum to be 0), the dice are in fact transitive with high probability. This to me is interesting because it shows the uniform distribution as rather precariously balanced — any shift and a total linear order pops out. But this also makes some sense: the case where the dice become intransitive happens when individuals essentially are choosing a random permutation of the candidates as their preferences. In face, the authors show that if you generate voters/votes this way and then condition on the election being “close” you get a higher chance of turning up a Condorcet paradox.

The details of the proofs are a bit hairy, but I often find ranking problems neat and interesting. Maybe one day I will work on them again…