The Petrie Multiplier

One of my friends on Facebook pointed out a blog entry on the Petrie Multiplier. The basic idea is this. If we assume that men and women are equally sexist, we might assume that men and women will encounter equal amounts of sexism. However, that is not the case if the populations are unequal. There are more men making sexist remarks, and fewer women to encounter them, so women actually encounter far more sexism than men. In fact, the difference in encountered sexism is the square of the ratio between the sexes.

The basic idea here seems sound. However, the assumption that people have a fixed number of sexist remarks to make is unrealistic. It has sexists searching out women if they can’t find them.

I got interested, so I wrote a python script to simulate something more realistic. The conditions are as follows.

Men and women have the same probabilities of making a sexist remark in a conversation. 50% of both sexes never do. 10% have a 20% chance of making a sexist remark, 10% have a 40% chance, and so on. In keeping with the original, 80% of the population are men, and 20% are women.

Every conversation includes a random sample of people from the whole population (which includes 50 people, to have one woman with every level of sexism, and the corresponding number of men). 30% of conversations involve 2 people, 20% involve 3, and 10% each involve 4, 5, 6, 7, and 8.

There is one other condition. People only make sexist remarks if they are not outnumbered, in that conversation, by members of the opposite sex. In a one-on-one conversation, either side may be sexist.

The script then counts up the number of sexist remarks directed against their own sex encountered by each member of the population, over a total of 500 meetings. (Note that each member only participates in a few of those meetings.)

The results of one run, in increasing order of sexist remarks encountered, look like this:

Men who encountered 0 sexist remarks: 34 (85%)
Men who encountered 1 sexist remark: 4 (10%)
Men who encountered 3 sexist remarks: 2 (5%)
Women who encountered 29 sexist remarks: 1
Women who encountered 36 sexist remarks: 1
Women who encountered 39 sexist remarks: 1
Women who encountered 40 sexist remarks: 1
Women who encountered 41 sexist remarks: 1
Women who encountered 45 sexist remarks: 1
Women who encountered 47 sexist remarks: 1
Women who encountered 49 sexist remarks: 2
Women who encountered 50 sexist remarks: 1

The results are broadly similar if I re-run the script, although the precise numbers obviously change.

It is important to note that men and women are equally sexist in this model. Nevertheless, women suffer from overwhelmingly more sexism.

What happens if we drop the probability of sexism, so that only 10% of men and 10% of women make sexist remarks, and then only do it 20% of the time?

The results of one 500-encounter run look like this:

Men who encountered 0 sexist remarks: 40 (100%)
Women who encountered 1 sexist remark: 2
Women who encountered 2 sexist remarks: 3
Women who encountered 3 sexist remarks: 2
Women who encountered 4 sexist remarks: 1
Women who encountered 5 sexist remarks: 1
Women who encountered 8 sexist remarks: 1

So, even in a situation in which sexism has been almost completely eliminated, women are still encountering a substantial amount of sexism. Indeed, because the logic is independent, we can produce representative results for a situation in which women are far, far more sexist than men, in that women keep the original chances, and thus half of them make sexist remarks at least sometimes, while only 10% of men ever make sexist remarks, and they only do it 20% of the time. We just paste together the results for men from the first run, and for women from the second. The results look like this:

Men who encountered 0 sexist remarks: 34 (85%)
Men who encountered 1 sexist remark: 4 (10%)
Men who encountered 3 sexist remarks: 2 (5%)
Women who encountered 1 sexist remark: 2
Women who encountered 2 sexist remarks: 3
Women who encountered 3 sexist remarks: 2
Women who encountered 4 sexist remarks: 1
Women who encountered 5 sexist remarks: 1
Women who encountered 8 sexist remarks: 1

In other words, given the gender imbalance, women will experience far more sexism than men even if women are far more sexist than men.

The assumptions here are only borderline realistic, but the results should give both sides in the debate pause. It makes it overwhelmingly likely that there is a serious problem with sexism against women in tech, and no problem with sexism against men, at the community level. However, that fact is no evidence that men in tech are, individually, more sexist than women in tech.

Here is the original script (Python 3.3, and I have absolutely no idea whether that matters), which may contain glaring errors as it is the first python program I ever wrote. Yes, the above results might be drivel. The logic looks OK to me, and the probabilities must be the right way round because reducing them reduced the amount of sexism. Still, approach with caution.

Edit 2014/02/09: I’ve added some more comments to the code.

Edit 2014/12/10: Thanks to Kim, I’ve formatted this to preserve the indentation. Pre tags!

import random

# Establish the list of sexism probabilities.

probabilities = [1, 0.8, 0.6, 0.4, 0.2, 0, 0, 0, 0, 0]

sex = ['male', 'male', 'male', 'male', 'female']

population = []

x = 0

# This section sets up the population. Each element is a person. w is their sex, v how likely they are to make sexist remarks, x their number in the population, and the final element is the number of sexist remarks they have encountered.

for i, v in enumerate(probabilities):
    for j, w in enumerate(sex):
        population.append([w, v, x, 0])
        x = x + 1

print(population)

group = [2, 2, 2, 3, 3, 4, 5, 6, 7, 8]

msexist = 0
fsexist = 0

# The for loop does the 500 meetings.

for count in range(500):

#   Choose the group size.

    size = random.choice(group)

#   Choose the appropriate number of people randomly from the population.

    meeting = random.sample(population, size)

    print(meeting)

#   Initialise the number of men, women, and sexist remarks.

    men = 0
    women = 0
    msexist = 0
    fsexist = 0

#   Count the number of men and women in the group.

    for i, v in enumerate(meeting):
        if v[0] == 'male':
            men = men + 1
        else:
            women = women + 1

    print(men)
    print(women)

#   Check for sexism.
#   First, if there are at least as many men as women, check to see whether the men make sexist remarks. If they do, increase the count of sexist remarks made by men by one.

    if men >= women:
        for i, v in enumerate(meeting):
            if v[0] == 'male':
                if v[1] >= random.random():
                    msexist = msexist + 1

#   Next, if there are more women than men, do the same for women. This should be "equal to or greater", but I think using elif here means that this section is skipped when the numbers are equal. Given that equal numbers will be rare, that shouldn't affect the results too much, but there was a logic problem in the code.

    elif women >= men:
        for i, v in enumerate(meeting):
            if v[0] == 'female':
                if v[1] >= random.random():
                    fsexist = fsexist + 1

#   For every man in the group, add the number of sexist remarks made by women to the number of sexist remarks he has encountered. Then copy him back into the population. (I suspect that this is unnecessary, because Python actually operates on the elements on the population rather than on clones, but having taught myself Python to write this code, I'm not sure.)

    for i, v in enumerate(meeting):
        if v[0] == 'male':
            v[3] = v[3] + fsexist
            population[v[2]] = v

#   For every woman in the group, add the number of sexist remarks made by men.

        else:
            v[3] = v[3] + msexist
            population[v[2]] = v

# Sort the population into order by number of sexist remarks, because the final analysis is done by hand.

population.sort(key=lambda population: population[3])

print(population)

Happy New Year!

I think it’s 2013 for just about everyone who reads this blog now, so happy new year! We’ve had an easy day at home, and visiting the local shrine for the traditional New Year’s Day visit. Mayuki got a new year’s present from them, as well.

I hope everyone has a happy, healthy, and prosperous 2013.

Merry Christmas

The presents under the Christmas TreeOnce again, it is 8am on Christmas morning, the sky is blue, Mount Fuji is visible in the distance, and Mayuki is still asleep. She was really excited last night, and put her stocking on the top of the bed, but now she is sound asleep.

The presents have been building up under the tree for a couple of weeks. Every time a new one was added, Mayuki asked “Is it for me?”, and was very excited when it was. However, she hasn’t been trying to peek inside. She even hid one of her dolls among the presents for me to find, without trying to look inside and see what the presents were.

This is not what I’d heard about five-year-olds at Christmas. I guess all children really are different.

We have video chats with the US and UK booked, I’ll be making Christmas dinner all morning, and in the afternoon we’ll open our presents. We have lots of snacks for the day, as well. It should be a good family day.

Annular Eclipse

We saw the annular eclipse this morning. The centre went right over Tokyo, so all we had to do was go outside the flat. Given that, there were surprisingly few people there.

We bought three viewing glasses, so we could all watch together. It’s a bit cloudy, but the clouds were thin, and the clouds over the sun were thin exactly when it was a ring.

It was really, really good.

Happy New Year

Happy new year, everyone. I hope you all have a really good one. Even though I was the only one to make it to the shrine at midnight, Yuriko and Mayuki are still asleep as I type this. Maybe next year Mayuki will be excited enough to remain awake until midnight.

We’re In

Yesterday, we moved into our new flat, and we slept here last night. Everywhere is full of boxes, but my computer is set up and working, and I am hopeful that I will be able to get the office clear of boxes before my first student arrives in five hours or so. The rest of the flat will still be a complete tip, of course, but the biggest advantage of the new place is that my students don’t need to see the rest of the flat.

In the end, the move seems to have gone off without any serious problems. Despite snow falling on Saturday, the next days, Sunday and Monday, the days we were moving, had perfect weather. It was dry, warm, and not too windy, without being hot. We could leave things on the balcony to keep them out of the way, and nothing got wet between the two flats. A local electrical goods shop sold us a new heater/cooler, and moved the old ones to the new flat, doing all of it on Sunday and fitting covers over the hoses between the interior and exterior units. Getting that done before the furniture came in was a big help.

The removals company (Kuroneko Yamato) sent people to pack our things up on Sunday, although they didn’t quite finish, so they had to come again on Monday. Then, on Monday, everything was loaded into trucks and unloaded into the new flat. They even managed to get all of my bookshelves into the positions I wanted in the office, which, given that they are double layer and there is about two millimetres clearance over one of them, was quite impressive. Some of the tiny metal cylinders that support the shelves seem to have fallen out at some point, so I hope I still have the ones that were left over. Of course, even if I do have them, I have no idea where I have them.

So, the new flat is now full of boxes. My first student is coming around 11am, so I have to get the office straight before then. One of the big advantages of the new place is that I can teach in the office, so there is no need for students to go into the rest of the flat. That’s just as well, as it’s still going to be full of boxes.

Yuriko’s parents have come up from Nagoya to help, and yesterday they mainly helped by looking after Mayuki all day (Yuriko’s mother also did some cleaning at the old flat). In the evening, when Mayuki came back to the new flat, quite a bit of the furniture was already in, and she was shocked. “That’s not right! Take it back!” she said (roughly, in Japanese). Unsurprisingly, she hadn’t quite understood what “moving house” meant. Still, she calmed down and watched her video, and then went to sleep, so I think she’ll get used to it.

Now I have to get on with putting books on the bookshelves.

All Change

The actual physical move is almost upon us. The removals company will come on Sunday to pack all of our things up, and our air conditioners will be moved on the same day. On Monday, our things will be moved to the new flat, and we’ll hand over the keys to this one to the new owners.

Also next week, or maybe the week after, Yuriko will start her new job, at a kimono rental shop. That will probably mean that the days Mayuki is in day care will change, and the school where she takes her music classes is also likely to change.

Fortunately, my job won’t change much; I’ll just teach my students in the new flat.

All these changes are, of course, keeping me quite busy, and I’ll blame them for the lack of interesting articles on this blog.

Mount Fuji

I mentioned before that we were supposed to be able to see Mount Fuji from our flat. Well, a few days ago the weather was clear, so I was able to confirm this. As you can see from the photograph, it is possible to see Mount Fuji from our flat.

A landscape that purportedly includes Mount Fuji, with a big helpful arrow

You can see it, can't you?

OK, maybe it’s a little too small in the photograph, even with a bit of help. Here’s a photograph I took by zooming in a bit.

Mount Fuji, above other mountains, in close-up

Can you see it now?

Actually, when you’re looking, it’s quite clear. A couple of days ago we were there in the evening, discussing the redecoration and such, and there was a very nice silhouette of Mount Fuji as the sun set behind it. On clear days, it will be a nice feature of the flat.

The blog has been a bit neglected, because we are having to sort out exactly what we are having done, as well as doing normal work and sorting out address changes. We’re a bit busy at the moment, even more so than normal. I really hope it will settle down in April.

New Flat

Yesterday we handed over the money and became the owners of our new flat. Well, new to us; it’s actually twice the age of the current one, and very close to it. So, why are we moving? The new flat has an extra room.

Mayuki standing in the corner of a Japanese-style room

Our tatami-mat room. You might just be able to see the colour change where the furniture used to be.

We had to go to Yokohama to borrow a room in a bank (the bank that gave me the mortgage) where we could transfer enormous amounts of money to the relevant people, including the estate agents, insurance companies, the scrivener who was changing the deeds, and, of course, the previous owners of the flat, who got this month’s ground rent/service charge and the remainder of this year’s property tax as well as the remainder of the price of the flat itself. That was straightforward, although it did take an hour to get all the paperwork done. (So, now not only have I received a Japanese mortgage, I’ve spent it.)

On the way back, I submitted my tax return. It’s been a busy few months.

Anyway, shortly after we got home Yuriko’s friend from university came over. He’s an architect, and is in charge of the remodelling we’re going to have done.

[I’ve just lost more than half of the blog entry. The log-in cookie expired while I was writing, so the autosave stopped working, and when I tried to save the draft, I was sent to the log-in window and the text vanished. This is a bug in WordPress, which I will have to report when I have time.]

A cityscape beyond which you cannot see Mt. Fuji

On a clear day, you can see Mount Fuji from the Japanese-style room. Yesterday wasn't clear.

The new flat is in a danchi. These are large complexes of flats built in the 1970s, while Japan’s economy was booming and everyone was moving to the cities. Unlike the equivalent structures in the UK, they have not turned into sink estates. They are, however, generally very big for the price, because they are getting old, and Japanese people like new houses. Because they were built for people moving out of traditional Japanese homes, with lots of tatami matting, they all had tatami rooms. Our flat has one such room left, but it quite possibly hasn’t been redecorated since the danchi was built, so one part of the remodelling will be renovating that. We’re going to leave it Japanese-style, however, because I’ve wanted a tatami room since I got to Japan.

We’re also planning to put a partition in the living room, to create an area where Mayuki can make train layouts, or doll dioramas, or lego constructions, and leave them up for days at a time. The main other work is likely to be a counter area in the kitchen, for cooking and eating breakfast, lunch, and some dinners. More formal dinners will be eaten in the tatami room, we think.

The room nearest the entrance is going to be my office, and I’m going to teach in there. That should mean that my evening lessons won’t interrupt Yuriko and Mayuki’s normal activities, and thus should make their lives significantly easier, particularly as Mayuki gets bigger.

I’m looking forward to seeing what the place looks like after remodelling. I think it will look much more interesting than it does now.

Happy New Year

Happy New Year to everyone reading this blog. It’s a beautiful day here in Japan, but our family are starting the year jet-lagged, having only got back from the US on the 30th. I made it to midnight hatsumode at Shirahata-san, the local shrine, but I was the only one.

One of my aims for the new year is to write more in this blog. Wish me luck.