As a follow up to our guest post on the numbers behind Labor’s broadband policy, here is a quick poll to see whose policy you prefer. Let us know what you think!
Broadband Poll
16 Replies
Labor’s National Broadband Network – Less than $10/month
Our regular guest contributor James Glover (aka @zebra) returns today with a look at the numbers behind the National Broadband Network. He asks: do you think it would be value for money?
The Labor Government’s proposed National Broadband Network (NBN) has many things to recommend it, not least speeds of up to 1GB/s (currently I am on 10Mb/s for ADSL; theoretical speeds of 24MB/s on ADSL2+ and 100MB/s on VDSL are also soon to be widely available, though the reality is dependent on many variables such as distance from an exchange). It would revolutionise the way we communicate as the higher bandwidth would allow not just interactive entertainment and fast downloads, but genuinely accessible cloud applications that really felt like they sat on your computer…and of course dishwashers waking up at 3.00am to negotiate the best electricity price. I doubt whether anybody on either side of politics would disagree that, in a perfect world, this is all desirable. But like all utopias, it comes at a cost and that is where the real divergence between the Labor Party and the Coalition’s broadband policies exists. I hope to cast some light on this cost argument using the power of the Time Value of Money, in particular calculating the real cost to you on a monthly basis so you can compare it with your existing broadband cost.
Labor wants an all-connecting fibre optic network (with subsidised satellite to cover really remote areas) that will cost an estimated $46bn. The Coalition wants a more modest effort: a fibre optic “backbone” network that uses existing copper wiring in urban areas and relies on market competition to pay for further improvements. It is estimated to cost about $8bn plus later commercial costs. Both of these figures seem extraordinarily high. How to decide if it is really worth it? Well if I told you that Labor’s NBN would cost you $10 per month would that sound too high? After all that only includes the infrastructure cost, not the access cost via an ISP. But most of us don’t pay upfront for our broadband or mobile (cell) phone bills, we pay monthly. The Coalition’s figure of $8bn works out at less than $2/month each (for those so inclined, you can read the details behind these figures). But it doesn’t include any additional costs charged by commercial companies building additional infrastructure. It also only claims to provide “peak speeds” of 10Mb/s which I already get on my ADSL+.
Is $10/month a lot of money? Or $2/month for that matter? It obviously depends on what your income is and how much you are currently prepared to pay for broadband. My broadband plan costs $50 for 120GB/month. I also live in a one-person household. It doesn’t sound much to me, but all those $10/month costs add up to the thousands we pay in tax each year. There’s no point paying more for little for no benefit. Of course it’s not going to be charged directly, but through increased taxes (or decreased services). I estimate $10/month to represent an average increase in the tax rate of about 0.5%. This seems reasonable to me. After all, if in 2020 a businessperson (or BusinessBot2020) came to Australia and found our broadband to be the equivalent of dial-up today, they’d hardly be impressed enough to invest in a technology business. Of course, by 2020 with super-fast broadband we should really be able to do most business remotely, right? But we’ve been saying that since the invention of the telephone.
So I’m for the Government’s NBN plan…but what do you think?
Update: I have since writing this post changed my mind based on readers’ comments and some research. It appears that many of the benefits of the NBN are available already on ADSL2+, VDSL and 4G and the Coalition’s more modest plan to build a fibre-optic network backbone might be sufficient. There is also the question of whether a Government entity is best placed to oversee such a large scale project – it’s not like Peter Garrett is going to personally project manage the NBN but Governments in general are not (IMO) best placed to predict and respond to consumer demand. But I accept there are strong feelings on both sides. Sometimes that bright shiny thing in your vision is a light on a hill and sometimes it’s a white elephant blocking your view.
UPDATE: Let us know what you think by voting in this broadband poll.
The Mule goes SURFing
A month ago I posted about “SURF”, the newly-established Sydney R user forum (R being an excellent open-source statistics tool). Shortly after publishing that post, I attended the inaugural forum meeting.
While we waited for attendees to arrive, a few people introduced themselves, explaining why they were interested in R and how much experience they had with the system. I was surprised at the diversity of backgrounds represented: there was someone from the department of immigration, a few from various areas within the health-care industry, a group from the Australian Copyright Council (I think I’ve got that right—it was certainly something to do with copyright), a few from finance, some academics and even someone from the office of state revenue.
Of the 30 or so people who came to the meeting, many classed themselves as beginners when it came to R (although most had experience with other systems, such as SAS). So if there’s anyone out there who was toying with the idea of signing up but hesitated out of concern that they know nothing about R, do not fear. You will not be alone.
The forum organizer, Eugene Dubossarsky, proceeded to give an overview of the recent growth in R’s popularity and also gave a live demo of how quickly and easily you can get R installed and running. Since there were so many beginners, Eugene suggested that a few of the more experienced users could act as mentors to those interested in learning more about R. As someone who has used R for over 10 years, I volunteered my services. So feel free to ask me any and all of your R questions!
As well as being a volunteer mentor, I will have the pleasure of being the presenter at the next forum meeting on the 18th of August. Regular readers of the Stubborn Mule will not be surprised to learn that the topic I have chosen is The Power of Graphics in R. Here’s the overview of what I will be talking about:
In addition to its statistical computing prowess, R is one of the most sophisticated and flexible tools around for visualizing quantitative data. It can produce a wide variety of chart types, including scatter plots, box plots, dot plots, mosaic plots, 3D charts and more. Tweaking chart settings and adding customized annotations is a breeze and the charts can readily be output to a range of formats including images (jpeg or png), PDF and metafile formats.
Topics covered in this talk include:
- Getting started with graphing in R
- The basic charting types available
- Customising charts (labels, axes, colour, annotations and more)
- Managing different output formats
- A look at the more advanced charting packages: lattice and ggplot2
Anyone who ever has a need to visualize their data, whether simply for exploration or for producing slick graphics for reports and presentations can benefit from learning to use R’s graphics features. The material presented here will get you well on your way. If you have ever been frustrated when trying to get charts in Excel to behave themselves, you will never look back once you switch to R.
For those of you in Sydney who are interested in a glimpse of how I use R to produce the charts you see here on the blog, feel free to come along. I hope to see you there!
The Art of Conversation
Have you ever heard the question “Would you like a tea or a coffee” answered with a simple “Yes”? If so, the respondent almost certainly considers their response to be extremely witty. The questioner is unlikely to agree. There is also a high probability that the joker is someone’s Dad…or perhaps a mathematician.
I have to admit to having indulged in this “joke” in my time (more than once), but until recently it had not occurred to me that it in fact reflects a violation of a general principle of conversation. Enlightenment came when I read the seminal 1975 paper “Logic and Conversation” [1] by the philosopher H.P.Grice.
The humour (or lack thereof) of the coffee/tea gag lies in the conflict between the logical truth of the statement and its inappropriateness in conversation. While the statement “A or B” is logically true as long as at least one of A and B is true , in the context of conversation, logical truth is not enough. If you knew A was true and B was false, you would not bother saying “A or B”, you would just say “A”. Moreover, that is what others would expect of you. If I ask you to pass me a hammer, I don’t expect you to pass me a hammer and a spanner. In the same way, if you know you are going to Spain for your holidays, I don’t expect you to say “I’m either going to Spain or Canada”, despite the fact that, strictly speaking, it is a true statement. It is this distinction between simple logical truth and appropriateness in conversation that is the subject of Grice’s paper.
Grice bases his ideas on the notion of the “Cooperative Principle”, which he summarises as the requirement to
Make your conversation such as is required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange in which you are engaged.
People have conversations of many types for many reasons: to do business, to gossip, to seduce, to educate, to inform or simply for the pleasure of conversation itself. In every case, conversation involves (at least) two participants and the conversations that work best are the ones that take the needs of all of the participants into account. So it makes sense that a bit of cooperation is the foundation of a good conversation.
Based on the cooperative principle, Grice goes on to postulate a number of “maxims of conversation”. Here are the maxims as he describes them:
Quantity
- Make your contribution as informative as is required (for the current purposes of the exchange).
- Do not make your contribution more informative than is required.
Quality
- Do not say what you believe to be false.
- Do not say that for which you lack adequate evidence.
Relation
- Be relevant.
Manner
- Avoid obscurity of expression.
- Avoid ambiguity.
- Be brief (avoid unnecessary prolixity).
- Be orderly.
The term “maxim” is carefully chosen as Grice notes that one need not follow all of the maxims at all times, while still being cooperative. The main reason that a maxim could be violated is if it is in conflict with another maxim. An example would be providing less information than required (violating Quantity 1) because you are not confident you have the facts right (and you don’t want to violate Quality 2).
Viewed in terms of Grice’s maxims, the coffee/tea joke is a clear violation of the first maxim of quantity.
As I have already admitted to this particular breach, the obvious question is: have I violated any other maxims? Some who know me well would take the view that, while I may take pains to avoid a violation of either of the maxims of quality, I regularly and flagrantly violate Quantity 2 and Manner 3 and probably Relation 1. I need to learn to stick to the point or risk being branded an uncooperative conversationalist! Or perhaps it’s too late.
[1] Available in the collection “Studies in the Way of Words” by H.P.Grice.
Emissions League Tables
Yesterday’s Sydney Morning Herald featured an opinion piece by Rodney Tiffen on Australia’s sluggish response to climate change. Deliberately provocative, the discussion was framed from the outset in the language of competition:
An international competition in self-righteousness would be closely fought. But Australia must be a strong contender.
Tiffen went on to draw on data from the International Energy Agency (IEA), but got his statistics slightly wrong in the process:
If we restrict the analysis to the most populous 130 countries, those with a population of 3.5 million or more, Australia is the world leader. Only a handful of small countries, especially oil producers such as Bahrain, Qatar and Kuwait, have higher per person emissions.
Australians may be disappointed to learn that we do not, in fact, take home the trophy in this competition. Both the United Arab Emirates and the United States have populations over 3.5 million and have higher per capita emissions than Australia at last count (2007). Nevertheless, coming in third place in this competition, Australia certainly punches above its weight, with per capita emissions running at 4.3 times the world average. Furthermore, as the chart below shows, we have been steadily catching up to the United States over the last 40 years. In fact, to give Tiffen the benefit of the doubt, the most recent IEA data is for 2007, so we may well be ahead of the USA by now.
CO2 emissions 1971-2007 (Source: IEA)
The reason Tiffen looks at per capita emissions is to ward off one common argument for inaction on climate change, namely that China and the United States are the only countries that can make a difference. There is no doubt that these two countries dominate the overall production of emissions. Throwing Canada and Mexico in with the United States brings North American emissions to almost one quarter of the world’s total. Add China and almost half the world’s emissions are accounted for.
Total CO2 emissions for 2007 (Source: IEA)
Nevertheless, if the aim is to attempt reductions in world emissions, Tiffen’s focus on per capita emissions is entirely appropriate. No-one would be convinced if the United States viewed its emissions along State lines, thereby arguing that their emissions were not so big by global standards after all (although, this defence would probably not be much use to California). While countries may be actors on the world stage through their political proxies at climate conferences, emissions are ultimately the product of people (both at home and at work) and not countries. Ranking countries by per capita emissions is thus useful as it gives some indication of where emission reductions may be more readily achieved. The chart below shows the top 25 (big and small) countries in terms of per capita emissions.
Top 25 per capita emitters for 2007 (Source: IEA)
Qatar ranks so high on this scale that it compresses the figures for all of the emitters below it, so here is the chart again with a somewhat truncated scale.
Top 25 per capita emitters for 2007 (Source: IEA)
There are certainly some small countries with high rates of carbon emissions per capita, but looking at a larger scale reveals that developed countries are the worst in per capita terms. It is worth noting, though, that Europe is doing better than the rest of the OECD and is also ahead of former members of the Soviet Union.
Per capita emissions by region for 2007 (Source: IEA)
Another useful approach is to consider emissions per dollar of economic output. This serves to highlight “inefficient” emitters, not to shame them but to identify where spending money on the problem is most likely to deliver significant results. It should come as no surprise that a league table of the highest emitters per dollar of gross domestic product (GDP) is a catalogue of troubled and/or small nations. Note that these figures are calculated based on conversion to US dollars using market exchange rates. Using purchasing power parity instead does reorder the list somewhat, but the names are largely the same.
Top 25 emitters by emissions/GDP for 2007 (Source: IEA)
This perspective suggests that when developed countries consider programs to assist developing countries to reduce their emissions, they could reasonably focus on significant but inefficient emitters. The chart below provides a possible target list, showing the 10 worst-performing countries in terms of emissions per dollar of economic output after restricting to countries with emissions of at least 150 million tons of C02 per annum.
Top 10 large emitters by emissions/GDP for 2007 (Source: IEA)
When will Julia go to the polls?
After taking Kevin Rudd’s scalp and now having done a deal with the miners, Australia’s new prime minister, Julia Gillard, is widely expected to call an early poll. The question is, when will the election be held?
As usual, my first inclination is to dig into the historical data. Looking at all of the Federal elections since Federation, December is far and away the most popular month for a poll. Although the election does not even have to be held this year, December is sufficiently far into the future that it fails to qualify as an early election. Unless the bounce Gillard has experienced in opinion polls proves to be extraordinarily short-lived, we should be looking at a somewhat earlier date. Interestingly, both July and August have only seen one election. On the admittedly spurious grounds of historical precedent, September would be a better bet.
Australian Federal Elections by month
But what of other sources of information? At the time of writing, the shortest odds from SportingBet were on August 7. In my own rather modest poll, August is also proving the most tipped month (it’s not too late to vote in the poll…just make your selection in the form below). No-one has voted for a date in July and I am inclined to agree that that is really a bit soon. Nevertheless SportingBet is still showing odds (admittedly long ones) for 31st July.
In a bid for contrarian status, I will diverge from both the bookies and voters in my poll and will tip a September election. But which date? History is not much help there. Of the four September elections in the past, there has been one on the 1st, 3rd, 4th and 5th Saturday of the month (1914, 1934, 1940 and 1946 respectively). So, I will veer as close as possible to the people’s choice of August, while still tipping September and predict that the election will be on Saturday 4th September. In choosing that date, I have not been swayed by the fact that the fourth Saturday of the month has been the most popular historically, other than to nominate 28th August as my fall-back selection.
Since I will most likely be wrong and you probably disagree with me, make sure to vote!
RSPT RIP – Long Live the MRRT
In the third in a series of guest posts on the subject of Australian mining tax, Zebra (James Glover) considers the changes to the proposed tax the new prime minister, Julia Gillard, has negotiated with miners.
The Govt has announced a replacement for the RSPT discussed in earlier posts to a Mineral Resources Rent Tax (MRRT). The principle differences are the tax rate – 30% and a change in the deduction. For established mines it is now based on market value depreciated over 25 years and the uplift rate is 12% not 5%. In addition there is a 25% deduction from earnings upfront which makes the base rate of tax 22.5% rather than 40%.
This post replaces an earlier one I put up about the MRRT in which I erroneously assumed that the opt-in about using the market value of assets applied in the way I proposed in my second post. The key statement here is:
“Miners may elect to use the book or market value as the starting base for project assets, with depreciation accelerated over 5 years when book value, excluding mining rights, is used; or effective life (up to 25 years) when market value at 1 May 2010, including mining rights, is used. All post 1 May 2010 capital expenditure will be added to the starting base.”
In the case where the mining company opts to use a market value approach I take it to mean the depreciation takes place before the MRRT is calculated. This means the formula is:
MRRT = 30% x (75% x Earnings – Price(2010)/25)
Currently the mining industry average for P/E (price to earnings ratio) is 14, though in the case of BHP-Billiton it is 19. For an average miner then Price(2010)/25 = Earnings x 14/25 = 56% Earnings so the actual MRRT is based on 19% of Earnings. However the Price is fixed at the May 1 2010 value so this will not increase over time even though earnings will. Should earnings continue to rise at the dramatic rate we have seen in the past decade then the MRRT will eventually look more like the 22.5% base rate.
It appears that the Govt and the mining industry’s compromise is to push the revenue from the tax windfall out from today to later years. In a sense the mining industry has also removed the contentious “retrospectivity” of the tax by using the current high price and choice of 25 years depreciation to ensure the current value of the MRRT is minimised but will rise at 22.5% of increased earnings going forward.
Thanks to an observant reader who pointed out my error. Mea culpa.
Surf
I hope this will not come as too much of a disappointment to anyone, but despite the title, this post has nothing to do with the ocean. Here “Surf” refers to the newly established Sydney R user group. While the acronym may be a little forced (it actually stands for “Sydney Users of R Forum”), as a long-time user of the R programming language for statistics and a resident of Sydney, I have signed up and will be doing my best to make it to the first meeting. Any other Sydney-siders who read the post on graphing in R and would like to learn more about R may be interested in coming along too as the group is aimed as much at beginners as old-timers like the Mule. I might even see you there.
If I do make it along to the meeting, I will report back here on what it was like.
UPDATE: I did make it along and will in fact be presenting at the next forum meeting.
The Monty Hall Problem
It’s probability time again!
The discussions about the Tuesday’s Child problem were intense, so a break from probability puzzles was in order. But now that your brains are well rested, it is time to move on to the next puzzle from the Probability Paradoxes post: the Monty Hall problem. If you thought that the first puzzle was controversial, you ain’t seen nothing yet! Monty Hall has generated so much discussion (and, at times, acrimony), that there was enough material for someone to write a book on the subject.
In a possibly futile attempt to avoid some of that controversy, I will be taking a different approach to the discussion this time. I tried to come up with the “best” or “most reasonable” assumptions needed to solve the Tuesday’s Child puzzle, but in the case of Monty Hall I will side-step those sorts of questions and simply provide a framework for calculating solutions for a range of possible assumptions.
So here we go. Remember that the scenario we are presented with is as follows.
Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?
I am going to jump right into the mathematics of conditional probability again. I will use “Car” to denote the possibility that door No. 1 (your door) has a car behind it and “Goat” to denote the possibility that it has a goat behind it. Without necessarily assuming Monty opens door No. 3, I will denote by R (for “reveal”) the possibility that Monty opens a door other than the one you have chosen and thereby reveals a goat.
With all of that in mind, I will compute the probabilities P(Car | R) and P(Goat | R), that is the probability that you have picked a car or a goat respectively, given that Monty has shown you a goat behind another door. Even allowing for the goat being as good-looking as the one pictured here, I will also assume that you really want to win a car not a goat. On that basis, you should switch doors if P(Goat | R) is greater than P(Car | R) and stick with your original choice if P(Goat | R) is less than P(Car | R). If the two probabilities are the same, there is no advantage or disadvantage in switching.
Despite being a very easy theorem to prove, Bayes’ Theorem is one of the most fundamental results in probability and I will make use of it here.
The probability P(R) can be broken down in terms of the two mutually exclusive possibilities ‘Car’ and ‘Goat’:
Combining this with Bayes’ Theorem and the (fairly uncontroversial) facts P(Car) = 1/3 and P(Goat) = 2/3, we can conclude that
Tidying this up a bit gives us a formula that will be able to deal with many (but by no means all) possible assumptions for the problem.
Of course, once we have this, we also know P(Goat | R) as it is 1 – P(Car | R).
All we need to do to use this formula is come up with assumptions that can be formulated in terms of P(R | Car) and P(R | Goat). Here are some examples of what we can do.
Case 1 (Classical)
Here we assume that Monty knows everything in advance about where the goats and the car are and that he can and always will show you a goat behind another door. This means that
P(R | Car) = P(R | Goat) = 1
Plugging this into the formula gives P(Car | R) = 1/3 and P(Goat | R) = 2/3, which means that we are better off switching. This is the standard solution to the Monty Hall problem and may come as a surprise to many people as the most common response, even with the assumption of an omniscient Monty, is that it doesn’t matter whether you switch or not.
Case 2 (Nice Monty)
This time we will still assume that Monty knows everything, but now he really wants you to win the car. So, he will only open a door to show you a goat if you have made the wrong initial choice. If you picked the car in the first place, he will simply open your door and congratulate you on your win. This means that
P(R | Car) = 0 and P(R | Goat) = 1 and so P(Car | R) = 0 and P(Goat | R) = 1. Once again you should switch. This time this conclusion should be obvious.
Case 3 (Nasty Monty)
Now Monty still has all the facts, but would prefer you to pick a goat. Perhaps Monty loves goats or perhaps the show is losing money and he doesn’t want to fork out for another car. Either way, these assumptions mean that
P(R | Car) = 1 and P(R | Goat) = 0 and so P(Car | R) = 1 and P(Goat | R) = 0. Now you should stick to your guns. Again, this conclusion should be obvious.
Case 4 (Lucky Monty)
Now we will stop assuming that Monty knows everything. When he opens the second door, he has no idea whether he’s going to spoil everything by revealing the car. If he does that, the show’s segment would, of course, end a little sooner than he had hoped. If you have picked the car, he will be fine, but if you picked a goat, he has a 50/50 chance of revealing the car instead of a goat. Translating all of this into mathematics gives:
P(R | Car) = 1 and P(R | Goat) = 1/2 and this time P(Car | R) = 1/2 and P(Goat | R) = 1/2. So, if Monty just happened to be lucky and show you a goat, it will not make any difference if you switch or not. Your odds will be the same either way.
Many other possible assumptions about what Monty does or does not know or do can also be cast in terms of P(R | Car) and P(R | Goat) and for each of these possibilities, it is therefore straightforward to decide whether to stick or switch.
In the debate over the Monty Hall problem, some have argued that Case 4 is a “better” interpretation of the puzzle than Case 1. While I won’t comment on that, I am sure that my attempt to evade the issue will not be enough to keep everybody happy with this solution. It seems that the Monty Hall controversy will not die.
Update: for anyone not convinced by the formula for the classical case, this spreadsheet may help.
High-frequency trading
In a recent episode, the ever-brilliant Planet Money podcast looked at the arcane world of high-frequency trading. The usual clarity of exposition was further enhanced by something of a Mule theme. It seems that Planet Money host Chana Joffe-Walt is, like me, a Tom Waits enthusiast and she found a way to fuse “Whats He Building in There?” from the Mule Variations album with the otherwise non-musical subject of the podcast. An inspired choice.
So, what is high-frequency trading? Here is how Planet Money describes it.
In high-frequency trading, people program computers to buy and sell stocks in quick succession under certain, pre-defined circumstances. The idea is to profit from fleeting changes in the price of a stock.
This type of trading is made possible by the increased use of electronic trading platforms for financial markets around the world and is a special case of so-called “algorithmic trading” (or “algos”). It has been estimated that as much as 75% of the trades on the New York stock exchange were generated by algos and perhaps 50% on some European markets.
High-frequency trading has been generating some controversy in recent years:
High-frequency traders often confound other investors by issuing and then canceling orders almost simultaneously. Loopholes in market rules give high-speed investors an early glance at how others are trading. And their computers can essentially bully slower investors into giving up profits — and then disappear before anyone even knows they were there.
Critics of high-frequency trading argue that it is a form of front-running, a practice which is illegal in most jurisdictions. The counter-argument in defence of the algos is that it increases the efficiency of the market. As Steve Rubinow of NYSE Euronext explains to Planet Money:
Every innovation of this type makes the market more efficient. … The faster we trade, and the more people you have trading, any aberrations that exist in the market are taken out of the market really really quickly, which makes for a fairer market for all participants … Those prices are about as fair as they could be.
Efficient markets are a good thing and I have used a similar argument here on the blog to defend short-selling. Nevertheless, there has always been something about high-frequency trading that makes me uneasy. In an interview with Edge, Emanuel Derman seems to put the finger on the source of this unease:
Also, people who benefit from it tend to over-accentuate the need for efficiency. Everybody who makes money out of something to do with trading tends to say, oh, we’re got to do this because it makes the market more efficient. But a lot of the people who provide this so-called liquidity and efficiency are not there when you really need it. It’s only liquidity when the world is running smoothly. When the world is running roughly, they can withdraw their liquidity. There is no terrible need to be allowed to trade large amounts in fractions of a second. It’s kind of a self-serving argument. Maybe a tax on trading to insert some friction isn’t a bad idea, just as long term capital gains are taxed lower than short term gains.
Derman started working as a “quant” in financial market around 25 years ago and had a long stint at Goldman Sachs. His response is not likely to be one of knee-jerk suspicion, but rather the considered voice of experience.
Joffe-Wolt’s reinterpretation of Waits conjured up an atmosphere of mystery and fear when exploring NYSE Euronext’s new data centre. Perhaps a bit of fear of high-frequency trading is healthy.
Image Source: Discogs