Election Game Theory, Or Why You Probably Voted for the Sex Party

By now most of you will have voted. 

Because I am one of those infuriating people who treat election day as if it was boring man's equivalent of Christmas, I thought I’d go through one of the examples that came up in Game Theory last year, dealing with voting preferences. 

Consider the situation where you have two parties (Douches and Assholes), and an odd-number N voters (we’re not going to allow ties). Voters 1 to k strictly prefer the D to A, and voters k+1 to N strictly prefer A to D. 

Each voter has two possible options - they can either vote for D or A. 

We will take every other voter’s action as given. 

Each voter feels happy if their preferred party wins the election, and sad otherwise. 

We will examine one voter’s decision. For argument, say he prefers D over A.

There are three possible scenarios:

1. More than half of the other voters vote for D. 
Voting for D or A does not affect the result. D wins regardless of his action.

2. Less than half of the other voters vote for D. 
Voting for D or A does not affect the result. D loses regardless of his action.

3. Exactly half of the other voters vote for D. 
Voting for D or A does affect the result. The voter’s decision wins the election.

What does this actually mean? It means that the voter’s decision only decides the election in the case that votes are split equally between the other voters. Even though he strictly prefers D to A it would make no difference to the election if he voted A instead. In Game Theory, we would call the decision to vote A over D a weakly dominated strategy (it is no worse than voting for D in the situation that a clear majority is found without the voter, and strictly worse than voting D when the votes are split).

How does this relate to the current election? In many seats a clear majority exists before the day of the election (call this a safe seat - one which always votes a particular way). In these seats, the individual’s vote doesn’t actually hold that much weight. You’re just as well off voting for a major party, or something like the Sex Party. It’s in marginal seats where a swing can be expected that the election is truly decided. This is reason why the Greens often described as holding the balance of power in the Senate, and why this balance is so important. It’s all about being that  voter. 

The Little Boy

There once was a little boy, who when asked what he wanted to be in life, simply replied: ‘Happy.’

His teacher told him that he wasn’t likely to find happiness in a book, so he wandered into the streets to find someone who was happy.

He first came upon a couple of fisherman, who were telling stories as they cast out their lines. “They sure seem happy,” thought the little boy. So he bought a box of tackle, and cast a fishing line until the sun went down. But he didn’t catch a single thing, and couldn’t get the smell of bait from his fingers for hours.

The little boy then saw a pair of businessmen, who were laughing and smoking cigars as they carried their bulging wallets. “I’ll bet they are happy,” thought the little boy. So he shaved himself for an interview, and filled his wallet with stones until it bulged. However it soon weighed down his pants, and they fell off when he gave out his resume.

The little boy then saw some well-dressed socialites, going to a party. “They look so happy,” thought the little boy. So he bought himself a suit and a hat, and went out to a party. However the trousers didn’t fit well; they flapped around his ankles and tripped him at the entrance.

Then the little boy saw a drunk, singing to himself in the street. “Now there is a man who is happy,” thought the little boy. So he bought himself a bottle of whiskey, but just became sick, and passed out in the gutter.

Finally, the little boy saw a young couple, who were sharing an embrace in the sunset. "They must be happy!" thought the little boy. So he found himself a girlfriend, and immediately thought "Yes, I am happy." But the girl said "I'm unhappy," and promptly walked away.

Melanie

Nearby, a few children were playing a game. The sound of delighted shrieks pierced the air.

Melanie shivered.

Children disgusted her. In their eyes was contained a whole future: pain, suffering; the petty hatreds and jealousies of adolescence; the sex and revelry of their later teenage years and twenties; the prudishness of their thirties; the senility, sickness and despair of retirement. And somewhere in there would be the child’s own children, born after a condom breaks when they are nineteen, or in an elated pre-menopausal midlife crisis; the filthy cycle continuing like a plant that germinates, seeds, and bursts forth in fruit to wither. In their eyes was the future of every dick and sociopath, every pretentious child, every naïve romance and fantasy. And so it would continue, ad infinitum, until her own bones had long been shrivelled to dust.

One of the children fell, scraping her knee. She burst out crying. Her mother rushed over, making hushing noises, while the other kids looked on awkwardly. The game had been extinguished instantly. The cries rose up to shrieks, which burst forth incessantly.

Get used to it, kid. For most of your life you’ll be searching for happiness, and it will always be taken in an instant. That’s the basis of a life. We were born in agony, brought shrieking into the world; most of us haven’t left that state, but have merely become quieter.

Melanie stared down at her coffee. It had grown cold. The milk would have a fatty taste, and a residue of sugar would have settled on the bottom. She left it, and turned to get up. She felt horribly aware of the mass of consciousnesses around her: most of the patrons had turned, awkwardly, towards the screaming girl. The scene concentrated them, channelled it like a flow, and Melanie felt sickened as it washed over her, aware that she was part of the maelstrom.

The screams rose, breaking to a coughing sob, before repeating. What a set of lungs on the child!

Melanie smiled wryly: perhaps she would take up singing. Her parents would make her take piano lessons, and she would be allowed to buy a violin in primary school after much begging. She would play for the grandparents each Christmas, and they would remark how proud they were after each recital.  She would take it in her head to start drawing; after a birthday present of a camera, she would attempt to become a photographer. She would soon convince herself that she had talent, and take pride in it immensely. Her friends would praise her, but she would deflect it deftly - “Oh, I’m quite terrible, really” – and drink in each compliment in secret.  She would read, of course, and dream, and write a diary – considering her thoughts both beautiful and unique. She would read Capote and Plath with rapture, and feel that they had been speaking directly to her. And her parents would be so, so proud when she got accepted to an Art school on a scholarship.

Eventually she would wind up sitting in a café listening to some brat scream.

Melanie bit her lip in a moment of self-disgust. She hadn’t meant for her thoughts to lead that way. A trace of lipstick had been left on her coffee cup. It seemed to her like dried blood.

By the playground, the child was settling down. Her mother was murmuring to her cheerfully, and she was laughing again.

Melanie walked away, a bitter taste left on her lips. 

All Stations

Michael stood in front of the rail tracks, and jumped.

Mentally.

He flung himself out over the chasm that divided the station like a fissure; beyond the lines which demarcated safety, consistency – the certainty of not rushing headlong into a pair of headlights, of not having your legs sheared off by fifty tons of steel and screaming passengers.

He felt himself hit the metal of the track and sprawl out over the gravel; his legs hurt with the impact, and the breath was knocked out of him. His hands grazed, and he felt immediately dusty.

The metal was warm, and vibrated slightly under his fingertips. A woman screamed on the platform; there was the sound of panic and rushing feet.  Michael was aware of it only distantly, as if listening to a conversation underwater. A mother would no doubt be turning her kids away, and a man further on would have buried himself in his newspaper.

The sound of a horn cut everything out, like the apocryphal horn of Gabriel. The line vibrated violently, as if the horsemen of the apocalypse were upon the track, beating the steel with leaden hooves. The roar of the engines combined with the clack-clack sound of carriages on tracks; it’s preceded by a blast of air, drawn out from the tunnel with a leviathan’s fury. A guide-light glared red with uniocular malevolence.

The brakes crescendo to a wailing banshee shriek and Michael has a single momentary view of the driver, a face frozen in a mask of terror. It’s a sight that will forever lie suspended, inscribed upon the glass of an eye’s final glance. Michael’s voice joins in the scream, a mind cauterised of all but terror and regret.

* * *

There’s a brief rush of air, and the train passes harmlessly in front of his eyes. The driver toots the horn to announce its arrival, and a female voice intones over the intercom. “The train arriving on platform three is an airport train, running express all stations from Bowen Hills to Eagle Junction.” There is a hiss of air as passengers disembark. An attendant blows a whistle to that the station is clear, and the train resumes its motion. Michael feels as if he’s about to cry.

“Mum, why is that man standing there like that?”

“Shh, dear. It’s rude to stare. He’s probably just deciding which train to catch.”

Le Fils De L'Homme

There was once a little boy who loved to stick things up his nose. He would stick pens and pencils, seeds and rocks – anything which was small, and would easily fit. It was his favourite past-time, and he considered it a very dignified one at that age.

“Oh now, stop!” his mother cried, as he stuck a coin up his nose. “We don’t have the money to spare, and if you keep sticking things in your nose, something will grow up there.” The little boy was confused. If the dollar would grow, then surely his nose would be a safer investment than the stock market given the state of the current economy. So the little boy didn’t listen.

As he was walking to school, the little boy chanced upon his neighbour, an aborist. A small twig protruded from each nostril like the mighty tusks of a walrus. His neighbour gave an exasperated sigh.

“If you keep sticking things up your nose, it will grow up there!” The little boy gave a happy laugh. Tusk length is a sign of virility among walruses, and a tusk extension could only help his chances come mating season.

At school, the little boy sat at the back of the classroom with an eraser deep within one nostril. He ducked as an eraser came flying towards his head. His teacher burst out, furious: “If you keep sticking things up your nose, something will grow up there!”

Little Betty sighed in the second row: “I wish he would put my heart up his nose so it would grow there,” who at that age had no idea what a terribly unromantic thing that would be.

Walking back from school, the little boy came across a small seed in the middle of the road. He considered it appraisingly, turning it in his hands several times before depositing it in a nostril with artisanal care. Delighted at his newfound fortune, the little boy continued on his way home, making a nasal whistling noise with every breath that he took.

The next morning, the little boy woke to discover a small vine emanating from his nostril. It was slight and green, twisting around his nose like the beginnings of a fine moustache. The little boy was stunned. He was too young for facial hair, let alone any that was green. He curled it contemplatively for a moment before deciding against the rigors of maintenance that a new moustache requires. He yanked against the vine quickly, and smiled as it gave a satisfying ‘snap’.

At school, the little boy was considering which piece of stationary to grant admittance to Chez Nez for the evening, when Little Betty came up to him. “Your moustache is quite pretty,” she said, fluttering her eyelashes. “And green is definitely your colour.”

With a start, the little boy felt towards his nose. Sure enough, curling like the hair of a greased Parisian, was the vine. He dropped the pencil case in despair. The room for rent was occupied.

At the front of the room, the teacher was giving a lecture on parasites. He noticed the vine protruding from the little boy’s nose and smiled.

“Why, there are even plants in the Amazon which are known to grow from a seed high in the branches of a host tree. The parasite sends out little snake-like shoots which curl around the host, strangling the very life out of it. Its roots spread out as the tree rots inside; eventually there’s nothing left except for the hollowed out husk, and a new tree where it once stood.”

The little boy was rooted to the ground with horror, though only figuratively.

Running home from school, the little boy came upon his neighbour again. The vine had begun sprouting leaves, and curved upward like a set of antlers. “You’ve got to help me!” he cried.

His neighbour peered at the branch with a professional interest. “You’ll need to watch closely to make sure it doesn’t get scale or root rot. You see the smallest sign, come straight to me.”

“You’ve got to help me get rid of it!” the little boy cried.

“Why? You’ll make a good tree for my garden!”

The little boy ran home screaming and saw his mother. Wordlessly, he pointed to the developing bush on his forehead. His mother considered it carefully. She had once studied horticulture at university, and was delighted at the chance to show off her skills. “I could trim it if you’d like,” she suggested. “If we get in early, we can shape it into something interesting, like a bunny rabbit or a swan.” Her major had been in hedge manufacture and design.

The little boy burst out crying. He didn’t want to become a rabbit or a swan, let alone one made entirely out of leaves. His tears trickled down his face, where a developing root system drank them greedily.

Resigned to his arboreal fate, the little boy made his way to bed. His mother put out a pot, in case he needed to take root in the night, and couldn’t make it to the garden in time.

In the morning, little boy’s vine had developed into a miniature tree, which sat above his head like a leafy green bowler hat. It would have been unsightly on St Patrick’s Day, and it wasn’t more fashionable now in September. The little boy felt like a bonsai.

At school the teacher was delighted at his transformation. “I had always hoped that you’d branch out into other areas,” he said, and he said it often, as he was proud of the pun.

Little Betty noticed him sitting by himself in the playground. She could see he had wood.

“What are you doing all alone here?” she said. “I think a little foliage adds character to a man. And look – there are even a couple of flowers.” Indeed, the little boy’s tree had burst into bloom with tiny pink and white flowers. “She reached up to pick one, before pulling her hand back with a shout: “Bees!”

Little Betty ran away without a second look.

The little boy’s teacher placed a comforting hand on his back. “Maybe you should just leaf for the day.”

The little boy walked home with a wooden expression on his face. If he was going to become a tree, then so be it. He would just root himself in the soil, and that would be the end of it. A squirrel chattered happily in the branches. The little boy sat down next to a large oak tree in the cemetery and waited.

The little boy sat there patiently, like a botanical Buddha  The wind whistled through his leaves. The squirrel chattered noisily and tried to stick an acorn in his ear. He had been doing his best to think tree-y thoughts, but it was nuts. He jumped up and shook his head violently. The squirrel leapt off in alarm and rushed towards his dislodged acorn. The little boy sat back down, and yelped as something fell into his lap. It was hard, and round, and shiny. The little boy reached up, and sure enough, the tree was filled with apples.

The little boy ran home delightedly. On the way, he ran past Little Betty, who was cradling her stung hand. Without stopping he threw her an apple. Little Betty bit into it carefully, and smiled – he had just become the apple of her eye again.

From that day on, the little boy was renowned for his apples, which were both juicy and sweet, and could be baked into the most delicious of pies. He eventually became quite wealthy with a cider he produced from the fruit, until the FDA caught wind of it, and he was shut down for numerous health code violations.

The Young Duck

Once there was a little town of ducks, called Splashville.

It was a little town in the countryside, filled with lots of ponds. It had a park, and the roads were made of cobblestone, which were hard and apt to hurt a young duck’s feet if she wasn’t careful.

‘Mummy, mummy,’ a young duck cried, as she tripped over a particularly hard cobblestone. ‘Can’t there be a better way to walk across town? The cobble stones are painful, and my feet are always bruised and battered.’

But the mother knew there wasn’t anything to be done, and so life continued as it always had: safe and happy, as long as you knew where to place your feet.

However the young duck was a clumsy one, and it seemed that no matter how hard she looked, or how carefully she stepped out on the stones there would always be a cobble there to find its way under her foot. 

And so, she spent most of her time swimming around in the pond, where there weren’t any nasty cobblestones, and where there was hardly any chance of running into them.

But her friends would all play featherball in the afternoon (which is a played lot like soccer with feathers, and is a duck’s favourite sport). It was played on the cobblestones, and so the young duck could only watch from the sidelines, or risk bumping or scratching or bruising her toes, which always made her sore in the evenings. She was very lonely, and wished that she could play like the other ducks.

One day, while swimming around in the pond (the other ducks had waddled off to play featherball some time ago), she came across a piece of rubber which had floated downstream, along with a piece of ribbon which lay beside it. The young duck was curious, and nuzzled the two inquisitively. The rubber was thick, but soft, and gave away under her touch. The ribbon was a bright red, and had no doubt adorned the hat of some sonsy lass. At last the duck gave a happy ‘quack’. She’d had an idea.

All through the night the young duck worked on her project: pulling and prodding, fashioning and fastening, until finally it began to take shape. Her mother hovered behind her, worried and curious, but the young duck continued her work unheeded, her crest puffed up in concentration.

In the morning a curious sight came into Splashville, and a crowd gathered all along Feather Way. What was in the middle of the crowd? Was it a horrific traffic accident? A fowl crime that would ruffle the feathers of all who saw it, and leave no duck unflappable? No. It was the young duck proudly waddling down the cobbled way. On her feet were two wellies fashioned from the rubber she had found. A piece of leftover ribbon had been tied around her neck and caught the wind and sun as she walked.

The young duck quacked happily as she waddled, giving no notice of the cobbles as she passed, much as you or I would give no notice of a pebble under our boots. The little duck was happy, and went on to have a semi-professional career in featherball, until she was indicted for her part in a match-fixing scandal which saw her banned professionally for life.

Picture credit: Stephen G. Johnson

The Problem of Externalities

Happy New Year! Or Happy Financial New Year at the very least.

It’s been a month since I’ve last written a blog, and while I’d like to say that I’ve been fighting Samoan pirates on the high seas, or staging a daring coup d’état that now sees me placed as the new King of Sweden, the fact of the matter is that I’ve been busy with final assignments and exams. That and I haven’t had a clue of what to write about.

I’ve been on holiday for the last week now, and my stubble has gone beyond the level of ‘acceptably shaggy’ and is well on the way to ‘unemployably scrubby’. I’m letting it go if only to see what grows, like an experimental Petri dish more likely to result in anthrax than penicillin.

As many of you should know, today also marks the introduction of the Gillard government’s new Carbon Tax, which is set to put a price on carbon emissions and give Tony Abbott supporters plenty of chances to wave their fingers and say: “See! See! She lied!” as if it were the first time they had ever watched a political campaign. It also marks the start of a set of offsetting reforms, which include the tax-free bracket increasing from $6,000 to $18,200. I’m a strong supporter of the Carbon Tax, so while I’m as unqualified as an elk to even discuss it, and at the risk of bush-lawyering, I thought I’d write a few words on the basic theory that underpins these kinds of actions.

Left entirely to its own devices the private sector is remarkably efficient in the allocation of resources. Inefficient practices have the effect of increasing a firm’s overall production costs. Over time, this provides an incentive to move to more efficient production methods, increasing overall profit.

 Similarly a free and competitive market provides an efficient allocation of resources as firms bid up the price of goods depending on their individual assessment of their value (two people value a piece of cake, they will continue to bid up the price until it’s just higher than what the other would otherwise be willing to pay). Where individuals can trade according to their individual preferences, the market will theoretically result in an efficient allocation.

The issue comes in when we’re dealing with a common resource (air quality, the environment, fishing stocks, etc). In this situation, individuals are not able to trade according to their own individual costs and benefits, and the resulting market allocation may not be socially efficient.

For example: a washing company may be remarkably effective in washing old socks and underwear in a nearby river, but has the unfortunate effect of poisoning it for everyone down-stream. This is known as an externality – a cost not included in the normal price allocation of supply and demand.

Externalities can be either positive or negative. A beekeeper provides a positive externality in the pollination of local fruits and flowers (and a negative in the increase of beestings). Positive externalities are benefits that can’t be captured by the profit system, and so too little will be produced. Negative externalities are costs that aren’t incurred by the producing firm and so too much will. In either case a market failure occurs, and there is potential scope for the government to intervene. Carbon emissions are a classic example of a negative externality.

The Carbon Tax introduces a base cost to the production of carbon. While the extent that this cost is passed onto consumers largely depends on the degree of market control a firm is able to exert, the effect is an overall reduction in carbon pollution. Over time it provides an economic incentive to innovate and switch to less carbon intensive forms of production.

It must be noted that the current fixed price is only a temporary measure. Eventually an Emissions Trading Scheme is to be implemented, where a number of free credits for the production of carbon are allocated, and the free market determines the price of these credits in the free market. This is generally seen as a more economically efficient model for reducing carbon emissions.

The potential effectiveness of the tax is a divisive issue. The effects of carbon emissions are distributed globally, as opposed to locally or nationally such as in acid rain (a similar example of a national ETS implemented in America) or chemical pollutants, and has led some commentators to declare it a Tragedy of the Commons rather than a matter of externalities.  However I remain personally optimistic in the overall effectiveness of the scheme, and that it will coincide with similar measures being enacted internationally.