Electoral reform, epilogue

After my last post people kept sending in more things, and I keep discovering more from following the leads they give me. The topic also has a deep academic history, which I should have guessed. I thought I'd wrap up here with a quick summary before moving on.

A friend Matt pointed me at a 2005 New York Times article entitled "Why Vote?". It's fascinating and worth a read, but the bit about "your chances of winning a lottery and of affecting an election are pretty similar" is demonstrably false, as shown in the last post: fact is that you're trillions upon trillions of times more likely to win the lottery than to affect an election.

As mentioned (and misattributed) in the article, Anthony Downs, the pre-eminent economist and political scientist, in his 1957 work "An Economic Theory of Democracy", concluded that "a rational individual should abstain from voting". This, "Downs's Paradox" can be stated as

In voting, compute the benefits (B) of having one's candidate win and weight them by the infinitesimal probability (P) that one's vote will be decisive. Then, since voting is costly (takes time, mainly), calculate the overall reward (R), proportional to the probability of actually turning out, as R = P×B - C. Because P is so small, this will be negative for almost any positive C. Thus, no rational individual should vote.

And yet supposedly rational people do in fact vote—hence the paradox.

Some attempts to resolve this issue have introduced a new term, D, to the equation, representing the reward one gets from expressing oneself, participating generally in the democratic process, or fulfilling an endogenous sense of civic duty. Then the reward and probability of turning out becomes R = P×B - C + D which may be positive even for minuscule P, explaining the empirically observed turnout.

This leads us to the research on the Swiss system which is referenced by the Times article. In that paper Patricia Funk postulates another factor contributing to the term D: that of exogenous social pressure to vote. From the paper,

The key innovation of this paper is to use a natural experiment, which allows me to shed light on this particular motivator to vote: the introduction of optional mail voting in Switzerland.

The intuition behind this experiment lies in the opposite effects, postal voting (or other modern voting tools such as internet voting) have on economic and social incentives to vote. Concerning the first, the obvious effect is a reduction in voting costs, with a positive effect on turnout. Secondly, mail-in or internet voting renders the voting act unobservable. If social pressure matters for voting decisions, the presence of mail-in ballots provides an opportunity to escape. Therefore, the more social concerns matter for voting decisions, the more distinctive the mail ballot system’s trade-off between cost reduction and a reduction in social incentives.

While previous voting models cannot easily account for a negative turnout effect of mail-in or internet voting alternatives, a positive turnout effect is consistent with both traditional voting models and with those that include a concern for social motives. The sharpest test for social pressure arises from looking at the effect of postal voting in different-sized communities. A large number of anthropological studies have documented that social control is particularly strong in small and close-knit communities. People know each other and gossip about who does their civic duty and who does not. Therefore, the relief from social pressure is supposedly the highest in small communities and ceteris paribus, also this negative "social effect" on turnout.

What the study found was that the reduction in voting cost afforded by the opportunity to vote by post didn't result in any statistically significant increase in turnout. In fact,

Turnout declined up to 7 percentage points in the [administrative division] with the highest share (i.e. 36%) of citizens living in small communities. A replication of the same procedure with community-level data confirms that the turnout decrease was particularly a “small-community”-phenomenon.

That is to say, once the Swiss were no longer obligated by the social pressure in close-knit communities to show their faces at the polling places, they didn't.

Smart.

One final note from my friend Andrew, who pointed me at the Asimov short story "Franchise" in which

the computer Multivac selects a single person to answer a number of questions. Multivac will then use the answers and other data to determine what the results of an election would be, avoiding the need for an actual election to be held.

I couldn't find an ebook so I ordered the paperback. Sounds like a good read.

Update 9.37pm December 30th: I couldn't leave it alone. Two final points, and then changing topic:

1. Read Hannah's comment on the original post. It brings in Toqueville, about whom I now feel I should be more educated and you might too.
2. I also wanted to add a super thought experiment which Robin threw in: what if government representatives themselves were simply chosen at random from the electorate? "It's super-duper jury service. Which, as an analogy, I realize, does not exactly fill a person with optimism," he writes but of course you've got to think past the implementation difficulties. Personally I'm pretty sure it'd be utter chaos in the short term but in the long term I figure the infrastructure surrounding these hapless "politicians" would adapt to the new regime. Probably they'd make it like the last.

Electoral reform, redux

I had a great set of responses to my recent post about electoral reform. I got emails, Tweets, blog comments, and comments on Google+. Many interesting thoughts and articles, which I thought I'd respond to in this follow-up.

Some folks argued with the decision not to vote. How could that be a good idea? What if everybody did that? This one's easy. Firstly, that'd be great. Secondly, it's irrelevant. Consider: I might do my bit about overpopulation by deciding not to have kids. Sure, if everybody did that then the consequences would be catastrophic but that doesn't disqualify it from being a rational individual choice. Indeed, many people do make that choice with net positive effect.

Nick provided an interesting post on the "fallacy of the deciding vote". It's a well reasoned piece, but premise (2) renders it inapplicable: the argument at hand isn't whether my individual vote unilaterally decides the result (which obviously it doesn't, as the article points out, in all but the most degenerate cases). It's about the probability that adding or subtracting my individual vote has an effect on the outcome. I don't need my vote to be the single deciding vote by any means.

So that we're clear, before we move on let's call a given individual voter democratically impotent in an election if the election has an identical outcome with or without their vote. Conversely the voter is democratically potent if removing their vote changes the outcome.

Dominic commented on the post presenting a syllogism:

Premise: Your vote is the same as everyone else's
Premise: Your vote literally counts for nothing
Conclusion: Everybody's vote counts for nothing

...and yet, we have a result. I suggest that premise 2 is faulty

and he's right. My hyperbolic "I literally count for nothing" should really have been "in the span of my lifetime, with overwhelming probability, I'm democratically impotent in every election in which I'm eligible to vote". There's a mathematical distinction but barely a practical one.

Interestingly, as you remove more and more voters from the electorate the chances of a voter which remains being democratically potent increase significantly. Thomas Pogge, Yale's Professor of Philosophy and International Affairs, showed in a post last year that in a small population of 63 voters, with each voter choosing independently and with equal probability between two electoral candidates, a given voter has a full 10% chance of casting a deciding vote.

I like those odds, but in large populations things look much bleaker.

In the simple equiprobabilistic model which Pogge presents, in an electorate of 100,001 people the probability of a given voter casting a deciding vote is about 1 in 400. Not bad at all! Assume instead, though, a slight general preference in the populace for one candidate over the other, let's say 49% to 51%, and suddenly your 1 in 400 chance of affecting the outcome in Pogge's model sinks to 1 in 193 billion.

Scale up from there to a population of just a million, and you as an individual voter are democratically impotent with a novemvigintillion to 1 probability¹. If you voted in an election of this kind every second for as long as you lived (or even, hey, every nanosecond for the entire lifetime of the universe), chances are—by an inconceivable margin—that you'd not affect the outcome of even a single one.

Little wonder, then, that cynicism about democracy comes so easy. Richard passed along a link to a passionate soi-disant rant including:

I am being sadly sincere when I describe [democracy] as a system which is much better at giving the feeling of participation than actual participation. To me, this is one of the terrible things about democracy (and part of why it is so successful) - because voting lets people feel like they can influence things. Even if they don't vote, they feel like they could have voted.

But any one vote never matters...

…as indeed is demonstrated above.

So we come back to that idea again of selecting the election winner by picking a single ballot at random and going with that. Now one's chances of democratic potency in an electorate of a million people voting between two candidates with a 49%/51% baseline preference is simply a million to one. Still sounds like long odds but it's a trillion trillion trillion trillion trillion trillion trillion times better than before. In this system people are thus vastly more individually empowered, the tyranny of the majority is ameliorated, and the end result remains proportionally representative, albeit with added statistical noise. It's a win-win-win!

At the end of the day, though, as James noted, whoever wins an election it's always a politician. A solution to that problem is left as an exercise for the reader.

Next in this series: Electoral reform, epilogue

¹ a novemvigintillion is a billion billion billion billion billion billion billion billion billion billion; about ten billion times the number of atoms in the universe.

Christmas 2011

A brief interlude to isaach.com regular programming: I thought I'd blog a few pictures from a Christmas Day in San Francisco. I already put a bunch from earlier in the season on Flickr, as well as a set from Christmas Eve, but here are some from December 25 itself.

Probably for the last Christmas in a while, we got up late in the morning: Lux slept an incredible 15 hours and didn't wake up until 10.30am. By that time I'd already had a lie-in and a good chat with my mom at home in the UK—both generous presents themselves, and altogether a lovely start to the day. When Lux did wake we had a family breakfast

and opened some presents.

It was a beautiful day, clear and bright and dry, so we headed up Bernal Hill for a walk. I feel very lucky to live in this climate, on this hill, in this place

with my favorite people

and

Seriously. The most precious companions (and one more family member on the way) as well as this view ten minutes' walk from your house on Christmas Day?

Truly I'm blessed.

Electoral reform

I don't vote. I've never voted. It's a long story.

If, though, at the end of my life you count the number of elections in which I was eligible to vote, whose ultimate outcome was decided by a single vote, and therefore could have been affected by mine, I bet you count zero. Add my vote, take my vote, no change in the result in any election. I literally count for nothing.

My vote would count for more in the following system I first saw described nearly ten years ago:

Instead of counting the ballot papers, and declaring the winner to be whoever got most votes, the ballot papers would be put into a tombola, thoroughly mixed and one ballot paper taken out. The winner would be whoever was voted for on that ballot paper.

To encourage a high turnout, only the winning candidate would retain his deposit. The remaining deposits would be given, as a prize, to whomever cast the vote which was taken out of the tombola.

In this arrangement I'm actually more likely as an individual to have my own vote affect the outcome than in the current system. It doesn't seem any less democratic: as the original post says it's just a statistically noisy form of proportional representation.

I note the following advantages over the "first past the post" system:

• sidesteps the tyranny of the majority;
• offers a chance to break out of the vicious cycle which leads to a two-party system;
• gives me, an individual voter, a non-zero chance of my vote affecting the final outcome;
• offers positive incentives for turnout; and
• has an exciting entertainment aspect.

The future of politics is right here! What's not to love?

Now read Electoral reform, redux, for more on the math and philosophy of this proposal—and why not to vote in the current system.

Lasting value

As I said, my dad's a teacher. And a few days ago @pichipsandgravy tweeted at me.

@isaach sorry to bother u Isaac, by chance was your farther a teacher called dave had a yellow 2cv car?

— Pie chips and gravey (@pichipsandgravy) December 14, 2011

Now it turns out that yes, when I was growing up my dad taught kids in elementary and middle schools in the north of England. And to my utter shame at the time the family car was indeed a yellow Citroën 2CV.¹

So I wrote

@pichipsandgravy yes! that was a while ago, mind. do you know him?

— Isaac Hepworth (@isaach) December 14, 2011

and then over the course of a few more Tweets (from me in San Francisco to @pichipsandgravy on an oil rig in the North Sea) established that yes, my dad was his teacher at school about 30 years ago. He'd learned guitar from my dad, and still plays. He remembered my father being a particularly special teacher; was hoping to get back in touch to say thanks.

My wife Wendy is a teacher too, and (on a smaller timescale) gets the same thing: kids of classes past making touching personal gestures of appreciation; being a part of the neighborhood's social history; local families recognizing her on the street and excited to see her.

It makes you think! I wrote my dad "I can guarantee you that nobody's going to be writing to me in 30 years being appreciative of my work and how it's affected their life!" and I believe it.

¹ which was desperately uncool until the same color and model featured in the Bond film For Your Eyes Only in 1981.

On conformity

My dad's a teacher. In his study when I was growing up he had a poem on a sheet of paper. I've always loved it.

He always wanted to explain things
But no-one cared
So he drew
Sometimes he would draw and it wasn't anything
He wanted to carve it in stone
Or write it in the sky
He would lie out on the grass
And look up at the sky
And it would be only the sky and him that needed saying
And it was after that
He drew the picture
It was a beautiful picture
He kept it under his pillow
And would let no one see it
And he would look at it every night
And think about it
And when it was dark
And his eyes were closed
He could still see it
And it was all of him
And he loved it
When he started school he brought it with him
Not to show anyone but just to have it with him
Like a friend
It was funny about school
He sat in a square brown desk
Like all the other square brown desks
And he thought it should be red
And his room was a square brown room
Like all the other rooms
And it was tight and close
And stiff
He hated to hold the pencil and chalk
With his arms stiff and his feet flat on the floor
Stiff
With the teacher watching
And watching
The teacher came and smiled at him
She told him to wear a tie
Like all the other boys
He said he didn't like them
And she said it didn't matter
After that they drew
And he drew all yellow
And it was the way he felt about morning
And it was beautiful
The teacher came and smiled at him
"What's this?" she said
"Why don't you draw something like Ken's drawing?"
"Isn't that beautiful?"
After that his mother bought him a tie
And he always drew airplanes and rocket ships
Like everyone else
And he threw the old picture away
And when he lay out alone and looked out at the sky
It was big and blue and all of everything
But he wasn't anymore
He was square inside and brown
And his hands were stiff
And he was like everyone else
And the things inside him that needed saying
Didn't need it anymore
It had stopped pushing
It was crushed
Stiff
Like everything else.

It's beautiful, tragic and moving, but what really takes your breath away is the coda: the author, a high school senior, committed suicide two weeks after submitting it as an English assignment.

Sadly, the actual story behind the work is unclear and likely lost to history. Still, it gives you pause.

The Littlest Twitter Term Counter

A basic need of many folks I work with is to count hashtags or terms on Twitter in real time.

The below isn't a complete solution by any means but it does the job in the simplest sunny-day case. If you, or your technical team, are looking for the most basic starting point then this is it:

curl -d 'track=TERM' -uUSERNAME:PASSWORD -s -o - \
https://stream.twitter.com/1/statuses/filter.json \
| perl -e '$|++; while (<>) {m/\{/ and $i++ and print qq{\r$i}}'

Fill in the values in CAPS (use your Twitter credentials) and you're all set.