Voting and uncertainty

Turning and turning in the widening gyre
The falcon cannot hear the falconer;
Things fall apart; the centre cannot hold;
Mere anarchy is loosed upon the world,
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity.

 From The Second Coming, William Butler Yeats

“The best lack all conviction, while the worst are full of passionate intensity.” Oh how I relate to those two lines, particularly in this election cycle.  Hate mongers fill cyberspace with passionate intensity. Yes, the “good guys” express their share of passion, too, but often I find that the most thoughtful, nuanced commentaries on current events are… thoughtful, not passionate.

In my work I sometimes think of myself as a professional skeptic. We conduct large scale experiments on educational interventions, and roughly 90% of the time I end up being the bearer of bad news to passionate advocates – their particular policy/cause/gizmo was just not as effective as they’d hoped. People are complicated; social change is hard work, with few turnkey solutions (even when we’ve managed to define the “problem” adequately).

Politically, I’m generally left-leaning. Without parsing that too finely, I advocate for personal liberty (control over one’s reproduction, sexuality, freedom of expression and association, etc.), as well as a vision of government as steward and protector of the commons, particularly against those organizations/corporations/tribes who would impose their will on others.  Some issues for me are no-brainers. As often as not, however, people with similar ends in mind can argue over means. What should one do, for example, about housing stock in San Francisco? Do we even agree that preserving an economically diverse city is worth attempting in the first place?

Around this time of year I often read commentary to the effect of “why bother voting, we’re just choosing the lesser of two evils, if voting could change anything it would be illegal, etc.” While I sympathize with the spirit of these nay-sayers, I’ve come down firmly on the side of voting, even if what we’re doing is little more than a coin flip. I could cite a number of civic-minded reasons why voting is important (not the least of which is that it sends a message to politicians that people are paying attention), but I want to focus on decision making under uncertainty.

For those of us “lacking all conviction” (or who can see both sides of an issue), it’s tempting to withhold our vote until we have a strong, defensible argument for picking among A, B, C or D. What if I choose badly? What if the policy/politician I’m endorsing has unintended consequences I can’t foresee? Here’s my question – do you think it is more likely than not that your choice will further your political agenda in a desired direction? Not with a strong degree of certainty, just simply better than 50/50.  If you believe even slightly better than 50/50 that your choice will have a positive impact, you should vote.

I work with numbers and statistics so frequently that I sometimes forget to go back to basics and understand where my intuitions come from. I’ve been thinking about voting as a very error-prone process, but one in which the law of large numbers (or the Wisdom of the Crowd, to use a popular term) can tip the balance decisively.

Here’s a thought experiment. Say we have 1,000,000 voters choosing between two candidates. These million voters lack all conviction, but there is a very slight preference for the policy of candidate A over candidate B. Let’s say that out of 1,000 voters, 501 – just slightly more than 50/50 – favor candidate A. If you run the numbers, in the end we expect 50.1% – or 501,000 voters – to vote for A over B, and A wins.  Now of course, randomness means that we would never have exactly 501,000 to 499,000 in an election, but how “wobbly” would those numbers be?  After all, candidate A wins by a mere 2,000 votes in a population of one million. Here’s the magic: If I wave my statistical wand, I can tell you that in over 97% of elections of this type, candidate A would win¹.

Let’s think about this. One interpretation is that if half the population was just a smidgeon more convinced that candidate A was preferable, candidate A would win almost every time. Another interpretation is that it only takes one in 1,000 committed voters in a sea of uncertainty to swing an election. I invite you to contribute your own interpretation (and critique) in the comments.

Obviously the real world is not as simple as this mathematical model – we have passionate factions on multiple sides of an election, the perceived costs/benefits of a good choice can vary, etc. But, having worked through the numbers, I’m struck at how little it takes to reliably tip the balance of an election in a particular direction.

Sometimes – often – the majority is wrong; our history is one of prolonged oppression of minority groups, until either a court intervenes or public opinion dramatically shifts. Still, all else being equal, I would prefer to have thoughtful citizens weighing in on an issue – even under extreme uncertainty – than any of the alternatives.

¹ Technical footnote: The standard error of the sum of 1,000,000 coin tosses with a 50/50 probability is sqrt(1,000,000*.5*.5) = 500. A final result of 501,000 votes is two standard errors above a tie. Using a Normal approximation, we find that a bell curve centered at 501,000 with standard deviation of 500 has 97.5% of its area above the 500,000 (50/50) mark. That is, 97.5% of elections under this scenario should come out in favor of candidate A.


One thought on “Voting and uncertainty

  1. Pingback: Voting, take 2 | The Learning Curve

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