Tag Archives: Information

Can a tiny bit of noise destroy communication?

If everyone knows a tenth of the population dishonestly claims to observe alien spaceships, this can make it very hard for the honest alien-spaceship-observer to communicate fact that she has actually seen an alien spaceship.

In general, if the true state of the world is seen as not much more likely than you sending the corresponding false message somehow, it’s hard to communicate the true state.

You might think there needs to be quite a bit of noise relative to true claims, or for acting on true claims to be relatively unimportant, for the signal to get drowned out. Yet it seems to me that a relatively small amount of noise could overwhelm communication, via feedback.

Suppose you have a network of people communicating one-on-one with one another. There are two possible mutually exclusive states of the world – A and B – which individuals occasionally get some info about directly. They can tell each other about info they got directly, and also about info they heard from others. Suppose that everyone likes for they and others to believe the truth, but they also like to say that A is true (or to suggest that it is more likely). However making pro-A claims is a bit costly for some reason, so it’s not worthwhile if A is false. Then everyone is honest, and can trust what one another says.

Now suppose that the costs people experience from making claims about A vary among the population. In the lowest reaches of the distribution, it’s worth lying about A. So there is a small amount of noise from people falsely claiming A. Also suppose that nobody knows anyone else’s costs specifically, just the distribution that costs are drawn from.

Now when someone gives you a pro-A message, there’s a small chance that it’s false. This slightly reduces the benefits to you of passing on such pro-A messages, since the value from bringing others closer to the truth is diminished. Yet you still bear the same cost. If the costs of sending pro-A messages were near the threshold of being too high for you, you will now stop sending pro-A messages.

From the perspective of other people, this decreases the probability that a given message of A is truthful, because some of the honest A messages have been removed. This makes passing on messages of A even less valuable, so more people further down the spectrum of costs find it not worthwhile. And so on.

At the same time as the value of passing on A-claims declines due to their likely falsehood, it also declines due to others anticipating their falsehood and thus not listening to them. So even if you directly observe evidence of A in nature, the value of passing on such claims declines (though it is still higher than for passing on an indirect claim).

I haven’t properly modeled this, but I guess for lots of distributions of costs this soon reaches an equilibrium where everyone who still claims A honestly finds it worthwhile. But it seems that for some, eventually nobody ever claims A honestly (though sometimes they would have said A either way, and in fact A happened to be true).

In this model the source of noise was liars at the bottom of the distribution of costs. These should also change during the above process. As the value of passing on A-claims declines, the cost threshold below which it is worth lying about such claims lowers. This would offset the new liars at the top of the spectrum, so lead to equilibrium faster. If the threshold becomes lower than the entire population, lying ceases. If others knew that this had happened, they could trust A-claims again. This wouldn’t help them with dishonest B-claims, which could potentially be rife, depending on the model. However they should soon lose interest in sending false B-claims, so this would be fixed in time. However by that time it will be worth lying about A again. This is less complicated if the initial noise is exogenous.

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Information won’t set you free by itself

Information storage and communication increases our ability to discover and accumulate knowledge. And if Stephen Pinker is to be believed, humans have become more peaceful over time. However, the connection between better access to information and our softer world is dubious at best according to Adam Gopnik:

N.Y.U. professor Clay Shirky—the author of “Cognitive Surplus” and many articles and blog posts proclaiming the coming of the digital millennium—is the breeziest and seemingly most self-confident. … Shirky believes that we are on the crest of an ever-surging wave of democratized information: the Gutenberg printing press produced the Reformation, which produced the Scientific Revolution, which produced the Enlightenment, which produced the Internet, each move more liberating than the one before. Though it may take a little time, the new connective technology, by joining people together in new communities and in new ways, is bound to make for more freedom. It’s the Wired version of Whig history: ever better, onward and upward, progress unstopped. In John Brockman’s anthology “Is the Internet Changing the Way You Think?,” the evolutionary psychologist John Tooby shares the excitement—“We see all around us transformations in the making that will rival or exceed the printing revolution”—and makes the same extended parallel to Gutenberg: “Printing ignited the previously wasted intellectual potential of huge segments of the population. . . . Freedom of thought and speech—where they exist—were unforeseen offspring of the printing press.”

Shirky’s and Tooby’s version of Never-Betterism has its excitements, but the history it uses seems to have been taken from the back of a cereal box. The idea, for instance, that the printing press rapidly gave birth to a new order of information, democratic and bottom-up, is a cruel cartoon of the truth. If the printing press did propel the Reformation, one of the biggest ideas it propelled was Luther’s newly invented absolutist anti-Semitism. And what followed the Reformation wasn’t the Enlightenment, a new era of openness and freely disseminated knowledge. What followed the Reformation was, actually, the Counter-Reformation, which used the same means—i.e., printed books—to spread ideas about what jerks the reformers were, and unleashed a hundred years of religious warfare. In the seventeen-fifties, more than two centuries later, Voltaire was still writing in a book about the horrors of those other books that urged burning men alive in auto-da-fé. Buried in Tooby’s little parenthetical—“where they exist”—are millions of human bodies. If ideas of democracy and freedom emerged at the end of the printing-press era, it wasn’t by some technological logic but because of parallel inventions, like the ideas of limited government and religious tolerance, very hard won from history.

Of course, if you stretch out the time scale enough, and are sufficiently casual about causes, you can give the printing press credit for anything you like. But all the media of modern consciousness—from the printing press to radio and the movies—were used just as readily by authoritarian reactionaries, and then by modern totalitarians, to reduce liberty and enforce conformity as they ever were by libertarians to expand it. As Andrew Pettegree shows in his fine new study, “The Book in the Renaissance,” the mainstay of the printing revolution in seventeenth-century Europe was not dissident pamphlets but royal edicts, printed by the thousand: almost all the new media of that day were working, in essence, for kinglouis.gov.

Even later, full-fledged totalitarian societies didn’t burn books. They burned some books, while keeping the printing presses running off such quantities that by the mid-fifties Stalin was said to have more books in print than Agatha Christie. (Recall that in “1984” Winston’s girlfriend works for the Big Brother publishing house.) If you’re going to give the printed book, or any other machine-made thing, credit for all the good things that have happened, you have to hold it accountable for the bad stuff, too. The Internet may make for more freedom a hundred years from now, but there’s no historical law that says it has to.

Some more gems from this piece are below the fold.

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