Month: January 2017

The Samuelson Bet

A version of the Samuelson Bet, named after the economist Paul Samuelson is as follows:

A single coin flip, heads you win $1000, tail you lose $500. Do you take the bet?

Most can see that in this bet, you are expected to win more than you lose. The expected value, matter of fact, is +$250. In other words, you are expected to become $250 richer each time you play this flip. However, with a potential $500 loss looming over your shoulder, other than those with deep pockets or a taste for gambling, most would shy away from making this bet.

Now imagine

Same bet as above, but we flip 1000 times. Each time you either win $1000 or lose $500. Would you now take the bet?

I cannot imagine anybody that would turn down that bet. But what changed?

What changed was not that you’re any less likely to lose each hand. The odds remains at 50/50 per hand.

What changed was as the number of attempts was increased significantly, the odds of you making money increases dramatically. Intuitively, the bet is a good deal, because the odds of winning and losing are even, and you’d win twice as much than you’d lose. Yet in one single play, some of us wouldn’t take that bet, because the odds of losing a significant amount of money ($500) is still 50%. When we expand the number of plays, however, it seems like the bet is looking more and more attractive as the effects of variance is greatly reduced. In a single flip, the result can go either way, but in 1000 flips under a normal Gaussian distribution, the standard deviation (sigma) becomes 15.81. So in 1000 flips, one can predict with an accuracy of ~69% that the coin will land somewhere around 500 heads and 500 tails ±16 (484H/516T ~516H/484T.) We can increase our prediction to ~95% by going 2 standard deviations away, meaning there is about a 95% chance that 1000 coin flips would land between 468H/532T ~532H/468T. This lead to the interest discovery that in order to NOT win money in the 1000 coin toss version, we would have to flip twice as many tails as heads (333H/667T). That is an event more than 10 standard deviations away, also called a 10 sigma event (1 in 1.5265*10^23). This means the odds of losing money is basically 0. By comparison, in a 10 flip trial, the odds of losing money becomes only 2 sigmas (1.58) away, which gives us around a 5% of losing money.

Danny Kahneman, a psychologist and Nobel economist, has an interesting take on the Samuelson bet in his book Thinking, Fast and Slow. He suggests that many of the risks in life should  be framed as a series of much less obvious Samuelson Bets, each with a much lower but still positive expected value (Something like heads you win $100, tails you lose $95.) Rather than narrowing viewing each opportunity as a singularity and obsessing over the potential losses in each case, we can take a broader frame of the situation. Just like in the Samuelson bet, although each individual bet will seems risky, the aggregate outcome of taking many smart and calculated risks in life will result in a net positive. It’s a wonderful message that I think all of us can take some time to ponder over.

 

Aside

There is a lot of talks about fake news these days. In my opinion there are two ways to defend against this problem.

1. Top-down centralized government agency monitoring and auditing of all news media. Which inevitably grants the government power to reduce and eliminate freedom of press. Because if government has no power to stop fake news, what is the point of the monitoring and auditing? Another way for the government to combat fake news without the coercive power to limit the spread is to create is own news agency and or endorse a current news media with a version of a “GOVERNMENT APPROVED” stamp. However, such methods are far less effective than direct fact-checking & elimination of fake news. In such event, news media will perpetually seek ways to obtain and keep the government stamp, possibly through lobbying and special interest donations, which destroys any objectivity in such a measure. Ultimately, government interventions will attempt either to eliminate news media of poor repute, or bolster the media of good reputation. The power to make a decision on what news sources is deemed fake or real, will lie directly in the hands of a centralized agency (probably directed by the “expertise” of some Pulitzer-winning journalist or Nobel economist.) Fake news writers will continue to attempt to outsmart the government agency, and the government will continue to crack down on the spread of virulent disinformation. Aside from the potential issue of corruption of absolute power, we will see even a benevolent government with a well-intentioned goal of filtering fake news for the public will face major problems.
2. Bottom-up decentralized development of a healthy dose of skepticism of ALL news media (Including, and arguably ESPECIALLY WaPo, NYT, CNN, FOX, NPR etc.) This is a form of development of from what economist Friedrich Hayek calls “spontaneous order.”  It wouldn’t require any centralized action by any governmental agency or any large entity for that matter. It would rather depend on the spontaneous generation and usage of localized knowledge from individuals. In our case, the cynics & stoics will be the first to develop skepticism against much of what they deem news media of ill-repute, while the more ideological would take a little more time to do so. However, as fake news start to permeate our society, people will be adversely affected by it. This is the first order effect of fake news. As more and more people becomes aware and affected by such fake news, more and more will learn from their own mistakes. Learning from mistakes is a second-order effect (effect of an effect). People will need to be allowed to make such mistakes, because the effects of such mistakes and subsequent learning takes form on an individual to small group scale. Small-scale changes are robust because none of the individual action and reactions amounts to any large impact on society. Individuals has liberty to make mistakes and misinterpret the outcome of those mistakes because the cost of such mistakes of any order is tiny. As much as the ardent photoshoppers and fiction writers tries to make their fake news stories go viral, it cannot spread unchecked for an long periods. It is generally quickly discredited by an equally ardent group of individual fact checkers.The reason that the whole country is debating about fake news merely months after its supposed effect on the election(whether or not it even had an effect is debatable) is from the quick recognition of the negative impact fake news has had on our society. So it is to be expected that as awareness of fake news develop, so will individual suspicion of news media. Eventually, most will generate some level of skepticism of news medias they deem to be from “untrustworthy sources,” At this point, the most popular fake news article determined to be untrustworthy by the public of will lose much of its effectiveness, because only the most popular fake news matter. Unpopular fake news is un-ingested poison. Harmless. In response to the skeptics, a cat-and-mouse game will develop between the fake news writers and fact checkers, as they attempt to one-up each other, while the public will continuously to make their own decisions on what to believe and find their own comfort level in the spectrum between the stone-faced cynics and the happy-go-lucky naives.
In both situations, we will be left with the cat-and-mouse game between fake news and fact checkers. The difference is each situation’s robustness to mistakes. We will ignore the very real possibility of government agency intentionally misinforming the public to their own benefit, but rather only examine what happens when the inevitable mistake is made by the government fact checker. As mentioned above, individual mistakes of any order matters very little. But when a government fact checker makes an error, either in allowing a fake news article to pass through its scrutiny, or wrongfully discrediting a true article, its centralized nature allows the mistake to disseminate rapidly on a huge scale. It will no longer be simply an article of fake news that spreads to your Aunt Marie through Facebook, but rather an article of fake news with a big, bold, and mistaken “GOVERNMENT APPROVED” stamp on it. If the government instead operates by directly blocking news article they disprove of, then by definition, all news articles published will have the proverbial stamp on it. The point is in a situation where a news article is assumed to be pre-checked or audited by the government, a lot more people will deem it trustworthy for no other reason than a simple trust to a higher authority. Such is the problem of any large centralized system, they are essentially not only too-big-to-fail, but too-big-to-make-a-mistake. Any errors in this process is going to spread the disinformation to more people much faster. The initial suppression of fake news is the first order effect, and the subsequent disproportional effect caused by a mistake is a second order effect. It’s like the Yellowstone forest fire in 1988 and the fire-suppression efforts that preceded it. Once you create a system sterile of fake news, people’s skeptical guard will be let down, and when the government shield inevitably fails, the effects will be as our next president says: tremendous.

Fake News