# Statistical Jokes (30): No Way to Bias a Coin Flip

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This excerpt from a scientific paper is not a joke, but it’s funny nonetheless, at least to me:

Dice can be loaded — that is, one can easily alter a die so that the probabilities of landing on the six sides are dramatically unequal. However, it is not possible to bias a coin flip — that is, one cannot, for example, weight a coin so that it is substantially more likely to land “heads” than “tails” when flipped and caught in the hand in the usual manner. Coin tosses can be biased only if the coin is allowed to bounce or be spun rather than simply flipped in the air. …

The law of conservation of angular momentum tells us that once the coin is in the air, it spins at a nearly constant rate (slowing down very slightly due to air resistance). At any rate of spin, it spends half the time with heads facing up and half the time with heads facing down, so when it lands, the two sides are equally likely (with minor corrections due to the nonzero thickness of the edge of the coin) … Jaynes (1996) explained why weighting the coin has no effect here (unless, of course, the coin is so light that it floats like a feather): a lopsided coin spins around an axis that passes through its center of gravity, and although the axis does not go through the geometrical center of the coin, there is no difference in the way the biased and symmetric coins spin about their axes. (source)

More on bias here; more statistical jokes here.

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# Statistical Jokes (23): Coin Toss

Apple's coin toss application, for all those occasions when a coin is hard to find

A statistics major was completely hung over the day of his final exam. It was a True/False test, so he decided to flip a coin for the answers. The stats professor watched the student the entire two hours as he was flipping the coin…writing the answer…flipping the coin…writing the answer. At the end of the two hours, everyone else had left the final except for the one student. The professor walks up to his desk and interrupts the student, saying:

“Listen, I have seen that you did not study for this statistics test, you didn’t even open the exam. If you are just flipping a coin for your answer, what is taking you so long?”

The student replies bitterly, as he is still flipping the coin: “Shhh! I am checking my answers!”

More statistical jokes here.

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# Children’s Rights (12): Child Soldiers, Why and How?

Why are children recruited for warfare? Why not just use adults who are likely to be more capable and reliable soldiers? There’s an interesting paper here looking at some of the reasons:

• Children are relatively easy to abduct, subjugate, and manipulate. They are more impressionable and vulnerable to indoctrination, and their moral development is incomplete and malleable.
• They are also seen as more loyal and less threatening to adult leadership.
• Children, despite their a priori disadvantages in terms of fighting skills, may have a particular functional value. They may be suitable for menial logistical support of the armed group, or they may even have certain tactical advantages: they can slip through enemy lines unnoticed, making them effective spies and bomb carriers. Also, the proliferation of inexpensive, lightweight weapons has made it easier to use children as soldiers. These small arms are easy to transport and use with little training.
• Rebel groups also make simple cost-benefit analysis: children require less food and no payment. Punishment of children is also less costly. Child soldiers are financially attractive. Rebel groups may be extremely resource-constrained and forced to recruit children.
• The use of child soldiers can present a moral dilemma to enemies: should they kill children?
• Rebel groups may recruit children in order to signal seriousness, commitment and ruthlessness, and thereby instill fear in the enemy.

How are child soldiers recruited? Patterns of recruitment of children vary according to the context. It’s usually a mix of punishment, promises of rewards and indoctrination.

• The recruitment of children is facilitated when they are forced to participate in an assassination (perhaps of one of their relatives, parents or friends). The objective is to break their will. The forced killing of relatives also destroys a child’s outside options: if the child were to flee, it has no place to go to, or the community may reject the child because of what it did.
• Armed forces will also destroy other outside options for children: schools, villages, farms etc.
• Armed forces abuse children’s feelings of desperation and traumas resulting from previous situations of extreme violence.
• Armed forces also abuse certain motivations of children: children may join armed forces because of the desire to take control of events, or because of the protection offered by being at the shooting end of a gun.

More on child soldiers here and here.

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# Self-Defeating Human Rights Policies (2): Child Soldiers

In this older post I gave a few examples of human rights policies that don’t work out the way we want them to. Almost any significant action has unintended consequences, and in some cases these consequences can turn out to be the exact opposite of what we intended. As Kierkegaard said, life can only be understood backwards, although it must be lived forwards. Some of the best intentioned human rights activism just perpetuates the rights violations it wants to combat, and perhaps even makes things worse.

Søren Kierkegaard

I now found another example in an interesting paper by Blattman and Beber. The paper is about child soldiering and looks at some of the things governments can do about it. Child soldiers are often recruited by insurgent groups. Governments can decide to increase counter-insurgency efforts in order to stop the insurgents from recruiting children. But this counter-insurgency increases the minimum force size requirement for the rebel group, hence also the rebel leaders’ incentives to abduct children.

Now suppose the government reaction is not to step up hostilities but to develop educational and economic opportunities for children so that children have larger outside choices which make it more likely that they escape from and less likely that they are lured by the rebels. However, according to Blattman and Beber, intermediate levels of development of such choices could push the optimal age of recruitment of child soldiers downwards. And if outside choices increase, the incentives for the rebel group to take over the country also increase. If rebel group incentives increase, the incentives to recruit children also increase.

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# Moral Dilemma (10): The Morality of Targeted Killing of Terrorists

The targeted killing of terrorists, either by special forces or by unmanned drone aircraft (aptly named “Predators” or “Reapers“), raises a number of moral questions. Let’s focus here on the drone attacks (and also exclude the cases where there’s an imminent attack, because those can be considered morally easy cases of self-defense). There’s an interesting documentary here. If you can’t watch it in your country, here’s a quote describing it:

A guy gets in his car and drives to work in an office in Nevada. From his office he controls drones in Afghanistan. Occasionally he kills people (who can’t shoot back at him, since he’s 8000 miles away). When he’s done, he gets in his car and drives home to his wife and kids. You can tell the difference between ordinary farmers and insurgents by the way they move across terrain, apparently. (source)

I can think of a few moral dilemmas coming out of this, and I would like to see how you vote on these. So here they are.

1. I know that one of the advantages of drones is supposed to be their effectiveness: compared to normal, long distance bombing (such as the shock-and-awe attacks on Baghdad from the Persian Gulf), drone attacks are said to be a lot less indiscriminate. After all, that’s why they are called targeted “killings”. However, to the extent we can judge – there’s no public database of drone attacks – it’s not uncommon to hear about drones mistakenly targeting weddings instead of evil terrorist meetings, or killing bystanders together with the terrorists. It seems that the main reason for using drones is that you don’t endanger your own flying crews, and certainly not your ground troops. After all, once you have identified a target, a drone isn’t more precise than a normal bomber plane. So, if that’s the motive, we can ask if the prioritization of the minimization of risk to soldiers on your own side over the minimization of risk to civilians on the enemy side, is morally acceptable in war.

2. To broaden the point somewhat: is it generally fair or rather cowardly to shoot people who can’t shoot back, or to harm people from such a distance that they can’t harm you back, or is it morally praiseworthy to shoot people while minimizing the risk on your side?

3. Is killing people by way of drone attacks an admissible act of war or a war crime, assuming that the people killed are actually combatants or terrorists (and assuming that terrorists can be treated like enemy combatants in a normal war) rather than innocent civilians, and that the technology is therefore effective?

4. If Al Qaida kills the operators mentioned in the quote, is it an admissible act of war or terrorism?

5. If you have checked the first answer in question #3, do you believe it’s logical to check the first answer in question #4 a well? If not, why not?  Add your reasons in the “other” box.

6. The same question as #4, but slightly modified, and assuming you checked the first answer in question #3. If Al Qaida detonates a bomb that wipes out an entire neighborhood, including the operators mentioned in the quote, can they claim their actions are equivalent to targeted killing by the U.S., given the fact that targeted killing isn’t always very precise either? Or are they wrong and are they in this case not engaging in admissible acts of war but in terrorism?

7. Again, a small modification of question #4, and assuming you checked the first answer in question #3: if Al Qaida detonates a bomb that wipes out an entire neighborhood, believing the operators mentioned in the quote were present, but they actually weren’t present, can they claim their actions are equivalent to targeted killing given the fact that drone attacks are known to have targeted places where terrorists were supposed to be but actually weren’t? Or are they wrong and are they not engaging in admissible acts of war but in terrorism?

More on targeted killings. More on the war on terror. More on just war theory. More moral dilemmas (which are still open to votes by the way).

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# Terrorism and Human Rights (26): Is Terrorism Caused by Unemployment?

girl holding bomb, by Bansky

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I don’t think I need to spell out the ways in which terrorism is a human rights issue (beyond the obvious violations of the human rights of the direct victims of terrorism there are serious human rights implications of the so-called ”war on terror“).

Some time ago, I linked to a paper claiming that poverty and lack of education do not, contrary to common belief, contribute to terrorism. If this claim is correct, then it has major implications for counter-terrorism efforts. There’s another paper here making a similar claim, looking at the correlation between violent insurgencies and levels of unemployment, specifically in Iraq and the Philippines. One often assumes that unemployment and the economic and social alienation resulting from it, are elements causing or facilitating political violence, and that efforts to promote employment can have a beneficial effect on social cohesion and political loyalty. The unemployed are believed to have the mindset (frustration etc.), the time and the opportunity to radicalize and be radicalized, whereas people who are employed have a lot to lose, economically, from political instability. Positively stated,

insurgency is a low-skill occupation so that creating jobs for the marginal unemployed reduces the pool of potential recruits.

However, the authors find

a robust negative correlation between unemployment and attacks against government and allied forces and no significant relationship between unemployment and the rate of insurgent attacks that kill civilians. … The negative correlation of unemployment with violence indicates that aid and development efforts that seek to enhance political stability through short-term job creation programs may well be misguided.

Some of the reasons given in the paper in order to explain this negative correlation are:

• Counter-insurgency forces usually spend money to buy intelligence from the general population. More unemployment means that the available money can buy more intelligence, hence bring levels of violence down.
• Insurgents also need to live. If there’s a lot of unemployment, they need to spend more time on basic survival and hence can spend less time on violence.
• Efforts to enhance security—establishing checkpoints and the like—damage the economy.
• etc.

The paper deals only with two countries, neither of which is perhaps a very typical case. Moreover, cross-border terrorism doesn’t seem to fit well into the analysis. But still, the findings are interesting.

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