Bluematter.

For Lucas, the incident, which occurred in "the summer of 1965 or '66," was strategy. Strictly business. Because, as Lucas recalls, "when you're in the kind of work I was in, you've got to be for real. You've got to show what you're willing to do."

"Everyone, Goldfinger Terrell, Willie Abraham, Hollywood Harold, was talking about this big guy, this Tango. About six five, 270 pounds, quick on his feet . . . He killed two or three guys with his hands. Had this big bald head, like Mr. Clean. Wore those Mafia undershirts. Everyone was scared of him. So I figured, Tango, you're my man.

"I went up to him, asked him if he wanted to do something, some business. I gave him $5,000 worth of merchandise. Because I know he was gonna fuck up. That's the kind of guy he was. Two weeks later, I go talk to him. 'Look, man,' I say. 'Hey, man, when you gonna pay me?'

"Then, like I knew he would, he started getting hot, going into one of his gorilla acts. He was one of them silverback gorillas, you know, you seen them in the jungle. A silverback gorilla, that's what he was.

"He started cursing, saying he was going to make me his bitch and he'd do the same to my mama too. Well, as of now, he's dead. No question, a dead man. But I let him talk. A dead man got a right to say what he wants. Now the whole block is there, to see if I'm going to pussy out. He was still yelling. So I said to him, 'When you get through, let me know.' "

"Then the motherfucker broke for me. But he was too late. I shot him. Four times, right through here: bam, bam, bam, bam.

"Yeah, it was right there," says Frank Lucas, 35 years after the shooting, pointing out the car window. "The boy didn't have no head. The whole shit blowed out back there . . . That was my real initiation fee into taking over completely down here. Because I killed the baddest motherfucker. Not just in Harlem but in the world."

"After I killed that boy," Frank Lucas goes on, gesturing toward the corner on the other side of 116th Street, "from that day on, I could take any amount of money, set it on the corner, and put my name on it. FRANK LUCAS. I guarantee you, nobody would touch it."

This is from 'The Return of Superfly', a New York magazine story that led to Ridley Scott's 'American Gangster'. The film is OK, though not a must-see. The NY mag story is fantastic, I'm probably quoting its least interesting part. Here is a recent discussion between Frank Lucas and Nicky Barnes.

If you listen to Bruce Bueno de Mesquita, and a lot of people don’t, he’ll claim that mathematics can tell you the future. In fact, the professor says that a computer model he built and has perfected over the last 25 years can predict the outcome of virtually any international conflict, provided the basic input is accurate. What’s more, his predictions are alarmingly specific. His fans include at least one current presidential hopeful, a gaggle of Fortune 500 companies, the CIA, and the Department of Defense.

More here, via MR.

Andrew Gelman weighs in the issue of voting allocation fairness in a two-stage voting system, such as block voting in the EU (an issue I covered, albeit from a different perspective, in an older post) and the electoral college in the US. Here's an edited down version of his argument:

Commentators and experts have taken two positions on the allocation of votes in a two-stage voting system, such as block voting in the European Union or the Electoral College in the United States. From one side (for example, this article by Richard Baldwin and Mika Widgren), there is the claim that mathematical considerations of fairness demand that countries (or, more generally, blocks) get votes in proportion to the square root of their populations. [...]

My claim (and that of Jonathan Katz and Joe Bafumi, my coauthors), thus, is that even if one accepts the voting power criterion, the square-root rule is inappropriate. Could we be right? Is it possible that the consensus of experts in voting power in Europe are wrong, and three political science professors from the United States got it right?

A quick summary of our argument: The square-root-rule is derived from a game-theoretic argument that also implies that elections in large countries will be much much closer (on average) than elections in small countries. This implication is in fact crucial to the reasoning justifying the square-root rule. But it's not empirically correct. For example, if a country is 9 times larger, its elections should be approximately 3 times closer to 50/50. This doesn't happen. Larger elections are slightly closer than small elections, but by very little, enough that perhaps a 0.9 power rule would be appropriate, not a square-root (0.5 power) rule.

[...]I think it's really time for the voting-power subfield of political science, economics, and mathematics to move beyond this silly model (i.e. the square-root).

The Economist's Certain Ideas of Europe blog weighs on the recent Polish proposal:

[...] Poland has grabbed everyone's attention by calling for a change in voting rules, so that voting weights in the EU council of ministers are based on a square root of each nation's population. This is a system that Poland considers much more equitable than the one on offer in the constitution, which says that votes pass when 55% of EU members, representing 65% of the EU's population, can agree.

Economists and game theorists have been busy weighing in on both sides. [...] All the studies of combinatorics that currently fill my email inbox fail because, early on, they concede that in the interests of clarity they assume that coalitions consist of nations taking decisions randomly. But they don't. Luxembourg and Belgium always vote for more European integration. The Nordics vote with Britain and the Netherlands on free trade things. Ireland has low taxes so votes with Britain against tax harmonisation, but has a powerful farms lobby so votes with France to preserve farm subsidies.

The EU is not about mathematics, because EU voting is not about numbers, it is about politics. This may sound like special pleading, given that the author of this posting is a political reporter and not a mathematician. But any analysis that looks at this on the basis of numbers is entirely missing the point.

Well, that's not true. The quoted piece does a very good job of putting the proposed reform into perspective: De jure power in the Council of Ministers is a small contributor to, and poor proxy for, de facto power. This, however, is not the same as saying voting weight reform is irrelevant and that 'the EU is not about mathematics, it is about politics' or that 'any analysis on the basis of numbers is entirely missing the point'. As is the case with the evaluation of any reform, what matters is how the balance of power changes at the margin.

While the UK will not lose 30 per cent of its ability to block legislation as the Spectator claims, it is equally wrong to say that Britain won't be worse off if the Polish proposal is accepted. Given the absence of a suitable theoretical framework and good data on the determinants of de facto power in the Council of Ministers, it is difficult to establish the magnitude of this loss; but this doesn't mean the mathematical approach is redundant.

For those interested in the 'mathematics' of square root voting weights, Vox EU offers an excellent treatment - a must read for budding game theorists and political scientists.

Postscript: The Certain Ideas of Europe blogger also mentions the fact that many countries tend to always vote the same way on given issues. This is a call for the analyst to dig deeper and assess how reform would affect the de jure power of any given country taking into account its effect on the power of its allies. Again, this is not an argument against mathematical analysis; it is a simple re-statement of the perils of simplistic approaches.

The Maspro Denkoh electronics corporation was selling its $20 million collection of Picassos and Van Goghs, but the director could not decide whether Sotheby's or Christie's should have the privilege of auctioning them.

So he announced that the deal would go to the winner of a single round of scissors, paper, stone - the children's game that relies on quick fire hand gestures, where stone beats scissors, scissors beat paper, and paper beats stone.

Sotheby's reluctantly accepted this as a 50/50 game of chance, but Christie's asked the experts, Flora and Alice, 11-year-old daughters of the company's director of Impressionist and modern art, and aficionados of the game.

They explained their strategy:

1. Stone is the one that "feels" the strongest
2. Therefore a novice will expect their opponent to go for stone, and will go for paper to beat stone
3. Therefore go for scissors first

Sure enough, the novices at Sotheby's went for paper, and Christie's scissors got them an enormously lucrative cut.

This took place back in 2005. (The excellent BBC News article also offers winning tips for Monopoly, Connect Four, Draughts, Othello/Reversi and Scrabble)

Graham Walker, via Andrew Gelman, provides a comprehensive list of winning strategies. For example:

When playing with someone who is not experienced at [Rock, Paper, Scissors], look out for double runs or in other words, the same throw twice. When this happens you can safely eliminate that throw and guarantee yourself at worst a stalemate in the next game. So, when you see a two-Scissor run, you know their next move will be Rock or Paper, so Paper is your best move. Why does this work? People hate being predictable and the perceived hallmark of predictability is to come out with the same throw three times in row.

Walker also offers an explanation as to why these tricks actually work:

Humans, try as they might, are terrible at trying to be random, in fact often humans in trying to approximate randomness become quite predictable. So knowing that there is always something motivating your opponent's actions, there are a couple of tricks and techniques that you can use to tip the balance in your favour.

I also have my own contribution to the literature on the inability of humans to act randomly. Ask someone to hide their hand behind their back and pick a random number of fingers. You would think that you would then have a 16.7% chance (not 20% - zero is a number too) of guessing the number right. However, that's not quite true. Zero and five are practically never chosen, while four or one will only emerge if you are asking someone who has tried this numerous times in the past. So, in most cases, you are only left to choose between two and three - a 50% chance of getting it right. And you can do even better than that: Most people's first instinct is to go for two, while if you allow them a few more seconds of thinking time they will revert to three - as one of my victims once explained, 'three is more difficult to guess'.

Addendum: A loyal reader (usually a reliable source) informs me of another trick: ask someone to come up with a number between 1 and 10, and most people will go for seven. According to the same source, this almost always works with girls, with guys being a tad bit less predictable.

Also, it's not only humans that occasionally have trouble with generating random numbers. Tyler Cowen recently posted a piece on Benford's Law, the tendency of many data series (such as the length of rivers) to include a surprisingly high number of entries beginning with the number 1.