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Entries in Maths (6)


Political Conservatism as Motivated Social Cognition

 Click to see where to vote.

In their study "Political Conservatism as Motivated Social Cognition" (Psychological Bulletin, Vol 129, No. 3, 2003), John Jost of Stanford University and Jack Glaser of U. Cal-Berkeley summarize the findings of many studies on political conservativism. They find conservativism to be something that involves much more than a static, individual opinion:

"The core ideology of conservatism stresses resistance to change and justification of inequality and is motivated by needs that vary situationally and dispositionally to manage uncertainty and threat."

Jost and Glaser's broad and thorough analysis of conservativism—as contrasted with liberalism, radicalism, and left-wing ideology—goes beyond politics in the U.S. to include 22,818 cases from 88 samples in 12 different countries.

The study integrates "theories of personality (authoritarianism, dogmatism–intolerance of ambiguity), epistemic and existential needs (for closure, regulatory focus, terror management), and ideological rationalization (social dominance, system justification)."

What Makes A Conservative?

The study's findings confirm these psychological variables are associated with having a conservative political ideology. Variables most positively coorelated (with their r-values) are:

  • Death anxiety (r = +.50)
  • System instability (r = +.47)
  • Dogmatism, intolerance of ambiguity (r = +.34)
  • Need for order, structure, closure (r = +.26)
  • Fear of threat or loss (r = +.18)

Variables negatively coorelated to conservativism are:

  • Openness to experience (r = –.32)
  • Uncertainty tolerance (r = –.27)
  • Integrative complexity (r = –.20)
  • Self esteem (r = –.09)

R Values?

An r-value in statistics is a measure of the degree of coorelation between two variables. It is a measure of the linear relationship between two things, not the cause of one thing by the other.

A positive r-value means, when an independent variable increases (say, death anxiety), the dependent variable tends to increase as well (conservativism).

A negative r-value means, when an independent variable increases (say, openness to experience), the dependent variable tends to decrease.

R-values range between +1 and -1, with a value of zero meaning the two variables are not correlated at all.

2012 Choice Summary: Fear vs. Openness

Because conservative strategists know these psychological coorelations, they exploit them by increasing perceptions of uncertainty, loss, and threats using dogmatic lies and intolerant arguments.

The simple fear of system instability—not actual, complex economic policy—makes middle- and low-income people vote in the interests of the wealthy, who in turn have the ability to make the economic system seem unstable by removing billions of dollars from circulation and claiming they are doing so because they don't know what's going to happen with policy in Washington.

Hogwash. Don't fall for it. Stop falling for it. Never fall for it again.

Let's vote for someone who recognizes the complexity in the world. Let's choose to have a middle class again. And jobs. And medical care. And forward thinking, civility, and citizenship to solve real problems—not kowtow to our fears and the urge to return to an old order in the name of a nostalgic sense of stability.

Can't you feel your self esteem going up just thinking about it?


March Madness Formula for NCAA Championship


Image from Tumblr

As reported on ABC TV moments ago, since the year 2000, 10 of the last 12 NCAA champions in men’s basketball had:

  • a streak of at least 10 wins during the regular season,
  • a non-losing road record,
  • a scoring margin of 10 points or higher, and
  • shot at least 37% from beyond the arc

The only teams to do that this year are:

  • Baylor
  • Belmont
  • Creighton
  • Kentucky
  • Missouri
  • Murray State
  • New Mexico
  • Weber State

The probability of the national champion coming from that bin of teams is apparently .833.

One Other Criteria

Add to that: 9 of the last 12 national champions were ranked in the pre-season Top 10. There’s only one team to meet all five criteria this year:


It would seem you could bet the farm on the Wildcats this year, especially if you like bluegrass. Otherwise, how about putting your money on the fighting Ninteenth-Century Boatcaptains—champs for the first time since 1951!

Happy Corndog Day!


Game Theory II: Hawks & Doves & Others

In game theory, a game called “Hawks & Doves” imagines a showdown between two birds, both of which act on instinct and with a survival tactic to win a resource, say food or a breeding opportunity.

Every bird’s tactic is one of two options: he either fights (hawk) or fakes like he will fight and flees if the other bird doesn’t back down (dove).

If two birds in conflict both be Hawks, they fight to the point of injury, and ceteris paribus each has a 50% chance of winning and a 50% chance of losing. It’s a probability coin toss.

Being nearly fatally injured is worse for the loser than winning is beneficial for the winner. You may win the fight and eat or breed, which is good, but that guy almost died, which is really bad.

We might score the fight +50 for the winner and –80 for the loser. Because all fights according to the conditions of the game are always 50/50 odds, the average payout for the fight is (50 minus 80) divided by 2 = –15, which means over the long run and after enough fights, all hawks average a loss.

If two birds in conflict both be Doves, then they both pretend to want to fight until one or the other eventually backs down. This could take a second, or it could last for days, but neither of them ever intend to fight, only display as though they will.

As with two hawk fights, the winner in a dove standoff gets a resource, which we valued at +50. The losing dove gets no resources, but he also doesn’t get injured, so that’s a zero payoff rather than a big negative.

However, both doves spend energy pretending they are going to fight, so that must count for something negative. Say they both spend the same energy posing like fighters and expend –10 of energy each, which means the winning dove nets +40 and the losing dove, –10.

Unlike with the hawks, the average payout for a two-dove showdown is a gain, (40 – 10)/2 which equals +15, which means over the long run and after enough chest-bump standoffs, every dove averages a win.

So why isn’t everyone a non-fighter for a positive average gain? Because when you’re a hawk, the payoff is risk-free when you encounter a dove. You take it all, +50, and, at the first little peck in the head the dove backs down and gets a zero.

In the game, the dove doesn’t even waste standoff energy when he sees he’s against a hawk. Hawks beat doves. Every time. In the game. It’s a more complex version of the game "Chicken."

Music break:

In "Hawks & Doves," there are NOT two kinds of birds. There is one species of bird with different tendencies to express either hawk or dove behavior. The species expresses hawk and dove behavior in proportion to how the payoffs for survival condition that behavior.

If most everyone expresses dove behavior, then a hawk can make a killing with little risk.

If most everyone expresses hawk behavior, then it’s going to get bloody with a lot of injured losers. And though he wins against doves, every hawk’s going to lose half the time when he fights another hawk.

If you crunch the numbers for payouts of +50 for winning, –80 for losing fights, and –10 for bluffing, then the average payouts for hawks and doves look like this:

Hawks: –15p + 50(1 – p) = 50 – 65p
Doves: 0p + 15(1 – p) = 15 – 15p

where p is the proportion of the population playing hawk, and (1 – p), the proportion playing dove.

In stable populations, the average payoffs between hawks and doves are equal, which makes p = 0.7 in the example: a world with 70% hawks and 30% doves.

  • If that world started far from stability, say with 1 hawk and 99 doves, it would many generations later have 70% hawks and 30% doves (The world would “approach” that proportion).
  • If that world started with 99 hawks and 1 dove, it would also generations later have 70% hawks and 30% doves.
  • If that world started with 50 hawks and 50 doves, it would still, generations later, have 70% hawks and 30% doves.

This all assumes the average payoffs stay the same through the generations. This also assumes the behavior stays the same: a species of bird exhibiting hawk and dove behavior, stuck in a timeless struggle against one another for an evolutionary stable strategy.

But that’s not what happens. Mutation happens. New behaviors begin to show hawk and dove behavior blended in the same strategy. Perhaps there's a new kind of bird that beats up on doves, but won’t fight any hawks. Bully!

Perhaps it's a bird that will sometimes fight hawks and win, but knows when to be a dove and take a dive rather than lose. Perhaps it's a hawk all its life and then, one day, switches, out of the blue.

In game theory, the hawk and dove behavior isn't choosen. The birds play out probabilities of possible phenotypes and successful mutations arise to either live or not live. They are automatons.

In the human world, we’d like to think we can choose. Suppose the birds choose, too?

Cooperation is the best choice for maximizing resources. Guaranteed. It's been proven mathematically and morally. If the Hawks & Doves and the crafty Mutations amongst them would all share, then we wouldn't have so much conflict. Perhaps that's true, depending upon how much of the resource was available and for how long.

What usually develops during cooperation is the simple game theory game, Prisoner's Dilemma, where the hawk may agree not to fight, but he's afraid the other bird is a hawk, too, and won't live up to his promise not to fight. So the cooperative hawk feels like he's going to get taken. He's afraid violence will disturb the peace.

In the 1950s, a contest was held to solve the problem of the Prisoner's Dilemma. What's the best strategy for hawks willing to be cooperative but distrustful of other bird's commitment to peace? Computer scientists, philosophers, mathematicians: answers came from all around. Organizers pitted strategies against one another. Some strategies involved extremely complicated math and decision matrices.

The winningest strategy was simple: Tit-for-Tat, "do unto others" until they do you wrong, then do to them as they did to you. Over enough games played, Tit-for-Tat won.

What a boring way to win.


Tennessee Songs: Memphis & MLK

Unlike other songs in the "Tennessee Songs" series, these three don't have "Tennessee" explicitly in them.

Rather, they contain the word "Memphis," the city where a great nonviolent reformer fell to an even greater system of organized violence, where the man who said "Civilization and violence are antithetical concepts" was shot in broad daylight.

"Oh muddy water,
Rolling to Memphis.
If you were there, you’d swear
It was more than a man who died."

In Memphis, on the evening of April 4, 1968, at 6:01pm, Dr. Martin Luther King, Jr. was assassinated while standing on the balcony outside Room 306 of the Lorraine Motel. Dr. King and his colleague Reverend Ralph Abernathy stayed in that room so often that it was referred to as the "King-Abernathy Suite."

The Lorraine opened in 1925 as the "Whites Only" Windsor Hotel. Walter and Loree Bailey purchased the property in 1942 and renamed it. It was one of the only hotels open to black guests in Memphis in the 1950s and 60s. Whenever Louis Armstrong, Sarah Vaughan or Nat Cole came to town, they stayed at the Lorraine.

By 1982, the city had foreclosed on the structure, which had by that time become low-income housing. The last resident, Jacqueline Smith, was forcibly removed from her apartment there in 1988.

The Lorraine has since been restored to its 1968 furnishings and now houses the National Civil Rights Museum. A 1959 Dodge and 1968 Cadillac sit in the parking lot under Room 306. It's one of the most overwhelming museums you will ever visit.

Dr. King was in Memphis to join the Sanitation Workers' Union Strike. The workers were on strike after the city failed to fix the situations that caused the death of two Memphis garbage collectors, Echol Cole and Robert Walker, who were crushed to death by a malfunctioning truck.

In response to the strike, Memphis Mayor Henry Loeb ordered police to mace and tear gas the nonviolent demonstrators on several occasions. Loeb called for martial law and brought in 4000 armed National Guard troops and tanks.

"Early morning [sic], April 4th
Shot rings out in the Memphis sky.
Free at last, they took your life.
They could not take your pride.
In the name of love.
What more in the name of love?" 

In 1964, at the age of 35, Dr. Martin Luther King, Jr. was the youngest man to receive the Nobel Peace Prize. He donated the prize money—$54,123—to charity. Forty-plus years later in 2006, the Nobel Peace Prize totaled about $1.5 million. The award was split between two entities: a person and a bank.

In 1968, the federal minimum wage in the U.S. was $1.60 per hour. At the time of the strike, Memphis sanitation laborers made two dimes more than minimum wage, $1.80 per hour, which Dr. King rightly called "starvation wages."

In fact, one account by a former Memphis sanitation worker puts the figure closer to 75 cents per hour. There were likely two separate pay scales: legal and illegal.

Starvation Wages
Adjusted for inflation, starvation wages in the U.S. have actually gotten lower over the past two generations. A recent study by the Economic Policy Institute shows that the federal minimum wage had its highest purchasing power the year Dr. King was assassinated. In 1968, minimum wage was $8.54 per hour. But by 2006, minimum wage was down to $5.46 per hour. (Both wage figures stated in equivalent 2009 dollars, the year of the study.)

After Dr. King's assassination, the Memphis Sanitation Workers Union continued their strike for basic rights and fair pay, which they never fully received. Based on searches in the Memphis phone book, it appears the union no longer exists.

Starvation wages still exist, continuing to dwindle with no job stability, no benefits and no political representation to stop it.

Violence continues, too. In fact, violence flourishes: as salable as ever, rewarded with riches beyond conscience, paying a mockery tithe to anyone who might slow it down.

"They asked me if I would do a little number
And I sang with all my might,
And she said, 'Tell me are you a Christian child?'
And I said 'Ma'am I am tonight.'
Walking in Memphis."


Game Theory

This photo taken for free (minus the guard's scowling from across the room) at Portland Art Museum's exhibit "Disquieted."

Coordination, Battle of the Sexes, Chicken, Prisoners' Dilemma: These are the four basic games in game theory. They compare how two players make a choice.

In game theory, payoffs for one player depend on the choices of the other player. Numbers represent the payoffs one player receives for himself relative to what the other player receives for himself; the numbers have no meaning beyond that relative comparison.

Players are assumed to be self-interested, meaning they want to get the highest payoff for any given decision. Also, the players make choices at the same time, so they can't conspire and work out what they plan on doing beforehand. 

1. Coordination Game
You just met Jo. You are taking Jo to Fancy’s on a first date. You and Jo both prefer to dress up formally, but either of you is willing to dress casually if that means you will match each other.

Neither of you wants to go formal if the other is going casual. Neither of you wants to go casual if the other is going formal.

The payoffs for each situation are assigned values in the table as two relative numbers: (You, Jo). Higher is better.



2. Battle of the Sexes Game
After a few dates, you both decide your favorite place is Mellow’s. Now, you want to start dressing casually, but Jo still wants to dress formally. Again, you’d rather match than not match, either way.

Battle of the Sexes


3. Chicken Game
You and Jo break up. (Stupid clothing arguments!) You want to go have a drink at your favorite place, Mellow’s, but you don’t want to go there if Jo is going to be there. That’s the worst thing that could happen. (Jo thinks so, too!)

Neither wants to be the one to go someplace else and have the other get to keep going to Mellow’s. Both of you would like to keep going to Mellow’s, and have the other find a new place.



4. Prisoners’ Dilemma Game
You can’t stand it. Why won’t Jo find a new place? That’s still what you want.

But you’d rather go to Mellow’s and scowl across the bar at Jo than go someplace else knowing Jo gets to enjoy Mellow’s free and clear.

And Jo feels exactly the same. (You two are made for each other.)

Prisoners' Dilemma

Why The Dilemma?
The prisoners’ dilemma is the most interesting case of the four. It’s the only situation where you both lose as a result of following your own self-interest. Both you and Jo are destined to lose when things get to prisoners’ dilemma stage. The decisions could play out like this:

In Coordination, times are good, and you and Jo both want the same thing. So if you think Jo will dress formally, you dress formally (because 2>0, and 0 is what you get if Jo goes formal and you go casual). If you think Jo will dress casually, you dress casually (1>0). Jo’s decisions and payoffs are the same.


In fact, there’s no reason Jo wouldn’t choose to dress formally and get a 2, unless she thinks you don’t want to, in which case you are not in Coordination at all, but rather …

Battle of the Sexes, which is the same as Coordination, except one of you is going to lose slightly when the other gets what he or she wants.

If you think Jo will dress formally, you still dress formally (1>0), though Jo will enjoy it more (2>1). Likewise, if you think Jo will dress casually, you still dress casually (2>0), and you enjoy it more than Jo does (2>1).

Battle of the Sexes

Either way, you both want to match, because not matching means zeros. If you didn’t care about matching anymore, you and Jo’s relationship would result in a breakup and become a game of …

Chicken, which takes a different turn. Think of two cars headed toward one another on a one-lane road. If both do not swerve, they both crash and get zeros. In Chicken, no one wants to crash.

So if you think Jo will go to your old favorite place Mellow’s, you go someplace else (1>0). If you think Jo will go someplace else, you go to Mellow’s (3>2). In fact, if you want to be sure you avoid a zero, your best choice is to always go someplace else, because you will at least get a 1 and you might get a 2.


The problem with going someplace else is that you really want to go to Mellow's. And Jo can win big if she knows you will always go someplace else, because she can go to Mellow's free and clear. That starts to bother you, making you jealous of her always getting a 3 to your 1. When you can’t get over it, the situation becomes a …

Prisoners’ Dilemma, where you are both trapped with a low payoff. If you think Jo will go to Mellow’s, you go to Mellow’s (1>0). If you think Jo will go someplace else, you still go to Mellow’s (3>2). And Jo’s payoffs are exactly the same to her.

Prisoners' Dilemma

So what happens is you both go to Mellow’s, scowl at each other all night, and get a 1—even though you both would get a 2 and be better off if you just went someplace else. (Ain’t it always the way?!)


"Facts of Life" image from Hulu

If You Play The Record Backwards
Maybe that's being too cynical. If we could run the story with Jo backwards, it might go like this instead:

Say you are in a prisoners' dilemma when you first see Jo at Mellow's: You're both in relationships with other people, and you both know going to Mellow's could tempt you to cheat, because you have seen each other several times and know you are attracted to one another.

After enough nights of winking (instead of "scowling") across the bar at Mellow's, you play a game of chicken and talk to one another. Both of you swerve, and you start a relationship at "a different place." (It's qismat! You both simultaneously picked the same different place. "Fancy seeing you here.")

At first, it's a battle of the sexes, where you're trying to decide who wants what and who likes what. But then you fall in love, and you both realize you want the same things. You're now coordinated, like the matching Adidas sweatsuits your aunt and uncle used to wear at family dinners.

Music break ...

Self-Interested Behavior is Inefficient
Unless you and Jo can stay together in your desire to match—or if you can’t cooperate after you no longer want to match—the prisoners’ dilemma seems inevitable. And it’s most inefficient, because the lowest possible combined payoff is guaranteed: 1+1 = 2, which is less than the other two possibilities, 3+0 = 3 or 2+2 = 4. (Again, the actual numbers are irrelevant, beyond a relative comparison.)

Why can’t you both go someplace else and leave Mellow's behind? Because neither of you can get past the mindset that says you must always do what gives you the most satisfaction: When you always act in your own self-interest, you are doomed to always go to Mellow’s and scowl (as long as it remains your favorite).

To the other player, it appears you've deliberately chosen lower satisfaction in order to inflict extra low satisfaction on them. Jo says, “Why would you come here and ruin both our nights, instead of going someplace else and both of us having a good time?” She can’t recognize the reverse schadenfreude: Each of you gets the most displeasure (0) when the other is most fortunate (3).

This reverse schadenfreude occurs in money-sharing experiments, too, where people are generally happy to receive $1 for nothing, unless they know the person giving them $1 was given $100, had to give at least $1 of it away (based on the rules of the experiment), and kept the maximum amount ($99) for himself.

When experimenters allow the recipient the option of killing the entire deal—where no one gets any money—the recipient will do so, and receive nothing in exchange for the other player receiving a “bigger” nothing. The receiver will continue to kill the deal until his portion gets above $20, or so.

This behavior is an evolutionary survival strategy—a concept of “fairness” in the face of unearned gains that seems to be common to all human beings.

Photo "Direction of Time" by the author

Without Fairness, The Best Choice is “I Don’t Care”
If a recipient does not have the option to kill the deal, then his only choice is to be happy with $1 (or whatever he is given). Period.

But don’t be too cynical about it, because some few people will choose to split the money $50/$50, and even some tiny number of people will opt for a $99/$1 split in your favor. Experiment proves this does happen. (Thank you, Mother Teresa!)

More likely, the only escape from a prisoners’ dilemma is not to give a damn about payoffs at all. Because if you are truly powerless to cooperate and fairness is entirely out the window, you can argue and protest as much as you like, but changing the game is outside your control.

It is in your control to give the other person Mellow’s and the 100 bucks and wipe your hands of the situation. Your new price is zero. Your new game is freedom. Imagination. You swerve out of the way every time. You walk away happy … as long as you never, ever, never look back. And as long as you don’t mind being a “chicken.” BwooOOOooock, booock, booock, booock, boock, bock.

Playground tactics still keep us in the game.


Source for game basics: "Games People Play," Scott Stevens