Paper: Evolving out of corruption

I previously summarized a paper which showed that an evolutionary population can cooperate if there's a subpopulation of "corrupt policers", hypocrites who punish others for defecting, while also defecting themselves.  A small population of corrupt policers is still better than an entire population of defectors, so the conclusion was that corruption can be a force for good.

"Evolving Righteousness in a Corrupt World" is a paper that disagrees with those conclusions.  They begin with the observation that in human societies, corruption doesn't really appear to be a force for good.  Then they show that there is an alternate possibility of a "righteous" population, where nearly everyone is a cooperative policer.

The critique in this paper is actually quite similar to the critique I made at the end of my last post.  I said that it didn't seem to describe police officers very well, since police are publicly funded.  So what would happen if we had a game where all cooperative non-policers paid a small fee to the policers?  The fee doesn't even need to be large, it can be a small perturbation.  This paper shows that this small change allows the existence of righteousness under certain conditions.

And that's this paper in a nutshell.

To promote righteousness, you basically need two things.  You need punishments to be more egalitarian (i.e. policers get punished almost as badly as non-policers do when they defect), and you need punishments to be harsh (at least harsh enough to offset the benefit of defecting).  In the context of police, that means not giving police officers special treatment when they break the law.  Hey, that seems like it should be a fairly obvious democratic principle!

On the other hand, I'm still wondering if this is a good model of the police.  After all, not everyone is a police officer, and those who are police officers aren't all corrupt.  Maybe you can think of certain people as being police for game theory purposes simply because they'll report crimes to the police.  Or maybe the model just needs further modification.  I'm sure there's some way to fund the police department without having the police be zombies who take over the entire population.

Paper: The value of hypocrisy

As promised, I will discuss this paper, "Power and Corruption" by Úbeda and Duéñez-Guzmán (henceforth U&DG).  The main point of the paper is that it is possible to maintain cooperation in an evolving population if there is a sub-population of corrupt police.

Yes, in this paper, corrupt policers are a force for good.  In a simple evolutionary model, you will have a population of cooperators and defectors, and the defectors always win out.  The question is if we can enforce cooperation by having "policers" who punish defectors, incurring a personal cost to do so.  This paper concludes that it is possible, but only if we allow policers to be "corrupt".  A corrupt policer simply means that they punish defectors while simultaneously defecting themselves.  They're hypocrites, in other words.

I'm not an expert in this field, but a couple years ago I discussed another evolutionary game theory study, where completely different conclusions were reached.  As I surmised, this is because different models were used, and here I briefly explain the difference:

• In the other model, the population plays a game called the Iterated Prisoner's Dilemma.  Individuals pair up, and play the prisoner's dilemma with their partners repeatedly, while responding to their partner's strategy.  The players in that model used "mixed" strategies, meaning that their decisions were determined by continuously varying probabilities.
• In the U&DG model, the population plays the "Corruption Game."  In this game, there are four strategies: cooperate, defect, honest police, and corrupt police.  Here, the players use "pure" strategies, meaning that they just pick one of four discrete options.  This vastly simplifies the problem.

 Here is an example payoff matrix for the Corruption Game:

[image modified from paper]

The upper left gray square is just the prisoner's dilemma.  But each player also has the option of being a policer, which means they will spend one point to punish a defector.  In this example, the defector gets penalized 10 points if they're a policer, 20 points otherwise.

It's only an example because you can replace these numbers with arbitrary parameters that obey certain conditions.  Which is what they do in the paper.  The paper finds that the situation depends on the arbitrary constants, specifically on how powerful policers are relative to non-policers.*  There are three regimes, helpfully illustrated by these three triangles:

Each point in space represents a possible mix of different strategies among the population.  The black circles indicate stable evolutionary equilibria; the white circles unstable equilibria.

The triangle on the right shows what happens if policers are not so powerful.  There is only one stable equilibrium (d) in which everyone defects.  The triangle on the left shows that if policers are very powerful, then a second equilibrium (k) will appear, describing a population of entirely corrupt policers.  In the middle triangle, there is an equilibrium (x) consisting of a mix of cooperators and corrupt policers.  The x point has better outcomes for society as a whole, despite the corruption.

U&DG have a lovely model, although it's not very optimistic, and rather simplistic.  It may apply to many situations but I'm not sure how well it describes the situation with police officers, who are publicly funded, after all.  If we give police officers less power, that won't make them disappear, because we can just increase wages until enough people want to be officers.  Also, I would have thought that corrupt police officers get along with each other.

Next time I'll discuss another paper, which appears to overturn these conclusions by demonstrating another equilibrium in which everyone is an honest policer.

Duéñez-Guzmán EA, Sadedin S (2012) Evolving Righteousness in a Corrupt World. PLoS ONE 7(9): e44432. doi:10.1371/journal.pone.0044432

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*Specifically, the constant that matters is q+d, as compared to p and s in this payoff grid.  Policers are powerful if q+d < s, and weak if q+d > p.

"Game theory's cure for corruption"

I found a sweet article about power and corruption in the context of evolutionary game theory, and how to stop it.  A taste:

In virtually all the eusocial insects, a few workers surreptitiously lay eggs of their own, eggs that can grow into reproductive males. By diverting shared resources away from the nest, these workers selfishly reduce the fitness of their nestmates. They play the system for their own advantage.

Wow, so I actually did not know that cheating attempts were a thing for eusocial insects.  The author, Suzanne Sadedin goes on to describe many other examples, including cancer and police corruption, and explains some profound conclusions evolutionary game theory research!

The initial conclusion of the research is that corruption is inevitable.  At best, you can have police who prevent corruption in all the non-police, but you cannot prevent corruption in the police themselves.  However, Sadedin's research showed that there is another evolutionarily stable state where there is not corruption.  This state, called "righteousness", has everyone policing each other on equal terms.

Sadedin notes that we are righteous with respect to some things, like murder, but corrupt with respect to others, like infidelity or digital piracy.  Indeed, this is not necessarily a bad thing, as there are certainly drawbacks to righteousness.  But understanding the difference could be quite useful, since we can discuss which issues are best treated with "corruption", and which with "righteousness".

I'm also very interested, because a couple of years ago, I looked into some papers on evolutionary strategies in the iterated prisoner's dilemma.  Based on the way Sadedin discusses the problem, I suspect that a completely different model system is being studied, and I would absolutely love to learn the details.  The two relevant papers are:

Úbeda, F. and Duéñez-Guzmán, E. A. (2011), POWER AND CORRUPTION. Evolution, 65: 1127–1139. doi: 10.1111/j.1558-5646.2010.01194.x

Duéñez-Guzmán EA, Sadedin S (2012) Evolving Righteousness in a Corrupt World. PLoS ONE 7(9): e44432. doi:10.1371/journal.pone.0044432

So when I have time I'll take a look and report back.

A modified prisoner's dilemma simulation

Recap

Over a year ago, I wrote a series of posts about the evolution of iterated prisoner's dilemma strategies.  Since it was so long ago, I will briefly recap, although reading the previous posts may be necessary.

1. I explained what the iterated prisoner's dilemma game is.  Then I program a simple evolutionary simulation where there is a population of individuals who play iterated prisoner's dilemma games against each other.  Rather than intelligently choosing strategies, the individuals blindly follow strategies determined by their "genes".


2. I explain an important scientific paper which demonstrates the existence of so-called "Zero-determinant strategies" (ZD strategies).  These strategies allow one player to unilaterally determine the score of their opponent, or unilaterally enforce a linear relationship between their opponent's score and their own.  The paper claims that this should lead to extortionate strategies in evolution.


3. I explain a response to the ZD paper.  In some sense, ZD strategies may "win", but this does not mean they are evolutionarily stable.  The paper explains conditions for evolutionary stability, and shows that several key ZD strategies are not evolutionarily stable.

In this, the final post of the series, I will modify my evolutionary simulation in light of what I learned from the papers.  I actually modified the simulation a long time ago, but I stalled while trying to figure out what parameters to use.  It was difficult to find a mutation rate which was low enough to allow for population stability, but high enough that the simulation would operate in a reasonable amount of time.

My primary conclusion, therefore, is that researchers in this field have their work cut out for them.  I could see using a supercomputer on this problem, and more fully exploring different variations.  But I'm not trying to contribute to the field, I'm just doing this for fun, and to better understand the field.

Modifications in the simulation

Here are the things I changed in my simulation in light of what I read in the literature:

• Previously, each individual was specified with three parameters.  Now I use four, because these individuals remember not only whether their opponents cooperated or defected in the previous round, but also remember what they themselves did.


• Previously, I calculated the average outcome after ten iterations of the prisoner's dilemma.  Using mathematical techniques from the literature, it now calculates the average outcome after an infinite number of iterations.  This modification eliminates the need to know what individuals do in the first iteration.  Also, the calculations don't work with "pure" strategies, so every individual always has at least 0.1% chance of cooperation and 0.1% chance of defection.


• I switched to a payoff matrix of 5/3/1/0, which is the standard in literature.


• Previously, the individual with the highest score reproduced, and the individual with the lowest score died.  In the literature, the chance of reproduction is proportional to score, and a random individual dies.  I found that the reproduction process makes a huge difference, because it's the difference between trying to be better and trying to be the best.  I changed it so that reproduction rate is proportional to score, and death rate is proportional to five minus the score.

I note that the literature seems to prefer a different mutation process than what I used.  I had individuals constantly mutating their parameters by small amounts.  They instead gave each individual a small chance of mutating a single parameter to a random value.  Both methods make sense.  If behaviors are controlled by many genes, there will be a large chance of small mutations; if behaviors are controlled by just a few genes, there will be a small chance of large mutations. I tried both ways, but stuck with my method because it was easier to make the simulation stable.

The results

The following comes from a population of 40 (which is far smaller than the populations used in the literature).  Each generation, each player plays against two randomly chosen opponents.  Then reproduction and death is assigned by the scores, and the genes of each individual are mutated by a random number between -0.005 and 0.005.

A million generations are shown.  It takes about seven minutes to run.

Here I plot values as they change over the generations.  The thick black line shows the average score (right axis).  The other four lines show the probability (left axis) of cooperating given the outcome of the previous iteration.  For example the CC line shows the probability of me cooperating if we both cooperated in the previous iteration.  The CD line shows the probability of me cooperating if in the last iteration I cooperated and you defected.  All of these values vary through the population, but what's shown are the population averages.

You could be forgiven for thinking that it all looks like a bunch of noise.  This is basically why my simulation stalled.  Is it all just noise from genetic drift?  Do I need a lower mutation rate or larger population?  Or am I biasing results by changing the parameters until the noise is reduced to my satisfaction?  I'm not paid enough to figure it out.

But you can see a few strategies showing up over and over:

• Defection.  All colored lines are near zero, and the average score is near 1.

• General cooperation.  In the literature, evolutionary simulations converge on the so-called general cooperation strategy, (0.935, 0.229, 0.266, 0.42).  My simulation is a bit different and not very stable, but you can see similar results whenever the green line is high and the other colored lines are low.

• Tit-for-tat.  This is the (1,0,1,0) strategy, when the green and orange lines are high, and the others are low.  It only appears a couple times, but seems stable.

 

• Other hybrid cooperation strategies (green plus blue, or green plus aqua) occur repeatedly, and generally precede a descent from cooperation to defection.  If I were to give this a narrative, it's sort of like the population goes soft on crime, and then the criminals take over?

•  I find myself very puzzled by the aqua only strategy, which occurs twice.  I call it the "submission" strategy, since it means that if you cooperate and your opponent defects, then you may just choose to cooperate again.  I don't understand how this could possibly be evolutionarily stable.  This was the sort of thing that made me wonder if my simulation was being wonky.  But here it is:

I also wanted to do a quick test to see how much the different strategies resemble ZD strategies.  I didn't figure out how to define resemblance though, so that was a dead end.

In summary, you can see the results are complicated, and that's why you have to pay researchers money instead of making them work for free.

Extra: Battle of the Sexes

My boyfriend was really curious what happens if you try the same simulation in an iterated Battle of the Sexes game.  In Battle of the Sexes, there is a married couple, and the husband wants to go to a monster truck rally, and the wife wants to go to the opera, or something ridiculously gendered.  Anyway, each person prefers to get their own choice, but going together is still preferable to going separately.

This is pretty easy to do with the same script I already wrote, I just need to replace the payoff matrix 5/3/1/0 with 5/0/0/3.

This is largely an afterthought, so I'm just running it for 100,000 generations.  The left axis shows the probability of giving in, given different outcomes of the previous iteration.

(ETA: I realized the legend is ambiguous.  "My choice" represents the probability that I will give in if in the previous iteration both me and my spouse went to my preferred event.  "Your choice" is the probability that I will give in if in the previous iteration both me and my spouse went to my spouse's preferred event.)

That was really straightforward.  If you're playing an infinite number of iterations of Battle of the Sexes, the evolutionarily stable strategy is to mostly avoid giving in.  But once somebody finally does give in, they continue to give in.  It's funny that the average score hovers around 3, instead of 4.  I guess it's common to have evolutionary players who just never give in.

I suppose this supports the idea that the Iterated Prisoner's Dilemma is really complicated, and it's not just that my simulation is noisy.

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This is the last part of a miniseries on the evolution of Prisoner's Dilemma strategies.
1. Evolution of prisoner's dilemma strategies
2. Extortionate strategies in Prisoner's dilemma
3. Prisoner's Dilemma and evolutionary stability
4. A modified prisoner's dilemma simulation

Debates are okay, not great

I don't watch debates.  Mainly it's an accessibility issue--spoken word doesn't really work for me, and I'll skip it unless I have a good reason not to.

So of course I also did not watch the Ken Ham/Bill Nye debate over creationism.  In fact, why am I even trying to write an opinion about it?  I would instead defer to Jason Rosenhouse, who is an expert on this issue.

A lot of people have questioned whether the debate is a good thing.  It was a fundraiser for the Creation Museum, so there's that.  It also appears to be lending legitimacy to creationism.  By pitting a creationist against a scientist we appear to be putting them on the same level.

Jason Rosenhouse rejects this particular view:

That is not the case with creationism. It is already such a socially acceptable view, even socially dominant in some areas, that I’m not so worried about making it seem more legitimate. It is evolution, and science generally, that needs to get the word out. Creationists have no trouble injecting their poison into the public discourse, and they have a lot of superficially plausible arguments to make. Scientists willing to take on the grim task of offering folks an alternative view should not automatically be excoriated for doing so.

 And I agree.  Anti-evolution, in the US, is really one of the most popular forms of anti-science around.  Rosenhouse puts anti-evolutionism around 50% of the population and young-earth creationists at 10-20%.  While some forms of antiscience are such small fries that they are best ignored, creationism is the very last thing I would call a "small fry".

Furthermore, Ken Ham is a young-earth creationist, and that particular group doesn't really feel the need for scientific legitimacy.  They believe in the Bible as a higher authority than science.  Now if Nye were debating an Intelligent Design supporter, that might have been more of an issue, since Intelligent Design tries much harder to pretend to be scientifically legitimate.

My major complaint about debates is that there's hardly any correspondence to who "wins" a debate, and who in the debate is correct.  Debates instead favor whoever is a more skilled debater.  Historically, this has often favored creationists because scientists usually have better things to do than hone their debate skills.

Debates are bad, but are other formats for arguments any better?  I think written format is far better, although it has less popular appeal.  In written format, it is much easier to provide citations, which are an indispensable part of truth-finding.  Even arguments in a court of law are better than the debate format.  US courts have mostly consistently ruled against the various forms of creationism.  I know many people have a very dim view of the court system, so here I suggest that you should have an even dimmer view of debates.

While the usual case against debating creationists is that we shouldn't give creationists attention, I see this as its main advantage.  Debates are an awful format, but many people pay attention to them.  I said at the beginning that I can't watch debates, but many people have the opposite problem--videos are fine, but they don't have the attention span to read about it.  A little extra attention to creationism can be a good thing.  Though anti-evolution is so common, it's easy for many people to ignore it.  I live in a major urban area and work at a university, so I never meet creationists.  People like me should nonetheless be aware that anti-evolution is a major issue in the US.

Prisoner's Dilemma and evolutionary stability

In the last post of this series, I discussed a paper which established the existence of so-called ZD strategies in the iterated prisoner's dilemma.  Using a ZD strategy, you can either unilaterally choose your opponent's score, or you can enforce a linear relationship between your opponent's score and your own.  You can choose an extortionate ZD strategy, wherein small increase in your opponent's score results in a larger increase in your own score.  Here, your opponent's best strategy is to cooperate fully, even though you reap most of the benefits.

The paper claimed that this is a powerful strategy against an evolutionary opponent, since you can cause your opponent to evolve into a tamer form.  Here, I will discuss a paper which disagrees:

Adami, C. & Hintze, A. Evolutionary instability of zero-determinant strategies demonstrates that winning is not everything. Nat. Commun. 4, 2193 (2013).

Evolutionary stability

A key concept in this paper is that of evolutionarily stable strategies.  As the title of the paper says, winning is not everything, and what makes a strategy "win" is not the same as what makes a strategy evolutionarily stable.

When we say that one strategy "wins" against another, we imagine the two strategies facing off directly, and the winner getting the higher score.  In symbolic terms, let E(X,Y) be the expected score of strategy X when playing against an opponent with strategy Y.  X wins against Y if

E(X,Y) > E(Y,X).

But when we say that one strategy is evolutionarily stable against another, we imagine that there is a population where one strategy is most prevalent.  We ask if mutations of that strategy will ever gain a foothold.  Rather than having X and Y face off against each other directly, they both face off against the most prevalent strategy, X.  X is evolutionarily stable against Y if

E(X,X) > E(Y,X).

In the case where E(X,X) = E(Y,X), then X and Y seem to be on equal footing, so we need to consider higher-order effects.  X may be the most prevalent strategy, but at least a few individuals will mutate into Y.  So at least some of the time, the opponent will be Y rather than X.  X is weakly stable against Y if

E(X,X) = E(Y,X) and E(X,Y) > E(Y,Y),

and X is weakly unstable against Y if

E(X,X) = E(Y,X) and E(X,Y) < E(Y,Y).

Already we can vaguely see how cooperation might be an evolutionarily stable strategy, even though it is unstable from a game theory perspective.  A key to evolutionary stability is how well you do against opponents that are like yourself.

Why ZD strategies don't work

Consider the ZD strategy where you unilaterally choose your opponent's score.  This isn't actually that great from the perspective of evolutionary stability.  For the ZD strategy to be evolutionarily stable, we want

E(ZD,ZD) > E(O,ZD),

where O is some other strategy.  But by unilaterally choosing your opponent's score, you force

E(ZD,ZD) = E(O,ZD).

At most this ZD strategy can be weakly stable.   In fact, ZD is weakly unstable against many other strategies.  For example, they show that it is always weakly unstable against the Pavlov strategy.¹  This is not only shown in the equations, but in a couple simulations.  These simulations pit a ZD population against a Pavlov population, and show that Pavlov dominates.

There's also another kind of simulation which allows strategies to mutate and evolve freely (as opposed to being constrained to just ZD and Pavlov).  In these simulations, if you start out with a ZD population, and have a very slow mutation rate, the population eventually settles on the "general cooperation" strategy.²  This is interesting, because the ZD strategy is evolutionarily stable against the general cooperation strategy.  Even though a ZD population would beat out a general cooperation population, small mutations cause ZD to be unstable, but do not cause general cooperation to be unstable.³  This is a second, distinct sense in which ZD is an evolutionarily unstable strategy.  The paper calls this "mutational instability".

But so far I've only discussed the kind of ZD strategy where you unilaterally choose your opponent's score.  The paper briefly considers extortionate ZD strategies, and finds that they do even worse.  When an extortionate strategy faces off against itself, it results in mutual defection.  This makes it very unstable.  Extortionate ZD strategies do in fact tame opponents into cooperation--and this will result in cooperators replacing the existing ZD population.

I have a criticism of this paper.  The paper only considers these two kinds of ZD strategies, which were the ones mentioned explicitly in the original ZD paper.  However, there are plenty of other ZD strategies not considered.

Communication: a force for evil?

In the BBC article about this paper, it's implied that the reason cooperation evolves is because of communication.  This is basically the opposite of what the paper says, no joke.

The paper says that perhaps ZD strategies can be evolutionarily stable against more cooperative strategies if ZD players recognize each other.  This isn't so much about communication (since communicators can lie) but about visible indicators of one's genetics.  If ZD players recognize each other, and selectively cooperate with each other (but not with mutants), this makes it more stable.

But there are a few problems with this solution.  First, if ZD players can recognize other ZD players, it stands to reason that other kinds of players can do the same.  Second, it's possible for other players to evolve "camouflage" to look like ZD players.  This would result in some sort of camouflage/detection arms race.

Explanation of my simulation results

The conditions for evolutionary instability very nicely explain the results of my simulation of the evolution of the iterated prisoner's dilemma.  In my simulation, I showed cyclic evolution from defection to tit-for-tat to cooperation, and back to defection.  After some thought, this makes sense, because each strategy in the cycle is evolutionarily unstable against the next one.  However, the instability of defection against tit-for-tat is extremely marginal, so I can see why the simulation seemed to get stuck in defection for long periods of time.

I was surprised to find that one of the simulations in the paper is quite similar to my own.  There are a few critical differences which I will discuss later.  It's become clear to me that in the next installment of this series, I will redo my simulation, with modifications in light of what I have read.

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1. The Pavlov strategy is to cooperate if and only if the previous game was mutual cooperation or mutual defection.  The notation is (1,0,0,1).  The Pavlov strategy is strange, but it plays well against itself because it always leads to mutual cooperation regardless of the initial game.

2. The general cooperation strategy is (0.935, 0.229, 0.266, 0.42).  In the literature, simulations have established that this is the dominating strategy under the condition of low mutation rates.

3. I believe that this result may depend on the particular implementation of the mutation.  The implementation used is that there is a very small chance that an individual will replace one of its four numbers with a new random number between 0 and 1. This is different from the way I implemented mutation in my simulation, for instance.

This is part of a miniseries on the evolution of Prisoner's Dilemma strategies.
1. Evolution of prisoner's dilemma strategies
2. Extortionate strategies in Prisoner's dilemma
3. Prisoner's Dilemma and evolutionary stability
4. A modified prisoner's dilemma simulation

Extortionate strategies in Prisoner's Dilemma

In an earlier post, I programmed a simple simulation of the evolution of prisoner's dilemma strategies.  I promised to read a bit of the established literature on the subject, and follow up.  In particular, I will write reports on the following two papers:

Press, W. & Dyson, F. J. Iterated Prisoners’ Dilemma contains strategies that dominate any evolutionary opponent. Proc. Natl Acad. Sci. USA 109, 10409–10413 (2012).

Adami, C. & Hintze, A. Evolutionary instability of zero-determinant strategies demonstrates that winning is not everything. Nat. Commun. 4, 2193 (2013).

The first paper demonstrates that in the Iterated Prisoner's Dilemma game, there exist extortionate strategies.  If you use such a strategy, your opponent can slightly improve their own score, but only by greatly benefiting you.  While this seems like a pretty powerful strategy, the second paper demonstrates that it is not evolutionarily stable.  This post will focus on the first paper.

The strategic landscape

In the previous post, I already explained the Iterated Prisoner's Dilemma.  I proposed a player who is described by three numbers: x, y, and z.  The three numbers describe the probability that the player will cooperate, given what their opponent did in the last round.  This player is known as a "memory-one" player, because they only remember the outcome of one previous round.  But I oversimplified it a bit.  In this paper, a "memory-one" player doesn't just remember what their opponent did in the previous round, they also remember what they themselves did in the previous round.  Thus you really need to describe the player with four numbers, each describing the probability of cooperating, given each of the four outcomes in the previous round.¹

You could also have a "memory-two" player who remembers the outcomes of the previous two rounds.  Or a player of arbitrarily large memory.  You'd think that more memory makes for a better player.  However, the paper proves that there is a sense in which this is not true.

Suppose that player X is a memory-one player, and chooses some particular strategy.  And suppose player Y is a memory-two player, who chooses the best strategy to respond to X's strategy.  But it turns out that Y's best memory-two strategy fares no better against X than does the best memory-one strategy.  Note that this is a precise statement, and it's not quite the same as saying that more memory is useless.² But it provides some justification for focusing solely on memory-one strategies.

In summary, each player is described by four probabilities.  Player X is described by p1, p2, p3, and p4 (for the outcomes cc, cd, dc, and dd respectively, where c is cooperate, and d is defect).  Player Y is described by q1, q2, q3, q4.  Since these are all probabilities, they must be between zero and 1.

Zero-determinant strategies

From this point on, there will be a lot of math.  Skip to "extortionate ZD strategies" to get past the math.

When I calculated scores in my simulation, I used what's called the Markov matrix.  It looks like this:

Fig 2A of paper

The Markov matrix tells you how to transform the probabilities of one iteration to the probabilities of the next iteration.  Each iteration is associated with four probabilities describing the likelihood of each of the four outcomes.  The four probabilities can be written as four components of a vector.  By multiplying the vector by the Markov matrix, you get the vector corresponding to the next iteration.  By multiplying the Markov matrix many times, you can get the probabilities after many iterations.

But if you multiply the Markov matrix many many times, the outcome should approach some limiting state, called the stationary state.³  I didn't calculate the stationary state in my simulation, because I wasn't really sure how.  But the authors of the paper are a little bit more knowledgeable, and can calculate the stationary state.  In my simulation, I calculated the average outcome of the first 10 iterations, but here the authors effectively calculate the average outcome of an infinite number of iterations.

Once you calculate the stationary state, you just need to calculate the scores.  To do this, you do a dot product between the probability vector and the score vector.  The score vector is (3,0,5,1) for the first player and (3,5,0,1) for the second player.  It turns out that this dot product is equivalent to the determinant of a special matrix:

Figure 2B of paper.  v is the stationary vector, while f is the score vector.

Why is this matrix so important?  Because player X has complete control over the second column, and player Y has complete control over the third column.  This allows for "zero-determinant" strategies (henceforth ZD strategies), where the player forces the determinant of the above matrix to be zero.  All you need to do is choose probabilities such that your column is exactly equal to the last column.  If a matrix has two identical columns, its determinant is zero.

You might wonder, why would you ever want to set the determinant to zero?  Doesn't that just set someone's score to zero?  In fact, it does more than that.  You could, for instance, set the sum of your score and the opponent's score to zero.  Instead of using (3,0,5,1) or (3,5,0,1) for the score vector, all you have to do is use the sum of these two vectors, (6,5,5,2).  In general, you can enforce equations of the following form:

Equation 7 from the paper.  s_X is X's score, and s_Y is Y's score, while the rest of the variables are parameters chosen by the player using the ZD strategy.

This equation should make you skeptical.  Can X choose a strategy such that s_X - 10 = 0, thus causing their average score to be 10?  Clearly this is impossible, since the maximum score is only 5.  If you try such a ZD strategy, you must set p1, p2, p3, and p4 outside their allowed range between zero and one.  This is the catch of the ZD strategy: not every ZD strategy is possible.

Extortionate ZD strategies

So far, I've shown that a player using a ZD strategy can enforce a linear relationship between their own score, and their opponents score.  However, not all linear relationships are possible.  What linear relationships are possible?

One thing you can do is unilaterally choose your opponent's score.  In a game where the outcome scores are 5/3/1/0, you may set your opponent's score anywhere between 1 and 3.  However, you can't unilaterally choose your own score using ZD.  After all, it would be a contradiction if both you and your opponent had complete control over your score.

Another thing you can do is enforce a positive correlation between your score and your opponent's score.  Thus, the more your opponent helps you, the better it is for your opponent.  One such ZD strategy is known as the "tit for tat" strategy, where you simply copy the action of your opponent in the last iteration.  In the tit for tat strategy, your opponent's average score will exactly equal your own average score.

But there are more extortionate ZD strategies, where you benefit far more than your opponent does.  For example, player X could enforce the rule (s_X-1) = 6*(s_Y-1), meaning that if Y tries to improve their own score, then X's score improves six times more than Y's does.⁴  In general, you can be as extortionate as you want, although at some point your opponent loses incentive to bother trying for such meager rewards.  Or if your opponent is smart, they may give up on those rewards to spite you.

Consequences for evolution of altruism

It might seem like the existence of extortionate strategies is bad news for the evolution of altruism.  In fact, it's more complicated than that.  You can use extortionate strategies to hurt your opponent, but hurting your opponent doesn't necessarily help yourself.  The mere existence of an extortionate strategy doesn't lead to selfishness.  However, ZD-extortionate strategies have an additional property that I think was not properly emphasized in the paper.  The more extortionate you are, the greater your own rewards when your opponent cooperates.

For example, the least extortionate strategy is the tit for tat strategy.  If you persuade your opponent to fully cooperate, your average score will be 3.  But if you instead use the extortionate strategy above, with (s_X-1) = 6*(s_Y-1), and if your opponent fully cooperates, then your average score will be 4.  The problem with ZD strategies is not that they're extortionate, but that they benefit more extortionate players.

So imagine that you are playing against an evolutionary opponent.  You can choose a ZD-extortionate strategy, and watch your opponent evolve towards a more cooperative strategy.  When they cooperate fully, you can use a more and more extortionate strategy to reap greater rewards (while also hurting your opponent).

Of course, in this picture, we're imagining that one player is intelligently choosing a ZD strategy, and the other player is blindly evolving.  The paper also briefly discusses the case where both players are using ZD strategies, or if one player has a "theory of mind".  I am a bit unsure about the applicability to evolution.  Even the most intelligent agents are not going to choose a strategy based on its eventual evolutionary outcome, many generations down the road.  If agents are not intelligent, I'm not sure if ZD would ever evolve.  Does a ZD strategy really give you an advantage if you're mostly playing against siblings and cousins who are using similar strategies?

I suspect that the next paper, which shows that ZD strategies are not evolutionarily stable, will bring up one or more of these issues.  I will read the paper and see.

-----------------------------------

1. Actually, a memory-one player requires five numbers.  The first four numbers specify what to do in the case of the four possible outcomes of the previous game.  The fifth number specifies what to do in the very first game.  However, in the long run, the first game doesn't really matter (except in the scenario mentioned in footnote 3).  And this paper uses some special calculations that don't use the outcome of the first iteration.

2. The key thing is that if the low-memory player chooses a strategy first, and the high-memory player responds, then there is no advantage to having high memory.  However, if the high-memory player chooses a strategy first, and the low-memory player responds, there is a disadvantage to having low memory.

3. There's also the possibility that the game-state will circle around the stationary state without ever reaching it, and I think it's possible for there to be many stationary states.  The authors don't really address these possibilities, but they're smart so I'm sure they know what they're doing.  I think we can safely ignore these possibilities because they only occur for pathological cases.

4. To get this outcome, try (p1,p2,p3,p4)=(3/5,0,2/5,0).  Tit for tat is (1,0,1,0).

This is part of a miniseries on the evolution of Prisoner's Dilemma strategies.
1. Evolution of prisoner's dilemma strategies
2. Extortionate strategies in Prisoner's dilemma
3. Prisoner's Dilemma and evolutionary stability
4. A modified prisoner's dilemma simulation

Evolution of prisoner's dilemma strategies

While I was in France, I couldn't spend all my time going to the beach and talking about physics.  I mean, sometimes the beach had too many jellyfish.  And we had no internet for a time.

Our arch-nemesis, the jellyfish

So I might have spent an hour or two programming an evolutionary simulation of Prisoner's Dilemma strategies.  The inspiration was that my boyfriend described to me an awful article on BBC news which completely distorted a paper (update: corrected link) on evolutionarily stable strategies for the iterated prisoner's dilemma.

This is all based on multiple hearsay, since I have read neither the news article nor the paper.  So my evolutionary simulation may be completely off the mark.  It's okay, this is just for fun.  Later I will look at the paper and compare what they did to what I did.

Introduction

I assume readers are familiar with the prisoner's dilemma.  The prisoner's dilemma contains the basic problem of altruism.  If we all cooperate, we all get better results.  But as far as the individual is concerned, it's better not to cooperate (ie to defect).  It gets more complicated when two players play multiple games of prisoner's dilemma in a row.  In this case, even a purely selfish individual may wish to cooperate, or else in later iterations of the game, their opponent might punish them for defecting.

The iterated prisoner's dilemma can be analyzed to death with economics and philosophy.  But here I am interested in analyzing it from an evolutionary perspective.  We imagine that individuals, rather than intelligently choosing whether to cooperate or defect, blindly follow a strategy determined by their genes.  I parametrize each person's genes with three numbers:

x: The probability of cooperating if in the previous iteration, the opponent cooperated.
y: The probability of cooperating if in the previous iteration, the opponent defected.
z: The probability of cooperating in the first iteration

I believe everything is better with visual representation, so here is a visual representation of the genespace:

Each square represents an individual.  Each individual is described by three numbers x, y, and z, which are visually represented by the position and color of the square.  The major strategies of the iterated prisoner's dilemma are associated with different quadrants of the space.  In the upper right quadrant is the cooperative strategy.  In the lower left quadrant is the defecting strategy.  In the lower right, is the "tit for tat" strategy, wherein you cooperate if your opponent cooperate, and defect if your opponent defects.  The upper left quadrant... I don't think there's a name for it.

And of course, there are hybrid strategies.  For example, between cooperation and "Tit for Tat", there's "Tit for Tat with forgiveness".  In the evolutionary algorithm, the only way to get from one strategy to another is by accumulating mutations from generation to generation, so the hybrid strategies are important.

The simulation

I tried to perform the evolutionary simulation in the simplest way possible.  Start with some number of individuals (here I use 20 individuals).  Have each pair of individuals play an iterated prisoner's dilemma (here I used 10 iterations).¹ Afterwards, I total up all the scores, and remove the individual with the worst score while duplicating the one with the best score.  Then every individual mutates by randomly making small changes in x, y, and z.

Upon testing, I found that this simulation favors defection far too much.  The trouble is that it's really a zero sum game.  There is no absolute standard for what sort of scores are good or bad, it's just a comparison between the scores of different individuals.  Even if defecting doesn't benefit you directly, it's still beneficial to hurt your opponents so that you come out ahead.

I'm not really sure how to solve this problem, and I'm very interested to see how researchers solve it.  I tried several things, and settled for a simple modification.  Rather than playing against every other player, each individual will play against two random individuals.²  It's still beneficial to hurt your opponents, but not that beneficial since you are only hurting a few of them.  It's also possible that an individual will play against itself, and by defecting hurt itself.

I believe that researchers typically use the following payoffs: mutual cooperation is 3 points, mutual defection is 1 point, and if only one player defects then they get 5 points while the cooperating player gets 0.   However, I wanted to find some interesting behavior, so I adjusted the parameters to better balance the cooperation and defection strategies.  I eventually settled on 4/3/1/0 instead of 5/3/1/0.

Results

Interestingly, rather than there being a single preferred strategy, multiple strategies can be evolutionarily stable.  Actually, this may not be so surprising, since I basically adjusted the parameters of the simulation until I saw interesting behavior.  But it's still fun to watch.

Often the population will settle into the defection strategy and not move for a thousand generations.  But sometimes there is a shift to a cooperative tit-for-tat hybrid strategy.  This hybrid strategy is not very stable, and always seems to eventually fall back to the defection strategy.  Here I show an example of this happening:

Why does this happen?  I'm not quite sure.  But I think that when everyone is defecting, there's no real disadvantage to taking a tit-for-tat strategy.  So genetic drift will sometimes cause the population to shift towards tit-for-tat.  Once there is a critical mass of tit-for-tat, it becomes advantageous to cooperate, since you will get back what you paid for.  Soon everyone is cooperating or using tit-for-tat.  But then, perhaps by genetic drift, we lose too many tit-for-tat individuals, and it becomes advantageous to defect again.  And so begins the cycle again.

Here I also show the average scores of the population over time:

If the population is defecting, then the average score will be 1.  If it is cooperating, the average score will be 3.  Here you see a punctuated equilibrium behavior.

Of course, you cannot draw any real conclusions from this simulation, since I did a lot of fine-tuning of the parameters, and because I'm not really interacting with the established literature.  The conclusion is that this is an interesting topic, and now I feel motivated to read some papers.  When I do, I'll report back.

--------------------------------
1.  Actually I don't have individuals really play an iterated prisoner's dilemma against each other.  Instead, I calculate the average result of an iterated prisoner's dilemma between those two players.  There is no chance involved in this calculation.
2. This means that each individual plays four games on average.  Two games where the opponent is chosen randomly, and two games where that individual was chosen as the opponent.

This is part of a miniseries on the evolution of Prisoner's Dilemma strategies.
1. Evolution of prisoner's dilemma strategies
2. Extortionate strategies in Prisoner's dilemma
3. Prisoner's Dilemma and evolutionary stability
4. A modified prisoner's dilemma simulation

Just how bad is evolutionary psychology?

This week there was more bloggy drama because Rebecca Watson and evolutionary psychology (eg see John Wilkins).  I won't comment on the Watson-related drama, but I am interested in the evolutionary psychology (henceforth EP).

Nearly everyone on both sides of this drama agrees that popular EP is terrible.  The question is, how deep does it go? 

1. Journalists are misinterpreting and exaggerating studies.
2. Journalists understand correctly, but pick out terrible studies from a generally reputable field.
3. There are large sections of EP which are just bad, but attract more media attention.
4. EP is rotten all the way through.

Case study: Argumentative Theory

The trouble is that you can hardly talk about EP without talking about specific examples of EP.  And if you only have a few examples, people can accuse you of not having a large enough survey.  But it's hard to investigate more than a few examples, because we're lazy and/or have jobs.

I'm among those people who are lazy and/or have jobs, so I'm just going to use one example, and it's not even a new example.  I wrote about this in 2011:

Someone sent me a link to a NY Times article called "Reason Seen More as Weapon Than Path to Truth". [...]  It's about "argumentative theory", which claims that human reasoning evolved to win arguments, rather than to reach truth.  In this view, even our many cognitive biases are adaptations to improve debate skills.  This goes against the more common view that cognitive biases represent limitations of natural selection.

Given these two diverging views, I was curious about the evidence for each side.  But I was disappointed in how little evidence the article presented.  In fact, it presented no evidence at all!  I've decided the article is a self-referential parody.

So the NY Times article was terrible.  But was it terrible because there's no evidence for argumentative theory, or is it terrible because the journalist botched the evidence for argumentative theory?  The answer lies buried in this fifty-page review on which the NY Times article was based.

Yeah, I'm not going to read through fifty pages.  But my boyfriend read through it.  He said that it was a good review of fallacies and cognitive biases, but did not advance any other kind of evidence for argumentative theory.  In his opinion, the biggest hole in the paper was its failure to give any account of the evolution of persuadability.  How can anyone win arguments if no one ever gets persuaded?  I asked him if the paper at least showed evidence that cognitive biases lead to winning more arguments, and in his recollection it did not.

Naturally I'm obligated to believe what my boyfriend says, but you're welcome to look at the paper yourself.  Massimo Pigliucci also read the paper independently, and had an even more negative opinion.

But maybe this is just one bad paper that the journalists picked out because it was bad.  It's hard to say without being familiar with the field.  However, there are measures that even a non-expert can use.  According to the Web of Science, "How do Humans Reason? Arguments for Argumentative Theory" was the most cited paper in Behavioral and Brain Sciences in 2011, receiving 38 citations.  As for Behavioral and Brain Sciences, it has the highest impact factor in the category of behavioral science, and third highest impact factor in the category of neuroscience. It's possible that all 38 citations are saying, "Look at this terrible paper", but I doubt it; by all accounts this is a very authoritative paper.

Now that doesn't mean that all of EP is bad.  It could be that only one segment of EP is bad, a large enough segment to cite this paper 38 times.  Given that even anti-EP people agree that at least some parts of EP are decent, this is a good place to settle our inquiry.

TL;DR: I read an awful article about EP, and found that the awfulness comes from the researchers, not the journalists.  It was also a very authoritative study in its field, though this does not imply that all of EP is bad, just parts of it.

Discussion: What is the problem?

First let me note that there is nothing politically "incorrect" or "correct" about argumentative theory.  I have no problem with it, and argumentative theory seems like a reasonable possibility.  Unlike many of the other EP studies that people complain about, it clearly has nothing to do with race or sex.  You may hypothesize that people oppose EP because its conclusions are at odds with liberal politics.  My own hypothesis is that the racism and sexism just draws people's attention to the shoddy arguments that exist in EP.

And what are those shoddy arguments?

If I may generalize based on the above case study and a few other examples I have seen,* evidence for EP (at least that which appears in major media) comes in this form: Based on our theory, human evolution should have selected for trait X.  We did an experiment confirming the prevalence of X across cultures.

*Since I am only waving at other examples vaguely, you are welcome to distrust my conclusions from this point on.

Part of the problem is that it's hard to guard against post-hoc theories constructed just to fit the evidence (whatever that evidence might be).  There's nothing to stop researchers from performing the experiment first and then coming up with an EP theory to justify the results.  Alternatively, it could be common wisdom that X is common, and the EP theory is created to explain X.  Occasionally it turns out that the common wisdom is mistaken, and EP theories can be falsified in this way.  Yes, EP is falsifiable!

But you can imagine there are plenty of cases where the common wisdom is correct, just not for the reasons supposed by EP researchers.  In these cases, the EP theory will never be falsified by the kind of evidence they come up with.

In the case of argumentative theory, an alternative hypothesis that correct reasoning is more adaptive, but also costs a lot of other resources, or is otherwise difficult for evolution to achieve.  The paper points at all our cognitive hiccups, but this is just as consistent with my theory as it is with argumentative theory.  You can also imagine other reasons why cognitive biases might be adaptive.  For example, perhaps they allow you to lose arguments more often, which is good because winning arguments doesn't win friends.  Or cognitive biases could lead to more cautious behaviors (eg mistaking the wind for a tiger is better than mistaking a tiger for the wind).

TL;DR: The study is not bad because it is politically incorrect, it is bad because it makes "obvious" predictions.  These "obvious" predictions might be wrong, falsifying the EP hypothesis.  But falsifiability is not enough, because even if the "obvious" predictions are right, there are many explanations besides EP.

Some defenses of Evolutionary Psychology

The great thing about this drama is that several people are mounting defenses of EP, making it easier for me to gather some of their points.

Chris Hallquist talks about why large brains must be an adaptation.  Big brains are very costly, so there has to be some adaptive value to offset this.  He also mentions the theory that women are more "picky" about sex partners than men because women have to invest more in children.  This theory is evidenced by a cross-species study which verifies that in animal species with two sexes, the sex with more investment in offspring is the pickier one.

Those kinds of evidence overcome my objections, and so I do not object to them.  There could be further objections that I am not aware of, but for now I accept the null hypothesis that this is good science.  However, neither of these arguments apply to argumentative theory, which I still think is bad science.

Ed Clint also gives a quote by Elliot Sober from Philosophy of Biology:

Adaptationism is first and foremost a research program. Its core claims will receive support if specific adaptationist hypotheses turn out to be well confirmed. If such explanations fail time after time, eventually scientists will begin to suspect that its core assumptions are defective. Phrenology waxed and waned according to the same dynamic (Section 2.1). Only time and hard work will tell whether adaptationism deserves the same fate ( Mitchell and Valone 1990).

My interpretation of this quote is that adaptationism is not the assumption that everything is adaptive, it is a way of picking research topics.  You look at a trait and start with the theory that it is adaptive, not because you believe it's true, but because among all the possible hypotheses that's the best one to start with.  (This could be compared to methodological naturalism.)  Something like argumentative theory is just the beginning of a project.  And once argumentative theory becomes a big enough question, scientists will finally perform a solid, expensive experiment.  (I'm sure the cross-species study, for instance, must be quite expensive.)

I believe my interpretation is corroborated by this EP FAQ linked by Ed Clint:

It is true that many functional hypotheses have been offered for a variety of psychological phenomena, and it is also true that most of these hypotheses are probably wrong. However, hypotheses outnumber established theories in just about any field you care to name, and evolutionary psychologists are no less discriminating than other scholars.

I think this is a fair defense of EP, though it leaves a few questions.  Why do researchers so happily talk about their hypotheses to the media as if they were true?

And at most, it leads me to a middle ground between the two sides.  If I read a story, or a scientific study proposing an adaptive explanation for a human trait, should I believe it?  No, I should not.  Because in the field of EP, the adaptive hypothesis is just the starting hypothesis.  It's the idea that the researchers toss around, until it gains enough weight and they bring in the real evidence.  Should I believe in argumentative theory?  No, not at all.  Should I believe in the pickier women theory?  Yes, but only after I heard about the cross-species research.

TL;DR: There are some kinds of evidence in EP that I find persuasive, such as cross-species research.  Another defense of EP is that adaptationism is not so much an assumption of EP, as it is simply a good starting point.  If that is the case, then I should reject adaptive claims from EP until I'm sure that they've advanced beyond the starting point.

More panadaptationism: cognitive biases

Someone sent me a link to a NY Times article called "Reason Seen More as Weapon Than Path to Truth".  (The age of the article tells you something about how long these ideas sit in my draft bin.)  It's about "argumentative theory", which claims that human reasoning evolved to win arguments, rather than to reach truth.  In this view, even our many cognitive biases are adaptations to improve debate skills.  This goes against the more common view that cognitive biases represent limitations of natural selection.

Given these two diverging views, I was curious about the evidence for each side.  But I was disappointed in how little evidence the article presented.  In fact, it presented no evidence at all!  I've decided the article is a self-referential parody.

The article instead talks about how resilient cognitive biases are. 

Mr. Mercier, a post-doctoral fellow at the University of Pennsylvania, contends that attempts to rid people of biases have failed because reasoning does exactly what it is supposed to do: help win an argument.

If cognitive biases are adaptive this does not imply that they are harder to be rid of.  If cognitive biases represent limitations of evolution, this does not imply that they are easier to be rid of.

“People have been trying to reform something that works perfectly well,” he said, “as if they had decided that hands were made for walking and that everybody should be taught that.”

Never mind that no evidence has been put forward for argumentative theory, let's march onwards to even more questionable conclusions!  In this case, the inference is that if we're adapted for something, we better not mess with what nature wants.

Later, the article gets into the political implications of argumentative theory.

Because “individual reasoning mechanisms work best when used to produce and evaluate arguments during a public deliberation,” Mr. Mercier and Ms. Landemore, as a practical matter, endorse the theory of deliberative democracy...

I'm not sure what this has to do with argumentative theory at all, but then, we don't even know whether argumentative theory is true or not, so what does it matter?

The NY Times article does cite its original source, which is a hundred-page paper in Behavioral and Brain Sciences.  I not willing to read this paper, so I will remain agnostic as to whether the lack of evidence is NY Times' fault, or the scientists' fault.  However, my boyfriend was trying to read the paper earlier, and said it was merely a review of evidence for cognitive biases, without any evidence that these are adaptive.  There is additional hearsay from Massimo Pigliucci, who says, "The first substantive thing to notice about the paper is that there isn’t a single new datum to back up the central hypothesis."

I could write a rant about panadaptationism, but then it's not like these rants are in short supply.

Bering is still wrong

Following the discussion of whether homophobia is an evolutionary adaptation, Bering responded to his critics with an interview with Gallup, the author of the original study.

There is a lot of incidental wrongness in Bering's response.  Like when Gallup says that men have a monopoly on paraphilias and kinky sex... Really, Gallup, you think so?  Yoder points out even more errors.  But I will have to ignore most of these so I can stick to the main point.

I agree with Bering on a few points.  First, Gallup's theory in no way implies that Gallup is or is not a homophobe.  In fact, that was never the issue.  Second, I agree that minor-attracted people get short shrift in this whole discussion.  If it were true that gay men were more likely to be attracted to minors, then those people deserve to be helped, not ignored.  However, my agreement with Bering on these points only serves to underscore the fact that political incorrectness was never the problem.

The problem is that Gallup's evidence fails to even partially exclude alternative hypotheses.  In other words, it fails to behave as evidence.

Here are some alternative "plausible" hypotheses which are also completely consistent with Gallup's data:

1. Null hypothesis: Culture causes many to believe that gay men will harm their children or turn them gay.
2. Partially null hypothesis 1: Homophobia is adaptive.  However, people's specific fear of homosexual contact with children is culturally learned.
3. Partially null hypothesis 2: Fearing for one's children is adaptive.  Culturally learned homophobia interacts with these fears.
4. Spandrel hypothesis: There is a genetic basis for wanting to protect children for homosexuals.  The same gene also causes some other trait which happens to be adaptive, and that's why the gene prevailed.
5. Alternative just-so story: Homophobia, especially to protect children, is adaptive, but not for the reason Gallup supposes.  Gay men can still have opposite-sex partners and reproduce, but this is less likely if as children they have contact with gay adults.

What new evidence do Bering and Gallup bring to exclude these hypotheses?  None.  None at all.

In response to concerns about "adaptive storytelling", Gallup responds:

We’ve shown that a person's voice is also related to fitness. Just as people with more attractive faces are more symmetrical, the same is true for people with more attractive voices. The sound of a person’s voice conveys information about their gender, age, body configuration, hormonal status, when they lost their virginity, how many sex partners they’ve had, their propensity for infidelity, whether they are on birth control pills, and whether they are in the fertile phase of their menstrual cycle.

Wow, that is... completely irrelevant!  Even if they have enough evidence to show that a person's voice is related to fitness (and PZ suggests that they don't), what does that have to do with the fact that they don't have enough evidence for the adaptiveness of homophobia?

Another new piece of evidence is a replication of the study in Taiwan.  Not only does this fail to prove cultural universality, but cultural universality would fail to prove a genetic basis, which would fail to prove adaptiveness, which would fail to prove the particular just-so story that Gallup thought up.

And the next piece of evidence... oh, that's it.

I have not been sufficiently convinced that this hypothesis even merits further research.  Not all questions are good research questions; in fact, very few of them are.

Adaptive homophobia: politically incorrect?

Speaking of political correctness, Bering in Mind discussed a scientific question he considers politically incorrect: Is homophobia a product of natural selection?

Unfortunately, the discussion that follows is a tiny bit of science followed by fantastic leaps to conclusions.  The tiny bit of science is an old Gallup poll showing that homophobic reactions increase when the homosexual person is in proximity to children.  The fantastic leap (made by Gallup, not Bering) is that this is because homophobia evolved to reduce the likelihood that one's offspring would turn gay from contact with gay people.

Bering has already been criticized by biologist Jeremy Yoder:

Lots of people, including some evolutionary biologists, speculate about the adaptive value of all sorts of traits—but in the absence of solid evidence for heritability or fitness benefits, such speculation tends to get derided as "adaptive storytelling."
...
What this amounts to is arguing that homophobia is an adaptation favored by natural selection because homophobia is a thing that exists.

And here's another biologist, Jon Wilkins:

In fact, it is trivially easy to come up with a plausible-sounding evolutionary argument to describe the origin of almost any trait. More importantly, it is often just as easy to come up with an equally plausible-sounding argument to describe the origin of a hypothetical scenario involving the exact opposite trait.

According to Jon Wilkins, it's fairly common for evolutionary psychologists to claim that they're just being attacked for political incorrectness:

[Evolutionary psychology] deflected criticism by claiming that politically correct academics didn't want them to ask these questions, painting itself as a field of martyrs who were bravely trying to do science, when the actual criticism was that the science was bad.

Obviously, the biologists can say it better than me, so follow those links for more.  However, I would like to comment on Bering's posturing as politically incorrect.

Consider this a warning: the theory I’m about to describe is likely to boil untold liters of blood and prompt mountains of angry fists to clench in revolt. It’s the best—the kindest—of you out there likely to get the most upset, too. I’d like to think of myself as being in that category, at least, and these are the types of visceral, illogical reactions I admittedly experienced in my initial reading of this theory. But that’s just the non-scientist in me flaring up, which, on occasion, it embarrassingly does. Otherwise, I must say upfront, the theory makes a considerable deal of sense to me.

This seemed rather strange to me for several reasons.  For one thing, science doesn't require that people be unemotional, just that they use a method which cannot be affected by such biases.  For another, science isn't about what makes "sense", since what makes sense to people can be about as biased as their emotional reactions.

As for whether this is politically incorrect, I'm not upset at all by the idea that homophobia could be adaptive.  I'm pretty sure that would have no relevance to whether it's morally acceptable.  What's possibly more upsetting is the suggestion that homosexuals are more likely to be pedophiles, and their victims more likely to become homosexual.  Gallup offers some evidence for this claim, but Yoder showed that it doesn't really hold up.  Yoder also commented that the hypothesis originated in the 1980s when it aligned with prevailing attitudes.  Politically incorrect, or just incorrect?

[Aside: This isn't the first time I've seen Bering posture a bad idea as politically incorrect.  He wrote an article on asexuality which was generally positive, but ended with the "unsavory" suggestion that studies should subject asexuals to erotic stimuli.  Actually I don't think that's all that unsavory if it's necessary for study, but I do think that it's an unfruitful direction for research.]

Question: Does emotion play any role in our rejection of Gallup's claim that homophobia is adaptive, or is it just a matter of looking at the evidence?

I think emotion does play a proper role in science: motivation.  Gallup's claim is personally relevant to me and other gay people, so of course we would take a closer look at the evidence!  If the evidence is found wanting, we have motivation to loudly call it out.  But the method for examining the evidence is itself neutral.  In fact, I've criticized evolutionary psychology even when it's made conclusions I liked.

(via Pharyngula)

Meme skepticism

"Meme" is a word coined by Richard Dawkins in The Selfish Gene.  It's used as an analogy between biological evolution, and the evolution of ideas.  The genes that survive are those that are best able to replicate themselves.  The ideas that survive are also those that are best able to replicate themselves.

It's a useful analogy, helpful for a basic understanding of both biological evolution and culture.  It powerfully conveys the truism that ideas can't survive without winning new minds.  It demonstrates that the basic process of natural selection is just an abstract principle that can apply to many things that replicate.

But I think people are too enamored with the analogy (Daniel Dennett in particular). Does it really work as a theory of social interaction?  The source of the idea also rings skeptical bells.  Just as I don't expect new revolutionary physics to first be published in a book written by an engineer and marketed to popular audiences, I don't expect a new revolutionary theory of social science to first be published in a popular science book about evolutionary biology written by an evolutionary biologist.

When all you have is a hammer, everything looks like a nail.  And perhaps, when you're an evolutionary biologist, everything looks like natural selection.  And since I'm a skeptical blogger, everything looks to me like a claim to be questioned.

I can't really speak to the expert criticisms of meme theory (though a cursory glance at Wikipedia indicates that there are many), but there's at least one flaw in the meme/gene analogy that jumps out at me.  What is the origin of a meme?  While ideas aren't created in a vacuum, it's difficult to describe them as "descendants" of other ideas.  Many ideas just have no traceable source, or they look completely different from their source. As far as biological evolution is concerned, it's extremely important that the offspring look at least a little like their parents.  The traits that improve survivability need to be consistently heritable for evolution to go anywhere.

And many ideas come from more than one source.  There's hardly any speciation of memes, they all just mix and cross-hybridize.  Even in religion (a common example of a meme), syncretism is absolutely commonplace.  Imagine if this were the case in evolutionary biology, we'd have crocodiles reproducing with ducks!

I know I've written a lot of posts expressing idiosyncratic disagreements with Dawkins, Harris, and other prominent atheists.  But that's not even what's going on here.  Based on things I've heard Dawkins say, I fully agree with him.  Take this interview from 2004:

When Dawkins introduced the meme concept a couple of decades ago, hopes were raised that the evolution of culture, or even of the human mind, might be explained as a sort of Darwinian competition among memes. But little has come of this project, even if the word "meme" does continue to get tossed around quite a bit by pretentious intellectuals. I asked Dawkins if he had cooled on the meme idea over the years.

"My enthusiasm for it was never, ever as a contribution to the study of human culture," he said. "It was always intended to be a way of dramatizing the idea that a Darwinian replicator doesn't have to be a gene. It can be a computer virus. Or a meme. The point is that a good replicator is just a replicator that spreads, regardless of its material form."

Well, yeah!  Memetic evolution is a powerful tool to explain evolutionary biology to popular audiences.  It's not actually meant to contribute to the study of human culture.  I mean, isn't that what the social sciences are for?  I know we all like to hate on the squishy social sciences, but to take memetic evolution seriously does not strike me as an improvement.

Nature/nurture and causality

We intuitively understand that things can have many causes.  For example, what caused the election of Obama in 2008?  Obviously, it was a combination of factors, including public disapproval of the war, the disaster of hurricane Katrina, Obama's popular election campaign, and so forth.  Now I ask, what percentage of the victory was caused by McCain's choice of Palin as running mate?

To answer this question, we could perform a thought experiment where McCain chooses someone else, and then we predict how well Obama would have done.  Divide the change in votes by the total number of votes and we have a percentage.  But even supposing we could perfectly predict the outcome of this thought experiment, this answer is problematic.  Wouldn't it depend on who McCain chose instead of Palin?

Furthermore, if we did the same thought experiment for all sorts of different causes, the total percentage would be much greater than 100%, which just doesn't make any sense.

I think this is because the question simply isn't well-defined enough that it can have a definite percentage as an answer.

And yet, when it comes to human biological traits, we ask the same question and expect a definite answer.

What percentage of a given human trait is caused by genetics rather than environment?

This question is problematic, because it's unclear how exactly we would do the thought experiment.  How much do we vary genetics in our thought experiment?  How much do we vary the environment?  And you can't just say that we vary genetics and environment by the same amount.  Given a certain variety of genes, how much is an equivalent variation in environment?  There simply isn't an answer to these questions, because they are bad questions.

But even though it's a bad question, scientists still deliver!  Scientists talk about measuring the "heritability" of a human trait, which is just a number between 0 and 1 that can be experimentally observed.  How do scientists answer the impossible?

They do it by being tricky.  In fact, heritability is the answer to a different question.  If you're a non-scientist, now you are put in the odd situation of having a number for an answer, but not knowing what the original question was.

Google knows all the answers

But enough suspense.  Heritability answers the following question:

How much of the variation in a given human trait is due to genetic variation between individuals of a population?

The question sounds almost the same, but perhaps that's just because I couldn't word it more precisely in a single sentence.*  This question calls for a thought experiment where we take a large population, and hold all environmental conditions constant.  We vary just one factor, genes, and we vary it by the amount we see in the real world.  What percentage of the trait's variation in the population remains?  Alternatively, we can try a thought experiment where we take a large population, and leave their environment as is.  But we change the population's genes, making them all genetically identical.  By what percentage does this decrease the trait's variation in the population?

*The more precise definition has to do with variance, which is a statistical concept that I won't attempt to explain.

 This is a convenient definition because we no longer have to rely on thought experiments to vary the genes and environment.  Now we can look at the real world, and use the real world variation in genes and environment.  The primary difficulty is isolating the two factors.  This is usually done using studies of identical and fraternal twins.  It's by no means a straightforward experiment, and there are all sorts of methodological difficulties, but it's possible.

But even if we can measure heritability perfectly, there are some rather strange consequences of the definition:

1. Heritability increases as the genetic diversity of a population increases.
2. Heritability decreases if a population is exposed to a wider variety of environments.
3. Thus, heritability depends on which population we consider, and what point in history.
4. Heritability does not tell you how hard it is to change a trait by changing environment.

I should re-emphasize that last point, because it undercuts a lot of political abuse of heritability.  For example, let's consider a people that doesn't get any schooling.  How much variation in literacy is due to variation in schooling?  None, because there is no variation in schooling.  But that's not the same as saying that increased schooling will fail to increase literacy.  What it really means is that being a privileged member of this population gets you nowhere because not even the privileged go to school.

Even if heritability is close to 1, it might still be possible to change the trait by changing the environment.  You just have to change the environment by more than is typical for the population.  This could be easy or hard, depending on specifics.

Further difficulties are caused by the fact that genetics and environment are not exhaustive categories, unless you define environment to be everything that isn't genetic.  For example, what about random developmental factors in the womb?  Technically, this is an environmental factor.  But just like genetics, it's just a bunch of chemicals bouncing around in a way that we have no control over.

And we haven't even gotten into gene-environment interaction.  For instance, what if there's a gene that simply increases human receptiveness to environment?  Is that variation due to environment or genetics?  Nature/nurture is a false dichotomy.

Other posts in this mini-series:
Colds and Causality
Women and Causality
Responsibility and Causality
Nature/nurture and Causality
Physics and Causality 
Math and Causality