Wednesday, July 1, 2015

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.

Tuesday, June 30, 2015

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.

Saturday, June 27, 2015

"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.

Wednesday, June 24, 2015

Writing about writing about writing

One of the reasons I stopped writing so much about my attempt at a novel is that I hated all the encouragement I got.  It's not as if every bit of praise caused a jab of pain.  Rather, it was weeks or months later that the flattery slowly began to sour on me.

The first problem is that whenever I talk about my novel, it turns into an advertisement.  It gives me all the negative feelings I get from self-advertisement.  But unlike self-advertisement, I don't actually get any sales out of it.  It will be a long time before this novel is published, if at all.

Advertisement has never been my goal.  I just want to dabble a completely different kind of writing from what I'm used to, blather about all the junk that I learn, and vent about petty insecurities (see: this post).  I am not attempting to be deep or impressive.

The second problem is that I feel like people don't get excited about quite the same things I do.

For example, I feel burdened by the pervasive expectation that I am writing sci-fi, fantasy, or YA.  I want to write realistic (or surrealistic) literary fiction, but I can hardly tell what that means, or how it might be different from more popular genres.  I feel disconnected from most online conversations about writing, because I never know when the ideas that float around really pertain to what I'm trying to do.  I am used to living on the long tail of culture, but this is one instance when it really starts to grate, and I start ranting about geek cultural hegemony.

And people aren't sold on my novel, they're just sold on the premise.  In particular, readers of The Asexual Agenda were excited that I would have an asexual character.  This is understandable, since clear asexual characters are extremely rare in fiction, and indeed I wouldn't write asexual characters in if I didn't find the idea exciting myself.

But my mind already skips ahead to a future era.  Some day, there will be lots of ace characters in every conceivable medium and genre.  And 90% of everything will be crap.  I want judgmentalism, discernment.  I want stories that are different, even in the hypothetical world where there are lots of things to be different from.  I want to talk about what happens in the stories, not just the fact that the stories exist.

Sunday, June 21, 2015

Nintendo as cultural import

Tauriq Moosa had a good article on people of color in video games.  The article kicks off with a discussion of Rust, a western game which recently added POC to its previously all-white population.  In a simulation of reality, each player is stuck with one race forever, with no way to change it, not even by restarting your character.  I'm marveling at the sheer artistic brilliance of that idea.

You can read that article, but I'm going to go in a different direction.  As is typical of discussions of race in video games, there is a lot of focus on dark-skinned POC in western "realistic" games.  While this is certainly a worthwhile topic, it doesn't really address my experience as an east-Asian American who mostly plays Nintendo.

Japanese video games are fascinating, because they're possibly the most significant foreign cultural import to the US.  We here in the US are used to exporting our culture to the rest of the world, and experiencing Japanese imports is the closest thing to knowing what it feels like for other people in the world.

As I said, this topic is fascinating, but I also don't know what to say about it.  I am no student of Japanese culture, and I don't really understand which aspects of Japanese media are informed by Japanese culture.  There's something significant there, but I don't know what it is.  Is... is this perhaps what it's like for the rest of the world to experience US culture?  Hell if I know.

Indeed, it seems that most people in the US simply ignore the Japanese-ness of these video games.  The most obvious marker of a foreign culture tends to be the portrayal of non-white characters.  However:
  1. Most Nintendo games have cartoony aesthetics, and often no humans at all.  Compared to the "historical accuracy" excuse, this is a much more plausible reason to not portray different ethnicities.
  2. Japan, being colonized by the US after WWII, tends to portray a lot of white people, and otherwise admire white characteristics.
  3. Even when Japanese games portray characters that they think of as Japanese, Americans think of them as white anyway.  It doesn't help that Japanese people portray themselves with all sorts of hair colors.
For example, is Link white?  He may have blonde hair and blue eyes, but I think he's Japanese.  His facial features are Japanese, though they're not as exaggerated as they would be when Americans try to portray someone as distinctly Japanese.  He also obviously falls into the bishonen boy archetype, which Americans just interpret as androgyny.

Rinku: sooo Japanese.

Of course, officially, Link is Hylian, and he lives in a world with Gorons, Zoras, and, ummmm, the Gerudos.....

A race of dark-skinned thieves, not racist at all, Nintendo.  From ZeldaWiki.

I also think the preoccupation with cartoony aesthetics might be peculiarly Japanese?  But nobody seems to talk about that.

So given the Japanese influence on video games, you'd think we'd see a lot of East-Asian representation in video games.  And we do, more so than TV or movies or books.  But it's less representation than you might think because most characters are indeterminate, or appear white to American audiences.

Instead of character representation, I think we mostly get a lot of Japanese cultural influence.  But I don't recognize or understand the cultural influence, and as an Asian American it's not my culture in any case.

Thursday, June 18, 2015

Modal logic semantics

This is part of my series on debugging the ontological argument.

At this point in the series, we will shift gears, switching from predicate logic to modal logic.  Modal logic has produces some of the most complicated and interesting ontological arguments, but it is also a fascinating topic all to itself.  In this post, I will simply cover the necessary background on modal logic.

In modal logic takes propositional logic and adds modal operators.  In standard modal logic there are two modal operators denoted $\square$ and $\Diamond$.  A modal operator takes in any proposition P, and produces another related proposition.  The proposition $\square$P means "It is necessary that P", and the proposition $\Diamond$P means "It is possible that P".  The symbols are also related to each other by
$$\square = \lnot\Diamond\lnot\tag{1}\label{ref1}$$ $$\Diamond = \lnot\square\lnot\tag{2}\label{ref2}$$
(Note that \ref{ref1} and \ref{ref2} are equivalent to each other.)

The next question to ask is, what does it mean to be necessary?  What does it mean to be possible?

The key thing to understand is that $\square$ and $\Diamond$ don't have any inherent meaning at all.  They are just symbols which obey certain rules.  To talk about their meaning, we must shift from talking about logic to talking about semantics.

What we can do is create a semantic model, from which all the logical rules follow.  In general, there will be many possible semantic models which generate the same logical rules.  I will discuss one particular semantic model created by philosopher Saul Kripke in the 1950s and 60s.  I should warn that this is an exercise in rehashing the Wikipedia article, but Kripke's work is so important that the exercise is worthwhile.

Kripke Semantics

I can't think of a better way to explain Kripke semantics than with an illustration:
Figure 1.  If you borrow any of my images, please credit me.

Each of the gray ellipses represents a possible world.  A possible world has a true/false assignment to every proposition.1  In other words, if we have any proposition P, it may be true in some possible worlds, and false in others.  We say that world u "satisfies" proposition P (commonly denoted "u $\models$ P") if and only if P is true in world u.  This is called the satisfaction relation.  The satisfaction is a function whose arguments are a possible world and a proposition, and whose output is a boolean.2

One of these possible worlds (in darker gray, labeled t) is the actual world.   That's the one we live in!  We say that a proposition is true if the actual world satisfies that proposition.

I also drew lots of blue arrows going between possible worlds.  This arrow represents the accessibility relation.  If there is an arrow drawn from world w to world u, then we say u is "accessible" from world w (commonly denoted "w R u").  Worlds may also be accessible from themselves, or they may be inaccessible from themselves.

The big green box is the set of all possible worlds.  The set of all possible worlds, along with the accessibility relation, is called the frame.  The frame, along with the satisfaction relation, is called the model.

There are many different frames I could have drawn.  I could have drawn a different number of worlds or I could have connected the arrows in different ways.  I am not saying that there are many "possible" frames, because remember we're still trying to define what "possible" even means.

In Kripke semantics, $\square$ and $\Diamond$ are interpreted as follows:
$$[w \models \square P] \Leftrightarrow [\forall u \epsilon W ~(w R u \Rightarrow u \models P)]\tag{3}\label{ref3}$$ $$[w \models \Diamond P] \Leftrightarrow [\exists u \epsilon W ~(w R u \wedge u \models P)]\tag{4}\label{ref4}$$
Allow me to translate.  We say that a proposition P is necessary with respect to world w if P is true in all possible worlds accessible from w.  A proposition P is possible with respect to world w if P is true in at least one possible world accessible from w.

Figure 2.

If you're not sure you get it, here are some examples of statements which are true in the model shown in Figure 2.
1. $w \models \Diamond P$
2. $w \models \Diamond Q$
3. $u \models \square \lnot Q$
4. $u \models \Diamond P$
5. $v \models \square Q$
6. $\lnot (v \models \Diamond Q)$

S5 modal logic

Kripke semantics raises new question.  What does it mean for one world to be "accessible" from another?  We need another layer of semantics to explain that one.

There are actually multiple meanings we can assign to the idea of "accessibility".  For instance, we might say that a world u is accessible from world w if and only if u is a possible future of w.  If that is the meaning, then all accessibility relationships are one-way only, and no world is accessible from itself.

Another interpretation of "accessibility" is that world u is accessible from world w if and only if both worlds obey the same physical laws.  In this interpretation, all accessibility relationships are two way, and every world is accessible from itself.

The modal ontological argument does not require any particular interpretation of "accessibility".  However, it does require that "accessibility" conforms to a few specific rules.  Specifically, we want the following conditions:
$$w R w\tag{5}\label{ref5}$$ $$w R u \Rightarrow u R w\tag{6}\label{ref6}$$ $$w R u \wedge u R v \Rightarrow w R v\tag{7}\label{ref7}$$
\ref{ref5} is the reflexivity condition, and it says that all worlds are accessible from themselves.  \ref{ref6} is the symmetry condition, and it says that all accessibility goes both ways.  \ref{ref7} is the transitivity condition, and it says that it is always possible to access the worlds which are accessible through another accessible world.

Here is an illustration of a frame that fulfills the above conditions:

Figure 3.

With these rules, the frame can always be partitioned into one or more subframes.  In Figure 3, the subframes are {t,v,x}, {u,w}, and {y}.  Within each subframe, each world is accessible from each other world.  However, there is no access between  distinct subframes.  Since the different subframes are inaccessible from each other, we might as well just consider the one subframe that includes the actual world and ignore the rest.

These conditions on accessibility create S5 modal logic.  S5 contains additional axioms, which I show below for completeness.  It's not necessary to understand these axioms unless you want to follow the modal logic proofs step by step.
$$\text{If P is a theorem, then}~ \square P\tag{N}\label{N}$$ $$\square(P \Rightarrow Q) \Rightarrow (\square P \Rightarrow \square Q)\tag{K}\label{K}$$ $$\square P \Rightarrow P \tag{T}\label{T}$$ $$\square P \Rightarrow \square\square P\tag{s4}\label{s4}$$ $$\Diamond P \Rightarrow \square\Diamond P\tag{s5}\label{s5}$$
Among other things, these axioms imply that there are no meaningful "meta-modalities".  For example, the statement "it is possible that it is possible that P" is just equivalent to "it is possible that P."

Summary

Modal logic is interpreted through a "frame", or a set of possible worlds.  S5 modal logic, which is the kind used by the modal ontological arguments, requires that the frame is partitioned into one or more subframes.  One of these subframes contains the actual world.  $\square$ P means that P is true in all possible worlds within our subframe.  $\Diamond$ P means that P is true in at least one possible world within our subframe.

But here's what we don't know.  The frame can consist of any number of worlds, as long as there's at least one world.  The frame can be partitioned into subframes in any number of ways.  If I describe to you a possible world, even if you agreed that it exists you wouldn't necessarily agree that it's accessible.

I have final important point.  The frame isn't real.  The frame is a construction to help us understand what's going on.  We can equally well choose a different frame, and that frame is no more or less true than the first.  When we talk about S5 modal logic, we're not making an assumption about what the frame "really" is, we're just choosing to confine our discussion to a particular kind of frame.

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1. Each possible world can also be considered to have its own set of objects.  However, this isn't really relevant, since we won't be discussing predicates in modal logic until later.

2. I'm using basic computer programming terms, and I'm not sure how much I can assume people understand them.  A "boolean" is simply a single bit of information, containing the value "true" or "false".

Monday, June 15, 2015

Race is allowed to be complicated

Rachel Dolezal has recently made news for allegedly misrepresenting herself as black.  Note that I am not a newspaper, and I don't necessarily keep up with every single update, and my opinions are subject to update pending further details.  What I know is that she is a leader of a NAACP chapter.  She has four black adopted siblings.   Her two estranged white parents recently came forward saying that she has been misrepresenting herself as black.

Probably the weak point is the story is, has she really been representing herself as black?  The NAACP still seems to support her, saying they accept leaders of all races.  When asked directly by journalists, she gave a dodgy answer, which suggests that she tells people it's complicated, rather than telling people she's black.

I don't really know what it's like to be black, although from a half-Asian perspective I find the treatment of black/white boundaries in the US to be rather... black and white.  There's this one-drop rule, where if you have even a little black ancestry, then you're just black.  And there's hardly any discussion of black culture or the black community as separate from blackness itself.  I'm not saying that the way we think about blackness is wrong, I'm just saying that it's not the only logically coherent way to think about it.

Here's what I know about my own experience:

In college, I somehow ended up in the Filipino retention program (they had similar groups for most minority ethnicities) and I had to awkwardly tell my assigned mentor that I'm not really Filipino.  Sweating, I launched into an explanation of how I probably told the university I was Filipino, though I didn't remember it, and how my mother immigrated from the Philippines but she's ethnically Chinese, but it's not like I lived in the Philippines personally so I guess I'm just Chinese, I mean, half-Chinese.  I was also born in Korea but that doesn't make me Korean.  The mentor told me I was in the right place, but I wasn't sure and felt uncomfortable about it most of the time.  But now I think she was right.

Honestly, I've felt pretty white most of my life.  I am white, or half at least.  I've felt more Asian in recent years mostly due to having a white boyfriend.  We find our respective family's practices to be bizarre at times and I'm getting a better sense for Asian cultural markers in my experience.  These days I understand that English is an official language in the Philippines, and Catholicism is the main religion, and that's why I missed out on some of the more obvious aspects of being a second generation Chinese immigrant.

In short, race is complicated for me, and I sometimes identify as Filipino despite not having any Filipino blood.

I don't know what it's like to be black in this country.  There are some completely different things going on, with opression more closely attached to perceived race than to immigrant culture.  There's also a much more severe history of opression and appropriation.  There are probably good reasons why black and white groups are treated in such black and white terms.

But when there's one individual who says her experience is complicated, there's nothing inherently ridiculous about that.  I can certainly think of problematic motives for such a stance, but it's not necessarily wrong, and honestly how would I know?

Instead I would defer to people who know much better than me: the NAACP.   The NAACP has been supportive of Dolezal, and cites her impeccable track record as an activist.  That's good enough for me until such a time that NAACP changes its story.

...

I also heard from news sources that people on twitter are talking about Dolezal in terms of transraciality and comparing it to transgender.

Transraciality is one of those things that tumblr haters constantly hold up as an obviously ridiculous identity, in complete disproportion to its prevalence as an actual identity.  So I don't see the point of talking about transraciality, since no matter how good or bad it is, it's already been the subject of far more hand-wringing than it could possible deserve.

There's also the really obvious issue that without any clear group of proponents of of transraciality, there isn't any good way to verify the accuracy of its characterization.  You can attack the motivations of transracial people all you want but it's kind of pointless if I don't know whether it's their actual motivations.

In fact, how the hell do I know that purported transracial people are even identifying as transracial?  That's basically what's happening here, since to my knowledge Dolezal has never identified as transracial at all.  This entire line of argument is just taking all the internet stupid and smooshing it together.