Ethical Farmers and Zero Sum Games

In A Treatise of Human Nature, David Hume described a scenario involving two neighbouring farmers which closely matched an asynchronous prisoners’ dilemma – but apparently without the equivalent of a prosecutor.  If you haven't already, please see Ethical Prisoners for the ramifications of having a prosecutor involved - the conclusion to this article will probably not make much sense if you haven't read the preceding article.

Each of Hume's farmers may choose to spend one day helping the other to reap his harvest and minimise wastage in the fields, or commit to working independently and accept the loss represented by such wastage.  The problem is that they have to work on one farm one day and on the other farm the other day.

For this to work, the first farmer (let's call him Cain) must trust his neighbour (Abel) to make good on a promise to help while he himself actually commits to work on Abel’s field.  It seems that there is no-one for Abel to compete with except Cain, so rationally, Abel should betray Cain’s trust.  However, Cain should expect that and should therefore never extend that trust in the first instance.  Rationally it seems, Cain and Abel should work their own fields and accept inevitable losses, rather than expend effort on helping their neighbour.

Real-world examples indicate that this does not occur, but does this mean that farmers are irrational with regard to the trust that they extend to each other?  A reconsideration of the scenario shows that this is not the case.  While there is no human analogue of the prosecutor, farmers are very usually acutely aware that their major adversary is not their neighbour but rather nature herself.  Farmers don’t play against each other – they play against nature, fighting against weather, time and the very earth from which they wring their living.

When this is taken into account, it becomes entirely rational that farmers co-operate because if they don’t, nature will beat them both every time.

It should be noted that the situation with Hume’s farmers is not only asynchronous, but they seek to maximise a gain rather than minimise a penalty.  This can of course be reworded such that each collecting a full harvest is equivalent to a Minimum Punishment while both suffering waste because they both fail to co-operate is equivalent to Medium Punishment for both. 

If one farmer decides to co-operate with the other, and the other decides not to co-operate, then the co-operative farmer will lose time that could otherwise be devoted to his own harvesting.  A co-operative farmer with an unco-operative neighbour ends up in a worse situation than if he had been unco-operative as well – an equivalent to Maximum Punishment.  On the other hand, the unco-operative neighbour obtains a full harvest and doesn’t have to expend any extra effort – which is equivalent to being set free.

 

Considered thus it can be seen that co-operation is equivalent to staying silent and refusal to co-operate (defection) is the same as confessing, as can be seen by comparing the following with Larry’s first consideration in the previous article (Ethical Prisoners):

Neither the prisoners’ dilemma framed in the previous article, nor Hume’s farmer scenario, are truly zero-sum games.  In a zero sum game the "players" play within a closed system as it were – so if one player wins it is always at the expense of another player.  Imagine instead a game in which each player competes to turn the tiles on a board to their own colour.

Initially let us say that 32 tiles are blue and 32 tiles are yellow.  Each player can only prevail by taking tiles from the other player.  It is not possible to co-operate and thus create more tiles and failing to co-operate does not reduce the number of tiles available.  The game is "zero-sum" because the end result will be (32+X) tiles to the winner and (32–X) tiles to the loser, (X) + (–X) = 0.  So, the sum of the gains and losses within the game is zero.

Beyond actual games, it is exceptionally difficult to conceive a real life situation in which a ‘game’ is truly zero sum.  This is most probably because a zero sum game is played within a closed system and there are no closed systems in real life.  Even so, as it is possible that either heavily disguised zero sum games or games which are effectively zero sum exist in reality, we shall briefly look at the considerations that a player within such a game must make.

As a player can only win at the expense of another player, mutual co-operation or mutual refusal to co-operate (defection) result in no change in relative position.  Therefore, considering a game of coloured tiles:

 



 

The rational decision for the yellow player is to choose not to co-operate.  In a zero sum game there is no third player, overt or otherwise; it is inherent in the game that either one player wins and the other player loses or they draw.  Even if there were to be a third player outside the game who would lose if the number of blue and yellow tiles remained equal, that outcome can be achieved if both players consistently refuse to co-operate, without the need for either of the players inside the game to risk losing against the other by exposing themselves to the risk of betrayal.

It would be entirely irrational for any player in a zero sum game to trust the other player or to risk future betrayal by responding favourably to any trust extended to them.

It may be beneficial to compare the zero sum game with the prisoners’ dilemma.  If the prosecutor were not as clever as she might otherwise be, she might choose to offer the prisoners an alternative deal in which the Minimum Punishment and the Medium Punishment were the same, perhaps both 10 years.  Initially this seems to be in her favour because the range of outcomes now consists of: one conviction resulting in a Serious Punishment of 20 years, or two convictions resulting in two awards of Medium Punishment of 10 years.  She stands to secure 20 years of jail time either way.

Apparently she can’t lose.

This conclusion is, however, based on the assumption that the prosecutor doesn’t care how she distributes the 20 years of jail time.  This seems unreasonable in terms of the scenario since she could just put both in front of a court and not care whether they confess or not.  Her best outcome is to not make the offer in the first place and hope that at least one confesses on the stand – condemning both prisoners and resulting in two 20 year sentences.  By virtue of the fact that the prosecutor did in fact make the offer, we must conclude that for some reason she does care how she distributes the 20 years of jail time that she can be assured of.  She cares so much that she is willing to forego the possibility of securing two 20 year sentences in favour of what she calculates as a greater chance of securing one 20 year sentence.  It’s so important to her that, in the standard framing of the dilemma, she is even willing to risk only securing two 5 year sentences.

What could we expect if the prosecutor were to offer only two options: shared Medium Punishment for confess-confess or silent-silent outcomes; or Severe Punishment for one and freedom for the other for confess-silent outcomes? 

 

With this offer, the prosecutor would significantly reduce the likelihood of one of the prisoners staying silent.  Under these circumstances, a prisoner could only ever lose if he were to stay silent while the other confesses.  He cannot win against the prosecutor because the option of shared Minimum Punishment is not offered – the prosecutor wins (secures 20 years of jail time) no matter what choice the prisoners make.  Therefore the prisoners find themselves in a zero-sum game such that they can only play against each other so, given that they are rational actors and only stand to lose if they stay silent, they must rationally both confess.

If as rational actors they must both confess, then the prosecutor may be tempted to increase the Medium Punishment for bilateral confession, for example to 15 years each for a total of 30 years.  This, however, changes the dynamics once again – oddly enough giving control to the prisoners.  Now each prisoner has control over the game and can avoid a loss, depending on his chosen opponent.  Larry can choose to win against the prosecutor by staying silent which would deny her her best outcome of 30 years served (either through serving 10 years in prison together with Wally or 20 years alone, if Wally were to choose to play against Larry).  Alternatively, Larry can choose to ensure that he does not lose against Wally, which he can acheive by confessing, resulting in either 15 years in prison together with Wally (a draw) or freedom (a win).

 

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 Again it seems that the primary consideration in these games is "who are you playing against?"  We'll be returning to these issues in a later article.

 

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This article is one of a series.  It was preceded by Ethical Prisoners and is followed by Morally Circular Definitions.

The Risk in Sharing a World View - A Second Prelude to "My World View"

As mentioned before, I’ve had the misfortune recently to have listened to the ever-humble Don Johnson’s performance in some of his podcasts.

Humble Don and his shaved chimp sidekick (Brandon), both self-described as “evidentiary Christians”, are keen debaters of atheists, alternate theists and also incorrectly believing Christians.  Humble Don has written a book, which he occasionally refers to (read as “often refers to”), in which he tries to map out how Christians can successfully engage atheists, alternate theists and incorrectly believing Christians.

The recommended first step in a successful engagement is to ask the opponent to describe their world view.  The shaved chimp puts it like this:

“Everybody has a belief and they need to be able to make a positive case for it.”

Right, there’s a problem here.  While I’ve got no fundamental problems with describing my world view and I think it is only reasonable to establish up front what presuppositions both sides of the debate are grappling with, I do have a problem with presuppositions about my presuppositions.

I don’t have a belief in the same sense that Humble Don and the shaved chimp mean when they say “What are your beliefs?”  I’ve talked separately about my issues with the word “belief” in these sorts of debates, so I’ll just state up-front that if I am describing my world view, I am describing a world view, not (and I repeat NOT) a set of beliefs.

I remain a little wary of presenting my world view in certain contexts.  Don Johnson and his sidekick provide good reasons for this wariness.  Here’s an example.

In his podcast “Why Christianity is more reasonable and scientific than atheism”, Humble Don plays a short excerpt from Adam Savage’s speech at the Reason Rally.  Adam talks how he flew to Washington on a plane which was the result of tested and proven hypotheses, a product of reason and a direct consequence of “human capacity to make sense of the world”.  At no time during the speech does Adam mention the terms “positivism” or “scientism”.  At no time during the speech does Adam mention "David Hume".

Humble Don then speaks:

“Adam Savage describes a metaphysical world view, it’s called positivism or scientism, it’s the idea that all you can know must be measured through your five senses and perhaps mathematical equations based on those measurements. So you need to be able to empirically measure it with your five senses and you are then allowed to use mathematics to make certain conclusions based on that.  But beyond that, you can’t know anything … for certain.

“This goes way back, I’m going to give you a quote from Hume.  You know we had a guy on a few weeks ago who called himself a big Hume fanboy.  Well, Hume is a big hero to a lot of these guys.  Let me give you a little quote from Hume.  This is a presupposition that lies at the basis of this pseudo-scientific attitude.  Ah, this is what David Hume said:

“When we run over libraries, persuaded of these principles, what havoc must we make? If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.

“So, he says when you pick up a book in the library, does it offer you quantifiable number that you can measure and, no? Then burn it.  If it’s metaphysical at all, if it deals with big questions of life that you can’t measure, burn it.  This is David Hume.

“Now, those of you who might have thought through that little paragraph, that Hume wrote there, might already realise that it is self-refuting – on it’s face.  That the proposition that you cannot know anything unless it can be empirically measured, or calculated via mathematics, is itself not something that can be empirically measured or calculated via mathematics.  It’s a metaphysical claim, right.  He says: ‘Burn all those metaphysics books because they’re not empirically measured!’  How did you get that, David?”  (There is chittering in the background: “Burn your own book, man!”)

“How do we know that’s true, right, how do we know that what David Hume said there is true?  You … not via empirical measurement and not via mathematics!  It’s a metaphysical claim, it’s a metaphysical claim saying that all metaphysical claims can’t be trusted.  There you have it.  And y’know … and that lies at the heart of the irrationality of this project, okay.  Adam Savage says ‘I want stuff that’s testable and provable, like the way they built that airplane … and, this is what I’m gonna build my life on … and, this is the only thing you should build your life on …'

“Hold on, hold on, hold on.  How do I know that, Adam?  How do I know that that’s the only thing you should build your life on?  How do I know that this is all that there is to reality, that … that epistemologically all we can know is stuff we can measure?  Well, we can’t know it via measuring, right?  I mean this is just taking a huge leap of irrational faith to start your project, your intellectual project, saying ‘Oh, we’re, we’re just empir(ic)ists.’  Already, you can’t prove that.”

And they continue (it's worth listening to them with a critical ear; painful, but instructive).

It should be noted that Adam Savage is not, and has never been, David Hume.  It should also be noted that Adam Savage never claimed to be a devotee of positivism or of scientism.  Nor did he make mention of David Hume, or any of David Hume's views in his speech.

David Hume may be wrong about certain things, no-one doubts that.

Adam Savage may be wrong about certain things, no-one doubts that either.

But when Adam Savage is wrong about things, he is wrong about those things entirely by virtue of his own arguments.  You can’t claim, with any sort of intellectual honesty, that person A is wrong on the grounds that you think that person X is wrong about a subject that person A didn’t even mention.

Furthermore, Humble Don’s quote from Hume is the very last paragraph of his “An Enquiry Concerning Human Understanding” (EHU).  Earlier in the document, Hume makes clear what he means by “metaphysics”:

But this obscurity in the profound and abstract philosophy, is objected to, not only as painful and fatiguing, but as the inevitable source of uncertainty and error. Here indeed lies the justest and most plausible objection against a considerable part of metaphysics, that they are not properly a science; but arise either from the fruitless efforts of human vanity, which would penetrate into subjects utterly inaccessible to the understanding, or from the craft of popular superstitions, which, being unable to defend themselves on fair ground, raise these intangling brambles to cover and protect their weakness. Chaced from the open country, these robbers fly into the forest, and lie in wait to break in upon every unguarded avenue of the mind, and overwhelm it with religious fears and prejudices. The stoutest antagonist, if he remit his watch a moment, is oppressed. And many, through cowardice and folly, open the gates to the enemies, and willingly receive them with reverence and submission, as their legal sovereigns.  (EHU 6)

It was a specific type of “metaphysics” that Hume, some 240 years ago, was railing against.  He was not railing against a more modern philosophical definition of metaphysics”, per Wikipedia:

Metaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined.

In any event, Hume was not making a metaphysical claim; he was making an epistemological claim.  Humble Don accidentally confirms that he knows this is the case when he says “How do I know that this is all that there is to reality, that … that epistemologically all we can know is stuff we can measure?”  Epistemology is the philosophical field concerned with knowledge, what can we know?

Humble Don, who likes to claim that he uses his terms carefully, should not be using the term “metaphysical” at all, since it is unclear whether he means the term in its supernatural (beyond nature) sense.  He should be using either “epistemological”, as would have been correct here, or “ontological”, referring to the nature of being, existence or reality (“ontology” can be considered a part of classical metaphysics, the other parts being “natural theology” and “universal science”).

So, why does Humble Don use metaphysical?  If I were to make the generous assumption that he doesn’t do it deliberately to sow confusion, I would say it is because he’s a bit of an Aquinas fanboy.

According to Aquinas “something can exist separate from matter and motion ... because by its nature it does not exist in matter and motion; but it can exist without them, though we sometimes find it with them” and it is this something that is separate from matter that is the subject matter of metaphysics.  Therefore, things you cannot see or touch, or sense in some way, are sometimes – in the Thomistic sense – metaphysical.

But … and this is a big but … Aquinas in not just talking about something that “can exist separate from matter and motion”, but goes further to clarify that he is talking about something that “can exist without (matter and motion)”.

Ideas, such as being presented by Hume and Savage, satisfy the requirement stated in the first part of the description, if you twist your thinking enough.  However, ideas exist in physical brains which are composed of matter, they do not exist separate from matter and motion – unless you make a huge, unjustified assumption that the mind and body are separate.

Sorry boys, that’s a big embarrassing fail on your part.  Your straw man failed.  Your (ab)use of philosophical terms failed.  Your quote from Hume failed.  If you did indeed attempt to rely on Aquinas then that failed too.

Anyways, despite my misgivings that some idiot(s) might take my world view, misrepresent it, then compare it unfavourably to a misrepresentation of somebody else’s world view which, in reality, only obliquely resembles mine … I’m going to present that world view.