20. Morals By Agreement, Chapter 3: Strategy (Game Theory)

This is the second of what should be a few posts on the book Morals by Agreement, by David Gauthier.

In the last post, we covered chapter 2 of Morals by Agreement, where Gauthier sketched out his view of what it meant for people to behave 'rationally' in situations which didn't involve other people who might themselves be trying to act rationally and whose actions might depend on our actions and vice-versa.

So in chapter 3, Gauthier extends his model of rational behaviour to cover what he refers to as 'strategic interaction' - that is situations where people are interacting with each other, rather than acting on their own. Basically, in the terms I used earlier in this series, he is moving from rational actions, to rational transactions.

The formal branch of knowledge that studies transactions is Game Theory. The most famous game in Game Theory is the Prisoner's Dilemma, which I introduced earlier in the series here.

For more background on game theory here is the Wikipedia entry on game theory and here is the excellent Stanford encyclopedia of philosophy entry on game theory.

When it comes to game theory, examples are the way to go to gain understanding.

Consider a simple game, where Harold and Kumar are trying to meet up at a local restaurant for a meal, but they are not in communication with each other. However, they both know that there are only two restaurants in town, White Castle and Black Castle. Furthermore, they know that Black Castle is closed.

                                        Harold
                            White                     Black
Kumar   White:      [5,5]                 [3,0]
                 Black :     [0,3]              [2,2]

The best outcome is if they both meet at the White Castle (5 for both). For both Harold and Kumar, the next best option is if they go to White Castle and the other person goes to Black Castle - they don't get to meet up, but at least they can eat. For both players, the third best is to meet at Black Castle and the worst option is to go to Black Castle while the other person has gone to White Castle (alone AND hungry).

Gauthier defines rational behavior in transactions, or 'strategic interaction' as follows:

A)Each person's choice must be a rational response (i.e. utility maximizing) to the choices she expects the others to make
B) Each person must expect every other person's choice to satisfy A
C) Each person must believe her choice and expectations to be reflected in the expectations of every other person.

So in the example above, Harold figures that if Kumar goes to White Castle, he (Harold) is better off going as well. But even if Kumar doesn't go to White Castle, Harold is still better off going to White Castle. So condition A sends Harold to White Castle. Condition B tells Harold that Kumar will follow a similar logic and also end up at the White Castle.

The outcome where Harold and Kumar both go to White Castle is what is known in game theory as an equilibrium outcome. What this means is that, given that both Harold and Kumar are choosing to go to White Castle, there is no reason for either of them to unilaterally change their choice. Compare that with the situation where Harold is going to White Castle and Kumar is going to Black Castle - this is not an equilibrium because in this situation, Kumar would be better off to change his strategy.

Now let's look at a different type of game. Consider the question of what side of the road to drive on. For now, imagine that only two people live on a road, Adam and Eve, and they need to agree on which side of the road to drive on and they both own British cars that were designed for driving on the left side of the road.

                                        Eve
                            Left                     Right
Adam   Left:      [2,2]                 [-10,-10]
            Right :    [-10,-10]            [1,1]

Note that there are 2 equilibrium outcomes in this game, One where both drive on the left and both drive on the right. Even though both Adam and Eve are better off if they both drive on the left, if for some reason they are currently both driving on the right, neither has an incentive to unilaterally change their strategy. Only by working together could they shift from the sub-optimal equilibrium to the optimal equilibrium. Unsurprisingly, this type of game is known as a coordination game, where the coordination needed has two parts: 1) making sure that both people pick the same outcome and 2) making sure the equilibrium they end up in is the optimal one.

But what if we change the game slightly so that Adam has a car that is designed to drive on the left and he has always driven on the left so strongly prefers driving on the left. Meanwhile, Eve has a car that is designed to drive on the right, but she just got her license so she is less attached to driving on one particular side.

                                        Eve
                            Left                     Right
Adam   Left:      [5,2]                 [-10,-10]
            Right :    [-10,-10]            [2,3]

Again there are 2 equilibriums and Adam and Eve need to coordinate to make sure they drive on the same side of the road. But the situation is complicated now by the fact that Adam prefers the 'drive on the left' equilibrium and Eve prefers the 'drive on the right' equilibrium.

This now becomes a bargaining problem, one that has been much studied and argued over in the history of game theory. The reason I bring it up here is because Gauthier himself brings it up in chapter 3 - because it will be useful to him later on in the book.


Finally, I won't go over the Prisoner's Dilemma again, but it is worth noting (as Gauthier does) that in the Prisoner's Dilemma, the equilibrium that Gauthier's rules for rational behavior lead to is different from the (Pareto) optimal outcome. In other words, if people pursue their own utility maximization it will lead to sub-optimal outcomes where there are possibilities to make people better off without making anyone worse off, but these possibilties are placed out of reach by people's self-interested behaviour.

Gauthier will argue that morality consists of the constraints necessary to generate optimal outcomes for 'rational' people.

19. Morals By Agreement

This is the first of what should be a few posts on the book Morals by Agreement, by David Gauthier. Basically, it is a 'contractarian' attempt to show how rational self-interested utility maximizers in the standard economic mould would find it rational to agree to set of morals, or impartial constraints upon their actions.

Chapter 1 of Morals By Agreement by David Gauthier is an overview, which I'm going to skip. Instead, I'll start with chapter 2: 'Choice: Reason and Value', in which Gauthier sets out the basics of the view of the world that he is using for this book, a view that goes by the name 'rational choice theory'.

As Gauthier says,

"the theory of rational choice takes as primary a conception even more clearly subjective and behavioural than interest, the relation of individual preference"

The theory centres on individuals (as opposed to groups, or society as a whole) who take actions in order to achieve a certain outcome.

"the theory of rational choice defines a precise measure of preference, utility, and identifies rationality with the maximization of utility. ... "the theory of rational choice implicitly identifies value with utility"

"we shall develop a set of conditions for considered preference, which must be satisfied if utility, as a measure of preference, it to be identified with value, and the maximization of utility with rationality."

Utility is defined such that if a person prefers one outcome to another, the preferred outcome has greater utility. In this theory, the causation runs form preference to utility, meaning that you don't prefer one action to another because it has greater utility, one action has greater utility than another because it is preferred by you.


Gauthier spends the rest of the chapter on three notions:
1)What it means for a person's preferences to be 'considered'
2) What is means for a person's preferences to by 'coherent'
3) Why it is right to consider value as a subjective, relative measure.

1) Considered preference

Gauthier argues that a person's preferences are not rational if they say one thing and do another because their values are confused. As long as they do what say they want to do, we can assume that their preferences as revealed by their behaviour (the way that economists measure preference, typically) and their preferences as revealed by what they say, are in alignment, and rational (where rational means maximizing utility, and utility is maximized by doing what you prefer to do).

He then notes some of the ways that people's choices may fail to maximize their utility:
a) They might be misinformed. Someone might intend to drink a glass of wine but end up killing themselves because they didn't know the glass was poisoned.
b) They might be uninformed. Someone might choose a poor wine to go with his dinner because he has not experienced the more preferable combination of wine and food before.
c) Someone might agree to a proposal, only to instantly regret their impetuous agreement.

Gauthier then argues that if a preference is such that is is correctly informed and considered and that the action taken aligns with a person's stated intentions, then we can treat their actions as showing a 'considered preference' and meeting the demands of rational choice.

He then discusses and rejects three counter-arguments to this notion of rational choice as expressed via preference:

1) People may have preferences that contradict their interests
2) People may have preferences that cause them unhappiness
3) People may have preferences that cause them to maximize their present utility at the cost of their future utility.

Really, in my mind, these are all really the same objection, expressed in different ways, with the third expression being the clearest and most general. With that in mind, I will just repeat Gauthier's counter-argument to the consideration of prudence (i.e. not doing things you know you're going to regret later - the third point above).

"To maximize on the basis of one's present preferences need not be to ignore one's future preferences; one may take an interest in one's future well-being now, preferring a satisfying life to immediate gratification. But also, one may not. Our view is that prudence is rational for those who have a considered preference for being prudent, but not for those who on full reflection do not.

Our disagreement with the defender of prudence does not turn on whether future preferences are to be taken into account, but on how they are to be considered. We both agree that the unreflectively heedless person, who takes no thought about the morrow, chooses irrationally. One's considered preferences for possible outcome's of one's choices must take into account the expected outcomes on oneself. But one may choose to ignore those effects in what one does; one may choose to take no thought for the morrow. And this reflective heedlessness is not irrational on our view. The defender of prudence insists that rational choice must be directed to the maximal fulfillment of all our preferences, present and future, in so far as we are able to determine what they are. On our view, rational choice must be directed to the maximal fulfillment of our present considered preferences, where consideration extends to all future effects in so far as we may now foresee them."

The requirements for a person's preferences to be coherent in the sense that they will support a person's attempt to maximize their utility via their preferences are well-known and fairly prosaic. Wikipedia explains:

"Rational choice theory makes two assumptions about individuals' preferences for actions:

* Completeness – all actions can be ranked in an order of preference (indifference between two or more is possible).
* Transitivity – if action a1 is preferred to a2, and action a2 is preferred to a3, then a1 is preferred to a3.

Together these assumptions form the result that given a set of exhaustive and exclusive actions to choose from, an individual can rank them in terms of his preferences, and that his preferences are consistent."

Once we allow uncertainty into the results of our actions, there are some more requirements for coherent preference, the most questionable of which is that people are indifferent to uncertainty. i.e. if you offer me $10 for sure, or alternatively you will flip a coin and if its heads, you'll give me $21, and if its tails I get nothing, the theory assumes that people will always take the coin-flip, since the expected return (on average) is $10.50, which beats $10.

Finally, Gauthier defends his relative, subjective viewpoint.

There are two contrasts here:

1) A relative view in which what is 'good' or 'right' varies from person to person vs. an absolutist point of view in which what is 'good' or 'right' is the same for every person.

2) A subjective view in which the idea of 'rightness' or 'goodness' only exists in the presence of sentient beings vs. an objective view in which 'rightness' and 'goodness' are concepts that exist independently of whether there are any people around to actually act in a 'good' or 'right' way. In the objective view, the independent 'goodness' notion acts as a constraint upon the actions of the sentient beings (or ought to) whereas the subjective view sees no such independent constraint as existing.

Gauthier spends a few pages defending his contention that the 'true' viewpoint is the subjective and relative one, but to be honest, it's a bit too abstract for me to grasp, let alone summarize in a blog post.

Taking all this together, Gauthier note that under this rational choice framework, as long as a person's preferences are coherent (i.e. they don't prefer apples to pears, pears to peaches, and peaches to apples) and considered then we can't say that a person's preference is irrational. Even if a person preferred destroying the world to getting a bruise on their finger, that preference is still considered rational in this theory.

He concludes as follows,

"Value then, we take to be a measure of individual preference - subjective because it is a measure of preference and relative because it is a measure of individual preference. What is good is good ultimately because it is preferred, and it is good from the standpoint of those and only those who prefer it. ... Our concern is to demonstrate the possibility and the characteristics of a rational morality, given that value is itself subjective and relative."

18. Interlude

I was out running on the seawall on a rainy Saturday morning, a couple of weeks back, turning over in my mind what type of interpersonal behaviour would match up with the Commercial set of morals from Jane Jacobs' Systems of Survival:

A person who was purely self-interested might fail to be honest and might not shun the use of force and might not respect contracts, while a person who was sympathetic to others as much as they were sympathetic to themselves would likely 'go beyond' just the commercial morals into guardian morals like 'loyalty' and 'treasure honour' (and regard bargaining with someone with the same distaste that they might regard bargaining with a friend or family member).

It occurred to me as I was running that what might work would be someone who was not willing to harm another by stealing from them or defrauding them, but at the same time had no interest in helping another, i.e. someone who prefers to serve their self-interest, but isn’t willing to actively harm others directly to do so in a case where hurting others is the means to improving their self-interest, rather than a side effect.

After I got home and I was on the computer, I tried googling for notions of this type, and came across a description of 'Morals by Agreement' by David Gauthier – a book which was already been in my list of books to cover (sine many other works refer to it) so I moved it up to the next spot on the list.

Sadly, 'Morals by Agreement' is an academic book in tone, which means that it starts out by defining the meaning of the word 'the' and builds from there. So although it may be a little tedious, I might as well take the opportunity to also explain some of the 'building block' concepts used in economics and philosohpy, before launching into the heart of Gauthier's argument. But, I'll have to wait until next week to get started on that....