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Convention. Recap. What We’re Doing. The relation between a word and its meaning is conventional. To understand this we want to know what a convention is. To do that we are using certain ideas from game theory: Equilibrium point Coordination problem. The Disarmament Game. Equilibria.
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What We’re Doing The relation between a word and its meaning is conventional. To understand this we want to know what a convention is. To do that we are using certain ideas from game theory: • Equilibrium point • Coordination problem
Equilibria An equilibrium point is a square on the grid where no player can improve his position through unilateral deviation. Unilateral deviation is when one player changes strategy and all the other players do not.
The Disarmament Game Equilibrium
Coordination Problems A coordination problem is a game where there are multiple equilibrium points. The problem is to “coordinate”: make sure we play strategies that will put us at the equilibrium points.
Solving Coordination Problems How do you solve a coordination problem? Two ways are salience and precedent.
Example: Meeting Suppose two people want to meet, but they have no way of communicating with each other. It does not matter where they go, as long as they go to the same place.
Salience Suppose you and a friend are in a strange city and you get split up. It doesn’t matter where you go, as long as your friend goes there to. Where should you go? Your goal is to guess where your friend will go and go there. The salience of a location can suggest it as a good meeting place.
Precedent If you’ve successfully navigated this situation before you might choose to meet at wherever you met before.
Convention Finally, if you get in situations like this a lot, you might have a conventional rule that you follow for what to do. Example: my wife and I have the rule: always meet at Exit A of the closest MTR station.
Convention: First Definition It is a convention for a group to follow a rule in a certain situation, if whenever they are in that situation: • Everyone follows the rule. • Everyone expects everyone else to follow the rule. • The situation is a coordination problem. • Everyone following the rule is a solution to the coordination problem. • The reason why they follow the rule is (3) and (4).
Example: Money Throughout history, people have used different things as money: gold, silver, sea shells, salt (whence ‘salary’), goats, cigarettes (in prison), coins and paper currency. It doesn’t matter to me what I accept in exchange for my goods and labor as long as it’s what everyone else accepts (as long as I can spend it).
Accepting HKD is Conventional It is a convention for Hong Kongers to follow the rule “accept HKD” in exchange for goods and services, because: • Everyone gets paid in HKD and makes purchases with HKD. • Everyone expects everyone else to accept payment and make purchases with HKD. • Which currency to accept is a coordination problem. • Everyone accepting HKD is an equilibrium point in that problem. • The reason why we follow the rule is (3) and (4).
Not All Rules Are Conventions • Laws contain lots of rules. Many of these are not conventions: the reason we obey the law is not because other people do, it’s because we will be punished (however, compare driving on the right). • Mathematics textbooks contain rules for calculating the values of certain functions. Again, when we follow these rules it is not because others do– it’s because they get us the right answer! • Moral rules?
Language and Convention Many aspects of language are also conventional: • The meaning of each word. • Some facts about the grammar. • How the words get pronounced.
Not Everything Conventional “Certainly not every feature of a language is conventional. No humanly possible language relies on ultrasonic whistles, so it is not by convention that Welshmen do not… but so long as even two languages are humanly possible, it must be by convention that a population chooses to use one or the other.” – David Lewis
City of Gold Jungle of Danger
A Messenger General 1 wants to let General 2 know that he (G1) wants to attack at dawn. So he sends a messenger through the Jungle of Danger, with the hopes that he will get through the snipers and snakes.
A Worry General 1 is still worried: Did the messenger survive? I know that I want to attack at dawn, But I do not know that General 2 knows that I want to attack at dawn. If he doesn’t know this then he might not attack at dawn.
A New Messenger Luckily a new messenger arrives from the Jungle of Danger. The messenger says, “General 2 got your message!” General 1 feels relieved.
A New Worry But something is still wrong. General 1 now has a new worry: I know that I want to attack at dawn. And I know that General 2 knows that I want to attack at dawn. But General 2 doesn’t know that I know that General 2 knows that I want to attack at dawn. If he doesn’t know this he might not attack at dawn.
Another Messenger So General 1 sends another messenger into the Jungle of Danger to tell General 2 that General 1 got G2’s message that G2 got G1’s original message. Another message comes back from General 2 saying he got the latest message. General 1 feels relieved.
Another Worry But something is still wrong. General 1 now has a new worry: I know that I want to attack at dawn. And I know that General 2 knows that I want to attack at dawn. And I know that General 2 knows that I know that General 2 knows that I want to attack at dawn. But General 2 doesn’t know that I know that G2 knows that I know that G2 knows that I want to attack at dawn. If he doesn’t know this he might not attack at dawn.
Common Knowledge What the generals need is what Lewis calls common knowledge. It’s common knowledge among a group that P: • Everyone knows that P • Everyone knows that everyone knows that P • Everyone knows that everyone knows that everyone knows that P • Etc.
Common Knowledge Common knowledge might seem hard to get, but that’s not true. Imagine that there is no Jungle of Danger and the generals just meet the night before the attack.
City of Gold Attack at dawn!
General 1 Reasons… I know that G2 will attack at dawn, because he saw me say “Attack at dawn!” And I know G2 knows that I know that G2 will attack at dawn, because he saw me see him see me say “Attack at dawn!” And I know that G2 knows that I know G2 knows that I know that G2 will attack at dawn, because he saw me see him seeing me seeing him see me say “Attack at dawn!”
Lewis argues that conventions require not just following rules, but common knowledge.
Convention: Second Definition It is a convention for a group to follow a rule in a certain situation, if whenever they are in that situation: • It’s common knowledge that everyone follows the rule. • It’s common knowledge that everyone expects everyone else to follow the rule. • It’s common knowledge that it is a coordination problem. • Everyone following the rule is a solution to the coordination problem. • It’s common knowledge that the reason why they follow the rule is (3) and (4).
