Pivotal Voting

I was talking with Bernie Groffman just now and thought I'd make a record of the simple example of why apparent voting strength is not real voting strength. Suppose we have a committee on which Spain gets 50 votes, France gets 50 votes, and Andorra gets 1 vote. All have equal voting power, in fact. A winning coalition needs 2 and only 2 of the countries, and it doesn't matter which two.

Are the Tories Helping Gordon Brown?

A prominent Tory MP recently resigned to re-fight his election in protest against an extension of the 28-day imprisonment-without-cause rule to 42 days. That in itself doesn't make sense to me (his party already opposes the change, 28 vs. 42 seems to miss the point of suspending habeas corpus anyway, ... ), but TV pundits were saying that his party leader must be angry with him for shifting news attention away from Prime Minister Brown's unsteady position within the Labor Party.

I wonder whether the motivation might not be just that. Perhaps the Tories like Brown being at the head of Labor and are helping him out. The very oddity of the Tory resignation helps distract attention from Brown and allows the public mood to improve for him.

Two Game Theory Terms

From Wikipedia (my boldfacing):

A game in game theory is considered a potential game if the incentive of all players to change their strategy can be expressed in one global function, the potential function. The concept was proposed by Dov Monderer and Lloyd Shapley. Games can be either ordinal or cardinal potential games. In cardinal games, the difference in individual payoffs for each player from individually changing one's strategy ceteris paribus has to have the same value as the difference in values for the potential function. In ordinal games, only the signs of the differences have to be the same.

A game is a common interest game if it has a unique payoff-dominant outcome. Thus, a pure coordination game is not a common interest game, but ranked coordination is.

An Example Where Imperfect Message Transmission Helps. Myerson has an example on page 842 of this Handbook chapter with two possible states and three actions where communication fails if the messages always gets through, but helps some if they only get through half the time. Suppose the Sender knows the state of the world is A orB, with equal probability. The Receiver can choose X, Y, or Z. If the state is A, the Sender-Receiver payoffs are (2,3), (0,2), (-1,0). If the state is B, the Sender-Receiver payoffs are (1,0), (2,2), (0,3). If messages always get through, the Sender's message is irrelevant and the Receiver chooses Y, for a an expected payoff of 2 instead of 1.5 or 1.5. If the message is sent by a pigeon who gets shot down on the way with probability .5, then an equilibrium (not unique) is for the Sender to send the pigeon if the state is A but not if it is B and for the Receiver to choose X if the pigeon arrives and Y otherwise. Both players get higher expected payoffs as a result of using the "noisy" pigeon. See the link for more explanation.

Price Discrimination Terminology. Last week at the I.O. workshop someone had a good idea for replacing the old 1st, 2nd, 3rd degree price discrimination terminology. Exogenous-feature price discrimination is based on things the buyer can't change that the seller observes, such as his age. Endogenous-feature price discrimination is based on things the buyer can change, such as the quantity he buys or the quality he buys.

King Offa's Border Policy

I was reading about the border policies of King Offa, the Anglo-Saxon king of Mercia. He made no attempt to conquer Wales. Instead, he built Offa's Dyke, a boundary-marking ridge, and every few years he raided Wales. (Click here to read more.)

That is a common imperial boundary policy. Mark the boundary, so the barbarians know how far they're permitted to loot to, and if the barbarians make trouble, launch a punitive expedition and burn down some of their houses. Don't attempt to conquer them, because it's not worth the expense of keeping a garrison in a wasteland that won't yield much taxes anyway.

That's what we should have done in Iraq and Afghanistan, with the addition of pre-emptive expeditions to stamp out any preparations for barbarian raids.