Category: Games

Convexifying the choice set, an ongoing series

There is a new proposal for chess:

  • Slight Win: A player wins slightly if any of the following
    conditions hold:
    d. The opponent offers to concede a slight win and he or she agrees,
    e. He or she stalemates his or her opponent.
    f. Without making a move, a player calls the arbiter and proves that as
    a result of her opponent's last move, the same position has occurred thrice.

The player that wins slightly gets 4/6 points, and the player that loses slightly
get 2/6 points.

Why not go further and allow the players to bargain for a split sum of any magnitude?  "I offer you .5713 to stop playing now…"

Debating Economics

Intelligence Squared has held a series of debates in which they poll ayes and nayes before and after.  How should we expect opinion to change with such debates?  Let’s assume that the debate teams are evenly matched on average (since any debate resolution can be written in either the affirmative or negative this seems a weak assumption).  If so, then we ought to expect a random walk; that is, sometimes the aye team will be stronger and support for their position will grow (aye after – aye before will increase) and sometimes the nay team will be stronger and support for their position will grow.  On average, however, we ought to expect that if it’s 30% aye and 70% nay going in then it ought to be 30% aye and 70% nay going out, again, on average. Another way of saying this is that new information, by definition, should not swing your view systematically one way or the other.

Alas, the data refute this position.  The graph shown below (click to enlarge) looks at the percentage of ayes and nayes among the decided Underdogbefore and after.  The hypothesis says the data should lie around the 45 degree line.  Yet, there is a clear tendency for the minority position to gain adherents  – that is, there is an underdog advantage so positions with less than 50% of the ayes before tend to increase in adherents and positions with greater than 50% ayes tend to lose adherents.  What could explain this?

I see two plausible possibilities.

1) If the side with the larger numbers has weaker adherents they could be more likely to change their mind.

2)  The undecided are key and the undecided are lying.

For case 1, imagine that 10% of each group changes their minds; since 10% of a larger number is more switchers this could generate the data.  The problem with 1 and with the data more generally is that we don’t seem to see a tendency towards 50:50 in the world.  We focus on disputes, of course, but more often we reach some consensus (the moon is not made of blue cheese, voodoo doesn’t work and so forth).

Thus 2 is my best guess.  Note first that the number of “undecided” swing massively in these debates and in every case the number of undecided goes down a lot, itself peculiar if people are rational Bayesians.  A big swing in undecided votes is quite odd for two additional reasons.  First, when Justice Roberts said he’d never really thought about the constitutionality of abortion people were incredulous.  Similarly, could 30% of the audience (in a debate in which Tyler recently participated (pdf)) be truly undecided about whether “it is wrong to pay for sex”?  Second, and even more doubtful, could it be that 30% of the people at the debate were undecided–thus had not heard arguments in let’s say the previous 10 years that converted them one way or the other–but on that very night a majority of the undecided were at last pushed into the decided camp?  I think not, thus I think lying best explains the data.

Some questions for readers.  Can you think of another hypothesis to explain the data?  Can you think of a way of testing competing hypotheses?  And does anyone know of a larger database of debate decisions with ayes, nayes and undecided before and after?

Hat tip to Robin for suggesting that there might be a tendency to 50:50, Bryan and Tyler for discussion and Robin for collecting the data.

Questions that are rarely asked

Is euchre making a comeback?

I played frequently as a child, as I was taught by my partly Irish grandmother.  No one else in my grammar school knew the game.  Then I heard nothing about it for more than thirty years.  Now, twice in the last month, I've heard the game mentioned in public, "on the street" as it were.  What is up?

The alternative is that the question is rarely asked because, in fact, euchre is not making a comeback.

Levitt and Mankiw to Join Obama Team!

Steve Levitt and Greg Mankiw will join the Obama team.  Here is a key paragraph from the blog that broke this important story:

Colleagues at the University of Chicago economics department are cheering the move. “I could not think of a better choice than Steve Levitt to move to Washington and help the Obama team” says Nobel Laureate James Heckman, adding that he expects the job to occupy Levitt for two full Obama administration terms. “We will miss him, but he has an important job to do.”

Should chess moves be subject to copyright?

There has been a controversy:

Last week, ChessBase was apparently ‘forced to cease Internet broadcasting of the Topalov-Kamsky match’. As we noted
in our report on the first match game, live broadcasting of the chess
moves in this match without permission was prohibited by the Bulgarian
Chess Federation (although they didn’t seem to have a problem with
Chessdom’s, Crestbook’s, ICC’s and TWIC’s live coverage). This has led
to heated discussions on this site. The key question here is: can you copyright a chess move at all?

Plus this is transmission over the internet, so which law applies?  As I understand U.S. law, you can put chess moves into a book and the players have no rights to residual income from that book.  Which is how it should be.  Transferring income to chess players is not a goal per se.  Useful chess books usually contain many games, and requiring rights permission would make the volume harder to assemble.

Maybe grandmasters would play more games, or play better games, if they could charge for rights of reproduction.  When it comes to playing more games, I suspect there is already an ample supply of games and easy reproduction will do more to increase real consumption than spurring more contests over the board.  If anything is underproduced, it is the salience of the games which have been played (take a game between two 2550 players and call it "Clash of the Titans" and produce more excitement; most chess players won't know the difference between that and a game between the two best players at 2770.) 

And better chess?  I believe the effort elasticity is low with respect to residual rights income from reporting of the games.

Comparable debates have been held over residual rights to reporting real time stock prices and NBA scores.

Try to predict shifts in relative prices!

Matt Yglesias asks:

Brad DeLong observes
“In Agatha Christie’s autobiography, she mentioned how she never
thought she would ever be wealthy enough to own a car – nor so poor
that she wouldn’t have servants.”

This kind of thing gets a bit hard to get one’s head around when
thinking about the future. What do you think will be the equivalent 100
years from now of Agatha Christie’s car and servants?

I await your answers.

Odd terms

Isn't it funny how they call them the "toxic assets"?  OK, a lot of them aren't worth very much.  But would it not be better to speak of the "toxic liabilities"?  This may sound like a semantic point, but the toxic assets terminology breeds the idea that the mere creation of a "bad bank," built from these assets, will boost the financial system.  It won't.

Overpaying for the toxic assets is another matter entirely.  Yves Smith, by the way, has a good critique of current bank aid proposals and of course Paul Krugman has been making related arguments.  The frightening thing is that many brilliant people — such as those on the Obama team — think this is the best we can do, all constraints taken into account.  We'll see, as they say.

The other development is the proposal to limit executive pay to $500,000 for any bank taking "large amounts" of bailout funds; maybe that is the secret plan for keeping the bailout plan affordable.  The drawback is that it discourages relatively healthy banks from using the funds to buy out the sick banks which, although it sounds inappropriate, is actually one of the better chances for making the program work.

The median voter theorem, in action


Steven Chu, the Nobel laureate scientist who is President-elect Obama’s choice to be energy secretary, said in testimony prepared for his Senate confirmation hearing Tuesday that high oil prices were a threat to the economy, backing away slightly from statements made in his last job, as director of the Lawrence Berkeley National Laboratory, that gasoline prices should be higher.

Here is the story.  Technically speaking, all of his words are correct and do not contradict each other.  Still, if he can't get appointed for favoring higher gas prices, and in a honeymoon period at that…well…you see where this is headed.

More Krugman-Bush captions

Sadly typepad is slow with some comments, I believe due to a switch of platforms (you’ll notice some funny formatting and spacing in some posts as well; our apologies).  Some of the Krugman-Bush photo captions are still not up but I wanted to pass along a few of my not-yet-published favorites.

Can you show me that ‘push on a string” trick again?

Paul, I did everything I could to make that book of yours,
The Return of Depression Economics, a bestseller.

Boy, did we put one over on those gullible Americans

“I’m glad this is almost over, he must not understand what I

“They think we actually believe the $hit we say; pretty
funny, huh?”

My favorite is: “So Paul, ever been to Cuba before?”

If you think you can beat these, please let further suggestions in the comments on this post.