PolySciFi Blog

The Most Dangerous Game, now at the Criterion Contraption.
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Just because I swore I would bring up this topic quasi-monthly, I'm posting this highly related story: British woman marries a dolphin:(h/t KLo)

An unusual wedding ceremony was held in the southern resort town of Eilat on Wednesday, as Sharon Tendler, a 41-years-old Jewish millionaire from London married her beloved Cindy, a 35-years-old dolphin, Israel's leading newspaper Yedioth Ahronoth reported Thursday.

...

After the ceremony was sealed with some mackerels, Tendler was tossed into the water by her friends so that she could swim with her new husband.

I'm the happiest girl on earth," the bride said as she chocked back tears of emotion. "I made a dream come true, and I am not a pervert," she stressed.

Ummm... I'll go out on the limb and say that if they consecrate their marriage, she most certainly is a pervert.

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That's what a letter identified in the LAT says about what Upton Sinclair was told by their lawyer. (h/t Jane Galt)

In related news, OJ is still looking for the real killers.
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Taste of Cherry, now at the Criterion Contraption.
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Via Dave, comes this wonderful collection of "facts" about Chuck Norris which include the following:

Chuck Norris' tears cure cancer. Too bad he has never cried.

Chuck Norris once ate three 72 oz. steaks in one hour. He spent the first 45 minutes having sex with his waitress.

As a teen Chuck Norris impregnated every nun in a convent tucked away in the hills of Tuscany. Nine months later the nuns gave birth to the 1972 Miami Dolphins, the only undefeated and untied team in professional football history.

Chuck Norris sleeps with a night light. Not because Chuck Norris is afraid of the dark, but the dark is afraid of Chuck Norris

The quickest way to a man's heart is with Chuck Norris's fist.

Chuck Norris is 1/8th Cherokee. This has nothing to do with ancestry, the man ate a f*&king Indian.

Go read the rest of the top 30 Chuck Norris facts if for no other reason so you'll know what in the world Dave is talking about at the next Neel family reunion.
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A few different polyscifi fantasy leagues wrapped up this weekend. Here's the results:

Fantasy Football (with some 12 entrants)
1. Jacque's Straps (Jody Neel)
2. Giant Fezziks (David Neel)
3. The Nanothinkers (Roger Craig)

Reverse Fantasy Football (with some 8 entrants)
1. Fightin Illini (Michael Parks)
2. SeriousDarkHelmet (Brandon #1)
3. Rush Interference (Thason Jweatt)

NBA Survival League 1(New league to start on Sunday)
1. Jody
2. Thason (Incorrect Pick: LA over DC Dec 26), Spakkadi (Incorrect Pick: Memphis over Utah Dec 26)
4. Mike M. (Incorrect Pick: Denver over Atlanta, Dec 18)
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There really seems to be a Bob Loblaw Law Blog. And it's not a joke--it actually has summaries of federal appellate decisions.
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The Red Shoes, new at the Criterion Contraption.
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Survivors: Thason, Robin, Jody
Eliminated: No eliminations this round
Previous Entry Results

Survivors: 1) pick a game on Sunday or Monday, 2) pick a winner of that game, and 3) leave a comment to this post with your game and its winner.

Everyone else: We'll crap out soon enough and start another league...

Additional league info here. NBA schedule here.
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I ran across a citation question today that I don't know the answer to. I was thinking that maybe the writers in the audience might be able to steer me in the right direction.

The question: if an author changes his/her/its name after originally publishing the work you wish to cite, do you cite the author as he/she/it was called when published, or as he/she/it is called now?

If it helps, a) the particular author in question is the GAO which changed its name in 2004 from the General Accounting Office to the Government Accountability Office, and b) in a situation you may have been more likely to run across - what do you do when an author drops their maiden name for all future publications?

Currently, I'm leaning towards adopting a general practice of using the name under which the work was published, but I can see where that might not make sense for online government publications - in another couple years, if someone goes searching online for the General Accounting Office, I doubt that they'll still get an automatic redirect; at the same time I don't expect the Library of Congress to recatalogue works by people who change their name, but I think they might for Congressional agencies.
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Two bits about gambling from America's favorite dead stoner:

You know when you see an advertisement for a casino, and they have a picture of a guy winning money? That's false advertising, because that happens the least. That's like if you're advertising a hamburger, they could show a guy choking. "This is what happened once."

I saw a billboard for the lottery. It said, "Estimated lottery jackpot 55 million dollars." I did not know that was estimated. That would suck if you won and they said, "Oh, we were off by two zeroes. We estimate that you are angry."
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The decision in Kitzmiller et al. v. Dover Area School District is available here. The judge found in favor of the plaintiffs, which is to say in favor of science. Here's the best part of the decision:

To be sure, Darwin’s theory of evolution is imperfect. However, the fact that a scientific theory cannot yet render an explanation on every point should not be used as a pretext to thrust an untestable alternative hypothesis grounded in religion into the science classroom or to misrepresent well-established scientific propositions.

The citizens of the Dover area were poorly served by the members of the Board who voted for the ID Policy. It is ironic that several of these individuals, who so staunchly and proudly touted their religious convictions in public, would time and again lie to cover their tracks and disguise the real purpose behind the ID Policy.

With that said, we do not question that many of the leading advocates of ID have bona fide and deeply held beliefs which drive their scholarly endeavors. Nor do we controvert that ID should continue to be studied, debated, and discussed. As stated, our conclusion today is that it is unconstitutional to teach ID as an alternative to evolution in a public school science classroom.

Those who disagree with our holding will likely mark it as the product of an activist judge. If so, they will have erred as this is manifestly not an activist Court. Rather, this case came to us as the result of the activism of an ill-informed faction on a school board, aided by a national public interest law firm eager to find a constitutional test case on ID, who in combination drove the Board to adopt an imprudent and ultimately unconstitutional policy. The breathtaking inanity of the Board’s decision is evident when considered against the factual backdrop which has now been fully revealed through this trial. The students, parents, and teachers of the Dover Area School District deserved better than to be dragged into this legal maelstrom, with its resulting utter waste of monetary and personal resources.

As Michael noted when commenting on the lawsuit against the UC system, the real tragedy is the "utter waste of monetary and personal resources" that these battles cause. It should be noted that Judge Jones was appointed by George W. Bush.

Oh, also, this Doonesbury is pretty good.
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Survivors: Thason, Robin, Jody
Eliminated: Mike
Previous Entry Results

Survivors: 1) pick a game on Wednesday or Thursday, 2) pick a winner of that game, and 3) leave a comment to this post with your game and its winner.

Everyone else: We'll crap out soon enough and start another league...

Additional league info here. NBA schedule here.
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An insightful interview with C3PO at Cracked. Basically, all the rumors you've heard (and more!) are true. An excerpt:

After a couple of white wine spritzers, Vader was all over me. A bit of a lightweight with the booze, between you and I. The things he said to me that night...

"C-3PO, I hear that gold is a very pliable metal."

A very long history of the Sith.

Everything you wanted to know about the Death Star and more. Excerpt:

The inspiration for the Death Star came from a Separatist super-weapon called the Great Weapon. The Great Weapon was a moon sized-space station with a large laser cannon developed by the Trade Federation, Geonosians, and Techno-Union for use in their war against the Old Republic. It was never put to use and was captured by the newly formed Empire after the Clone Wars. The Great Weapon was never completed.

How a Light Saber Works, which includes some surprising uses...

If you are lucky enough to acquire a lightsaber, you are probably purchasing it for personal defense purposes. A lightsaber completely blows away a can of pepper spray as a deterrent in muggings or robberies. However, many new owners are pleasantly surprised by the many domestic uses of a lightsaber around the home or office.

Chewbaca sings Silent Night as only he can.

Stalin tried to breed Wookie warriors or at least that's how I interpret the article:

According to Moscow newspapers, Stalin told the scientist: "I want a new invincible human being, insensitive to pain, resistant and indifferent about the quality of food they eat."

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Seinfeld:

On my block, a lot of people walk their dogs and I always see them walking along with their little poop bags. This, to me, is the lowest activity in human life. Following a dog with a little scooper. Waiting for him to go so you can walk down the street with it in your bag. If aliens are watching this through telescopes, they're going to think the dogs are the leaders of the planet. If you see two life forms, one of them's making a poop, the other one's carrying it for him, who would you assume is in charge?

But what if the aliens harvest animal poop for dark matter fuel?
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League Details
Survivors: Everyone - new league
Available picks: All teams/games

To enter, 1) pick a game on Sunday or Monday, 2) pick a winner of that game, and 3) leave a comment to this post with your game and its winner.

Additional league info here. NBA schedule here.
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As I seem to have a little free time (papers and interviews are looming though, so we'll see how long this holds up), I thought I would go ahead and start the polyscifi NBA survival league.

In general, a survival league works as follows.

a) Each "turn", the remaining players choose a team that they think will win a particular game during that turn from among the teams they have not yet chosen to win.
b) If a player's team loses, then that player is eliminated.
c) If a player's team wins, then that player is among the pool of players that returns to step a) for the next turn.
d) Play continues until a single player is left. In the event that all remaining players are simultaneously eliminated, we'll just call everyone a loser.

For the purposes of the polyscifi league, we'll have a NBA based league with two turns a week, occuring on Sundays and Wednesdays. You can pick a winner for any game on that day or the next (i.e., Sunday and Monday for Sunday; Wednesday and Thursday for Wednesday) assuming you haven't picked that team before.

As I don't know of any free site that supports a NBA survival league (or for that matter a pay league), we'll run it on polyscifi. To facilitate the entries, I'll make a sticky post at least the day before (Saturday, Tuesday) that stays at the top of the page until at least 12:00 AM EDT on the turn day (Sunday or Wednesday). If you're interested in playing leave a comment in the post with your pick (winner, loser & game time).

No prizes, just pride on the line, by which I mean a bunch of lions which you'll have to travel to Africa and bag yourself. If you lose out quickly, don't worry as we'll start up another survival league at the end of each survival league - which tends to come quickly as after the the first few turns, it becomes little more than a crap shoot (Do I pick Atlanta or Toronto?... hmmm....).
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Via balloon juice comes this story

Municipal regulations normally ban anything from smoking in public places to parking in certain zones.

But officials in the Brazilian town of Biritiba Mirim, 70km (45 miles) east of Sao Paulo, have gone far beyond that.

They plan to prohibit residents from dying because the local cemetery has reached full capacity. [emphasis mine]

Well, hopefully if they repealed death, a repeal of taxes can't be far behind.

Update
For the few Pittsburgh readers we may have, rest assured, your lack of zombie preparedness will presumably keep your city from passing a similar ordinance.
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(Meta-blogging note - I'm having camera difficulties, or more accurately problems with msi - which says to me that it's time to reinstall the OS - so I still haven't gotten the pictures off my camera.)

I had a little time this morning to think over the pirate problem and I've decided the problem is ill-formed because of the wildly differing equilibria that result from changes in assumptions.

Suppose we make the following assumptions

• The pirates can't offer fractional gold pieces
• The pirates exhibit perfect Nash rationality
  
• Pirates weakly time discount, i.e., given two equivalent solutions, they prefer to take their first chance to take the equivalent solution
  
• Pirates don't die, they live on to fight ninjas
• Promises aren't binding
  

Note that if I change some of those assumptions, I get different solutions, which I'll illustrate in a bit.

Under those assumptions, the following backwards induction makes use of Thason's nomenclature which would appear a bit odd after 5 pirates, but fortunately we don't have to get there. Also for brevity, I'm listing payoffs as vectors cause I'm a dork like that (and I think it's clearer).

3 Pirate Scenario (3,4,5)
Technically, in this scenario, there are some 1+ 100x101 possible allocations to consider, which is quite a few. But how many are Nash equilibria? Thason notes that (99,0,1) is an equilibrium under some assumptions, but (99,0,1) is not an equilibrium for weak time discounting. Why?

Because pirate 5 is obviously indifferent to (100,0,0) (the result if 5 votes yes) and (0,100,0) (the result if 5 votes no). If we assume weak time discounting (which I think is a fine assumption), by accepting (100, 0, 0) 5 is slightly better off by voting yes and and getting the process over with a stage sooner (unless, of course, there's a pressing ninja problem). Thus (99,0,1) is not an equilibrium as 3 can improve his payoff by offering (100,0,0) which will be accepted because of weak time discounting.

4 Pirate Scenario (2,3,4,5)
Reasoning backwards to the 4 pirate scenario and applying weak time indifference, pirate 4 can offer (100,0,0,0) and be ok as 4 and 5 are indifferent to that outcome to an outcome of (100,0,0) and would prefer the whole thing just end by voting yes.

With weak time discounting, the problem scales up rather quickly to the most senior pirate getting everything, i.e., the allocation vector (100,0,0,...,0).

Considering some changes in assumptions, we get the following

• If we remove weak time discounting, but keep the other assumptions, and assume that when pirates are indifferent they flip a coin (some mechanism must be in place for resolving indifference), then we get Thason's solution (by risking the indifference of pirate 5 with an offer of (100,0,0), pirate 3 reduces his expected payoff to 50 from 99).
  
• If we remove weak time discounting, but kill pirates when offers fail and assume that no pirate wishes to kill another pirate when indifferent to allocations (it would presumably reduce future booty), then we get the (100,0,0,...,0) solution again (thus ties are broken in the favor of the offerer).
• If we remove weak time discounting and kill pirates but don't care about other pirates dying, then Thason's solution is the right solution (pirate 3 can't risk the indifference of pirate 5).
• If we remove weak time discounting, and permit fractional gold, then a solution different from those presented so far emerges. (Would depend on the smallest fractional size allowable).
• If promises are binding, then we get more solutions than I care to think about as the game transforms into a quasi-coalitional game which generally have a shload of equilibria (including Roland's) (mmmm.... Cores and Shapley values....)
• If the pirates aren't perfectly rational, then we're going to have to define their thought processes before I analyze the situation.
  

So if we tweak the assumptions around just a little, we get a bunch of different results. We've also implicitly assumed that there are no observable precommitments being employed (e.g., the burning dollar problem.)

So the takeaway from this little analysis is the following: because how to handle indifference is not clearly defined in the problem statement, changing reasonable assumptions results in radically different solutions.
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In the demo version of Whitesnake's "Here I Go Again," the line is "Like a hobo I was born to walk alone." Just thought you should know.
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There's an interesting discussion at the Volokh Conspiracy about hostility to atheists in America. Apparently we're more unpopular than even homosexuals when it comes to running for political office. Of course, part of the problem is that the atheists who do end up in the public eye tend to be nutjobs; the discussion began because of an email exchange between Eugene Volokh and a candidate for Alabama Attorney General who is not only an atheist but a holocaust denier and a David Duke supporter. Thanks, amigo! You're making things easier for me. Anyway, my favorite thing in the comments: someone brought up this old chestnut:

The comparison of largely Judeo-Christian America with the Marxist/atheist-police-state-of-your-choice seems to offer some pretty good emperical [sic] evidence.

and got this reply:

This does yield a pretty good result, but is a bit like comparing liberals to dog-raping, necrophiliac conservatives.

On a similar note, I recently read, and very much enjoyed Imagine There's No Heaven, an essay about atheism by Sam Harris. Harris is too much of a firebreather to make anyone who doesn't already agree with him pause for thought. But he's very good on the fuzzy thinking behind religious moderation.

While fundamentalists justify their religious beliefs with extraordinarily poor evidence and arguments, they at least they make an attempt at rational justification. Moderates, on the other hand, generally do nothing more than cite the good consequences of religious belief. Rather than say that they believe in God because certain biblical prophecies have come true, moderates will say that they believe in God because this belief “gives their lives meaning.” When a tsunami killed a few hundred thousand people on the day after Christmas, fundamentalists readily interpreted this cataclysm as evidence of God’s wrath. As it turns out, God was sending humanity another oblique message about the evils of abortion, idolatry and homosexuality. While morally obscene, this interpretation of events is actually reasonable, given certain (ludicrous) assumptions. Moderates, on the other hand, refuse to draw any conclusions whatsoever about God from his works. God remains a perfect mystery, a mere source of consolation that is compatible with the most desolating evil.

...

It is perfectly absurd for religious moderates to suggest that a rational human being can believe in God simply because this belief makes him happy, relieves his fear of death or gives his life meaning. The absurdity becomes obvious the moment we swap the notion of God for some other consoling proposition: Imagine, for instance, that a man wants to believe that there is a diamond buried somewhere in his yard that is the size of a refrigerator. No doubt it would feel uncommonly good to believe this. Just imagine what would happen if he then followed the example of religious moderates and maintained this belief along pragmatic lines: When asked why he thinks that there is a diamond in his yard that is thousands of times larger than any yet discovered, he says things like, “This belief gives my life meaning,” or “My family and I enjoy digging for it on Sundays,” or “I wouldn’t want to live in a universe where there wasn’t a diamond buried in my backyard that is the size of a refrigerator.”

The full article is worth reading (but be prepared for a pretty scathing tone) and can be found here. My own feeling is that a lot more people are atheist or agnostic than are willing to admit it, because atheism still bears a heavy professional and social stigma in most of this country.
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Just saw Joe Dante's "Homecoming" on a promotional DVD (thanks, Gersh Agency!) It's really funny, very angry, and the most direct movie about the Iraq war yet. If you haven't seen it or read about it, the premise is that a political consultant, booked on the same talk show as a Cindy Sheehan-type mother, tells her "If I had one wish . . . I would wish for your son to come back," so he could assure the country of the importance of the war. Well, he gets his wish; all the Iraq dead come back, and demand to vote against the incumbent president who sent them to their graves. There are a lot of nice little touches: the first zombies rise from their flag-draped coffins at Dover Air Force Base, and the two soldiers on duty split up because they're trying to stop a journalist from taking photographs of the coffins. Highly, highly recommend watching this as soon as it's available (which is right now, if you have Showtime). The last shot is fantastic.

On a more serious note, Syriana is also very good if you're willing to pay close attention. It seems to be getting a lot of heat from the right, but the fact is, it's not a particularly leftist film. Like Traffic, it's more of a "what a big goddamned mess we've made" movie. Oh, and while I'm at it, I can't recommend Capote too highly.
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As always, say my name and I appear.

I had some time to spend away from my final exam grading, so I decided to explain yet another of Jody's oblique references. This time, it happened most of the way down this post.

But more than that, I want to throw something out that will hopefully provide fuel for what I see as the two things best accomplished by the blogosphere: people expressing their opinions, and people blowing holes in the opinions of others.

And away we go...

Recently, I've taken up the habit of posting brain teasers and other such puzzles on my office door. It gives the people who are waiting to see me something to do while they wait. It's something I should have done a long time ago, back when I had larger crowds filling the hallways, but that's a different story altogether.

In any event, one of the puzzles that I posted ended up sparking a discussion between Jody and myself concerning the invalidity of its solution vis a vis its stated parameters. Only recently - one morning in the shower, no less - did I realize that we had ourselves ignored the stated parameters of the problem in the analysis we made of its flaw. Our potential mistake could actually restore the validity of the original solution. Unfortunately, I'll have to divulge the solution to give you the chance to give you the chance to analyze the problem, the solution, the "problem" with the solution, and the problem with the "problem" with the solution. (Whew!)

I invite you to leave comments concerning the flaw in my own logic.

First, the problem:

A band of five pirates have collected 100 gold pieces in loot. The five pirates decide to divide the loot according to the following procedure:

1. The most senior pirate proposes a division of the gold among the five pirates.
2. If at least 50% of the pirates vote in favor of the division, the gold is divided in the manner proposed.
3. If the vote fails by the requirements of point #2, the most senior pirate is killed, and the next most senior pirate makes a new proposal, per point #1.

All of the pirates are very greedy (each one wants as much money for himself as he can get) and very intelligent (each one will take action to ensure that he receives as much money for himself, and knows that the others will do so as well). But above all, none of the pirates wants to die.

As the most senior pirate, what proposal do you make that will maximize your take and keep you alive?

The primary mode of solution is to work backwards. Let's take the pirates to be numbered 1, 2, 3, 4, and 5, in descending order of seniority.

If there were only one pirate (Pirate 5), he would propose to take 100 gold pieces for himself, and he would vote in favor of his proposal.

If there were two pirates (4 and 5), then Pirate 4 can always propose that he recieve 100 gold pieces, and that Pirate 5 receive nothing. Further, by voting in favor of the proposal, it succeeds with a vote of 50%.

Things get serious when three pirates are involved. According to the previous development, Pirate 3 knows that Pirate 4 will get all of the money if Pirate 3's proposal fails. He also knows that Pirate 5 knows this. Therefore, Pirate 3 has to buy Pirate 5's vote with more money that Pirate 5 would get under Pirate 4's proposal. Since Pirate 5 will get nothing under an eventual proposal by Pirate 4, that amount happens to be 1 gold piece. So Pirate 3 proposes the following division: 99 gold pieces for Pirate 3, 0 gold pieces for Pirate 4, and 1 gold piece for Pirate 5.

Pirate 3 votes in favor of the proposal - after all, he's making out like a bandit, or a buccaneer, or some such. Pirate 4 votes against the proposal - he knows he can do better than 0, and so has every incentive to see Pirate 3 walk the plank. Pirate 5 votes in favor of the proposal - he knows that he'll do worse if Pirate 4 makes the proposal, and that Pirate 4's proposal will pass. So Pirate 3's proposal passes.

We'll come back to this point in a moment.

With 4 pirates, Pirate 2 must now buy one vote. By the previous development, Pirate 2 knows that Pirate 3's proposal will pass as described above. Pirate 2 therefore proposes the following division: 99 gold pieces for Pirate 2, 0 gold pieces for Pirate 3, 1 gold piece for Pirate 4, 0 gold pieces for Pirate 5. Pirates 3 and 5 will vote against the proposal - they both know that they can do better under an eventual proposal by Pirate 3. Pirate 4 will vote in favor of the proposal - he knows that he is doing better now than he will under a proposal by Pirate 3, which will pass as described above. So Pirate 2's proposal passes.

It should be trivial to demonstrate to yourself that Pirate 1 will propose 98 gold pieces for Pirate 1, 1 gold piece each for Pirates 3 and 5, and nothing for Pirates 2 and 4. The proposal will pass with the affirmative votes of everyone receiving money.

Now for the "problem"...

Since the pirates value their lives above money, then instead of viewing each proposal as the having senior pirate buying votes, we should view each propsal as the having the senior pirate buying his life!

With three pirates in play, suppose that it occurs to Pirate 5 to tell Pirate 3, "Give me all the money, or I'll vote to kill you." On the face of it, this is a credible threat. A pirate would never vote against his own proposal, as it puts him one vote closer to sleeping with the sharks. Pirate 5 also knows that Pirate 4 can do better, so he'll vote no anyway. In this situation, Pirate 5 would seem to hold the balance of power, and can (apparently) charge mightily for his services.

This is the point where Jody and I finished looking at the problem, noting that this flaw throws off all of the development that followed it above. In looking elsewhere for commentary on the problem, I found proposals that would correct this seemingly glaring flaw. Among them, constraints on discussion among the pirates before votes (something that I don't think helps as much as it could given that all of the pirates are intelligent enough to figure out all possibilities for themselves) and the replacement of killing the senior pirate with simply disqualifying him from a share of the booty if his proposal fails.

But maybe...just maybe, the simplicity of the original problem shows its genius.

To pick up with the "flaw" in the three-pirate game, Pirate 5 has a moment of clarity that chases away the feeling that people get when they are flush with victory. "Wait a minute. Both of the other pirates know that I can make that threat. Pirate 4 doesn't have to do anything, since if it falls to him to make the proposal, he'll get everything. But he also has to know that he won't get anything under my 'pre-proposal'..."

What we've hit upon here is that Pirate 5 knows that everyone knows that any 'pre-proposal' that he makes to Pirate 3 will result in a division of the booty, since Pirate 3 won't vote to kill himself.

Pirate 5 goes on thinking..."If Pirate 4 knows that he has a 100% chance of getting nothing if I get everything, he'll change his behavior. When I make my threat, Pirate 4 will no doubt think for a moment, and then he'll say. 'Alright, give me 99 gold pieces, or I'll vote to kill you.'"

While it is true that Pirate 4 knows that he would do better than 99 gold pieces if he got to make the proposal, he also knows that he'll never get to make the proposal based on whatever division satisfies Pirates 3 and 5. His only recourse is to make a threat that is "equally credible" but less costly monetarily to Pirate 3. Knowing what we (and they) know about Pirate 3's need to buy one of their votes (because really, we're back to that again), what we have here is a price war. Really, either pirate can threaten, but the other knows that if the threat goes unchallenged with a counter threat, that the initial threat will be accepted.

Pirate 5 continues..."Of course, I can bid down my 'services' to 98 gold pieces, but at that rate, eventually, Pirate 4 will bid 1 gold piece, and I'll get nothing. I might as well be the one to get the 1 gold piece, so I'll just keep my mouth shut."

Here's what we've figured out:

1. Pirate 3 only has to have one of the two less-senior pirates vote for him, and thus any threat made by one of the two guarantees that it will be accepted, unless the other one of the two can do "better" for Pirate 3.
2. Pirate 4 need not make a threat initially, since he'll get all of the money if Pirate 3 dies. However, rather than risk getting cut out of the money if Pirate 5 makes a threat, Pirate 4 will always make a threat that involves Pirate 3 giving away one less gold piece than does Pirate 5's threat. Even though he could do better if he gets the proposal, he knows that he has no chance of doing better if Pirate 3 accepts any threat made by Pirate 5.
3. The only threat that from Pirate 5 that Pirate 4 can't trump is a threat of 1 gold piece for Pirate 5. Rather, he could trump it, but wouldn't. He wouldn't propose to Pirate 3 that he keep all of the money, and this proposal wouldn't be accepted by either of the other two pirates anyway.
4. If Pirate 4 were to make the pre-emptive threat "Give me all of the money," the same development finds Pirate 5 bidding all the way down to 1 gold piece.

Therefore, even though Pirate 3 is buying his life, he can buy it cheaply since either of the other two pirates is in the same position to sell it to him. Further, each of them wants to get something out of the transaction knowing that they both can't.

Or can they? Can one of the two less-senior pirates buy the vote of the other less-senior pirate? Suppose that either Pirate 4 or Pirate 5 tells Pirate 3 "Give me x gold pieces, and give the other pirate (100-x) gold pieces, and I'll vote for you to live." The other pirate can always say, "I won't vote for that, but give me [1oo-(x-1)] gold pieces, and give the other pirate (x-1) gold pieces, and I'll vote for you to live." This will (or could) continue up to the limit point of one pirate "asking" for all of the money, and we've seen the "obvious" problem there.

It would seem though, that the equilibrium offer is 1 gold piece to whoever can't do better under any other circumstances. The "whoever" in this case is Pirate 5, which restores the situation in the original solution and presumably, the rest of the solution as well.

For those of you who cared to get this far, final thoughts and questions to which you can respond in the comments:

1. Where is the flaw in my new logic? Or were Jody and I just that "dumb"to have missed it the first time around?
2. Does the restoration of the three pirate case result in the restoration of the entire solution, or is there a credible threat in the four pirate case (where I suspect not, since the senior pirate only has to buy one vote from a non-senior pirate) or in the five pirate case (which I haven't analyzed)?

Wow, that was fun. I really need to get back to this. But for now, I have to get back to work. Or...playing Civ. Reviews of Civ 4 would also be accepted as comments, since I don't think my computer will run it.

Yarrrrr!

Update #1

I have read commentary elsewhere about the potential meaning of pirates casting "communicative sub-optimal votes." For example, in the five pirate case, Pirate 3 could vote "no" even though 1 gold piece is the most money he could hope for if every pirate plays the game true-to-form. He does this on the assumption that:

1. 1 gold piece is not a lot to lose, given that he could get more than that if other things go his way.
2. Turning down more money than he could get could communicate information to Pirates 4 and 5, namely, that he is willing to settle for less money than he could get under his best circumstances, given that he has already run the risk of getting less money than he would under the expected circumstances.

To some degree, this goes against one of the stated premises - that the pirates are each looking to maximize his gain given that he knows that all of the other pirates are looking to do the same. But if you still want to discuss the role of that piece of human nature in the game(that of - gasp! - compromise) please feel free.

Update #2

Thanks for the commentary! I've responded to a few of them to address some issues that may have been my fault in not explaining very well.

I'm almost sufficiently encouraged to get back into a regular schedule of writing more than once a season...work permitting, of course. Maybe I'll make a puzzler column or something - it works for Car Talk!

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I'm not going to shed tears for Tookie Williams one way or the other, but since we've been talking about the death penalty here recently, this story caught my eye:

So imagine it's around midnight and you're sound asleep with your eighteen-month-old daughter. You're woken by someone dressed in black paramilitary gear kicking down your door. This isn't in Iraq, and you have no criminal record. You do have a gun, with which you attempt to defend yourself. Unfortunately, you're a good shot, and the man you shoot is a police officer; worse, the son of the local police chief. Worse yet, you're black, he's white, and you both live in Prentiss, Mississippi (in Jefferson Davis County, which should give some picture of race relations there). This was Corey Maye's crime, and for it, he's currently sitting on death row. Some more relevant things about the case, before you jump to any conclusions:

• The police officers had a warrant to search Corey Maye's neighbor's house, not his; the two men shared a duplex. After raiding his neighbor's house, they went around to the side door, not realizing it was a separate residence. There's disagreement over whether they announced themselves as police officers before kicking the door in; the police say they did, Maye says they didn't (or perhaps they did, but he was asleep). There's little reason to believe they would have, since they believed they were re-entering the same house by another way.
  
  
• Maye had no previous criminal record. Police did find the remains of a marijuana cigarette in one of his ashtrays, but no other drugs.
  
  
• Maye's name wasn't on the warrant; police entered his home illegally (albeit by mistake).
  
  
• Mississippi law defines justifiable homicide as "When committed in the lawful defense of one's own person or any other human being, where there shall be reasonable ground to apprehend a design to commit a felony or to do some great personal injury, and there shall be imminent danger of such design being accomplished..." I think a jackboot breaking down your door at midnight qualifies as "reasonable ground to apprhend a design to commit a felony."
  
  
• Maye's jury was all-white. According to his lawyer (who isn't necessarily the most reliable source on this, since she lost what would seem to have been a slam-dunk case), two jurors told her after the trial that "the consensus among jurors was that Maye was convicted for two reasons. The first is that though they initially liked her, Maye's lawyer, the jury soured on her when, in her closing arguments, she intimated that if the jury showed no mercy for Maye, God might neglect to bestow mercy on them when they meet him in heaven. They said the second reason May was convicted was that the jury felt he'd been spoiled by his mother and grandmother, and wasn't very respectful of elders and authority figures."

The Agitator has more here, and here. I think that this case should be a rallying point for anti-gun control, anti-government intrusion libertarians; it seems to be pissing John Cole off, not to mention Glenn Reynolds, which is a good sign.

I think problems like this (dumb decisions by juries, incompetent counsel, over-aggressive prosecutors, &c., &c.) are endemic to our justice system and none are easily solved. I think as long as they're part of the problem, it doesn't make sense to allow our courts to impose the ultimate penalty, even though there are cases where I believe it is deserved. Allowing it in truly exceptional cases leads inevitably to common-place applications, which leads to mistakes that cannot be part of a just civil society. Allowing the state of Mississippi to execute Corey Maye would be one of those mistakes.

UPDATE: Here's Maye in his own words, from the Hattiesburg American:

Cory Maye, 23, said he was asleep on a chair in the living room of his Prentiss apartment as his 14-month-old daughter slept in the bedroom when he heard a loud crash at his front door. "I immediately ran to my daughter's room, got a pistol, put in a magazine and chambered a round," said Maye, who is on trial for capital murder in Marion County. "As I laid on the floor by the bed, I heard kicks at the back door. I was frightened, I thought someone was trying to break in on me and my daughter."

Maye testified that it was dark in his apartment when he heard someone breaking into the back door, which was located in the bedroom. "That's when I fired the shots," Maye said. "After I fired the shots, I heard them yell 'police! police!' Once I heard them, I put the weapon down and slid it away. I did not know they were police officers."

Disgraceful.

Update: It appears there was a separate warrant to search Maye's residence; so the officers weren't there illegally. However, there are still any number of problems with executing Maye for what happened that night; I recommend reading The Agitator on this story as it develops.
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Tom at Digital Warfighter has the definitive discussion of "the war on christmas." You can find it here, but here's his comment in full:

Is Christmas becoming a dirty word?

Yes. It is. Why? Because now I am embarassed to say “Merry Christmas” for fear of being mistaken for some crack-smoking conspiracy monger. Thanks for saving the holiday, you fucking loons.

Happy Holidays, everybody!
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Andrew Sullivan points out two interesting passages today. The first is from Dogs of God: Columbus, the Inquisition, and the Defeat of the Moors, and describes Torquemada's methods:

When the rack did not produce the desired result, the churchmen turned to the water torture. In this hideous remedy, the prisoner was tied to a ladder that was sloped downward, so that the head was lower than the feet. The head was held fast in position by a metal band, twigs were placed in the nostrils, and ropes winched tightly around his appendages. The mouth was forced open with a metal piece and a cloth placed over the mouth. Then a pitcher of water was brought, and water poured over the cloth. With each swallow, the cloth was drawn deeper into the throat, until in gagging and choking the victim nearly asphyxiated. The terror of suffocation was extreme, and the process was repeatedly endlessly, bloating the body grotesquely until the victim was ready to confess ... From the inquisitor's standpoint — for he was there to record every detail — the treatment was easy to administer and left no telltale signs.

The second passage is from the CIA's description of "Enhanced Interrogation Techniques":

The prisoner is bound to an inclined board, feet raised and head slightly below the feet. Cellophane is wrapped over the prisoner's face and water is poured over him. Unavoidably, the gag reflex kicks in and a terrifying fear of drowning leads to almost instant pleas to bring the treatment to a halt.

As Sullivan points out, we don't make our prisoners swallow the cellophane. The rest of the experience is identical. And note that Torquemada saw this as worse than the rack. Here's what it looks like. But as our president so helpfully reminds us, we do not torture. And neither did Torquemada, as long as he was waterboarding. Your tax dollars at work, ladies and gentlemen.
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(I appear to have a little free time, so I thought I would actually post something. Look for more this weekend as it will be post-semester including pictures of Matt, Mike Parks, and I chowing down on some Mexican food and drinking some beer.)

Implicitly in this post, and more explicitly in the comments Matt raises the following problem:

Assuming the death penalty deters as advertised and is administered impartially, how many executions of innocents are acceptable?

Matt says none, thus making the death penalty untenable because he cannot accept executions of innocents being performed in his name.

I come to a different answer taking an approach that considers both the benefits and the costs (both measured in terms of lost innocent lives).

The cost of the death penalty in terms of innocent lives are all lives lost due to wrongful execution. The benefits from the death penalty are all innocent lives whose murder was deterred because of the existence of the death penalty.

Note that both the benefit and the cost are effectively achieved "in my name" under the death penalty. Under the specified formulation of a deterrent death penalty, a government that does away with the death penalty condemns to death all those innocents whose murder might have been deterred. While we may not be able to specifically identify ahead of time who those innocents might be, we are nonetheless condemning them to death. Accordingly, I am assign the same magnitude (though opposite signs for obvious reasons) to an innocent life saved via deterrence and to an innocent life lost to wrongful execution.

In the real world, the current death penalty is not a perfect deterrent as evidenced by the fact that murders still occur. Nondeterrence can occur for a variety of reasons such as an expectation of not being caught, insanity, or believing that your death is actually justified as long as the victim dies (that's the calculus of suicide bombers).

So let us assume that if the death penalty is in effect, a considered murder is deterred [by the death penalty] with probability p, then we can find the break even point by solving
To simplify this equation, assume all murders are "solved" and that there is one convicted murderer for each murder. Note, by considering convicted murderers I am intentionally excluding manslaughter which by definition does not include premeditation and thus cannot be deterred. (Plus the death penalty doesn't apply to manslaughter). Then the number of convicted murderers is given by:
Now define r as the ratio of wrongful executions per convicted murderer, and the first equation can be rewritten as


Noting that we have the same term on both sides, the utilitarian break even point for the death penalty can be expressed in terms of the percentage of dettered (considered) murders [by the death penalty], p, and the ratio of wrongful executions, r, as
To help provide an intuitive feel for this equation, note that if p = 0, then r should be 0. In other words, if there truly is no deterrent effect from the death penalty, then executions should only be permitted if we were absolutely sure that no innocents were executed. As perfect certainty is not possible, we would then do away with the death penalty.

If however, p = 0.5, then it should be acceptable to operate with r = 1. While this may seem counter-intuitive, note that this situation corresponds to the situation where an equal number of innocent lives are saved via deterence to lost via wrongful execution (for every two considered murders, one actually happens). If p > 0.5, then by this utilitarian metric, we can actually execute more people than we convict and be morally neutral! Why? We're still balancing innocents saved to innocents lost. For p = 2/3, r = 2 because two murders are deterred for every murder that actually occurs. For p = 1, r = infinity. However this corresponds to an undefined number of wrongful executions as there would be 0 convicts to execute as all murders would be deterred.

Tabulating the numbers we get the following


As many people in the blogosphere have noted, we just had our 1,000 execution since 1976 and approximately some 600,000 murders since 1976. Shoehorning these statistics into our equation, let's assume that every execution was wrongful and that every murder resulted in a conviction. Then these wrongful executions are "acceptable" for a deterrent effect as low as p = 1/600 as r = 1/600.

To fill in actual numbers we need the number of murder convictions. I had a bit of trouble finding this (what I really want is the number of murder convictions since 1976), with the closest being this report (the feds seem to like to only compile federal convictions, the states compile only state convictions and I'm not going to sum all of these up by hand) from which I eyeball a mean US murder conviction rate at about 0.05 of the population from 1981 to 1995. Assuming a mean population of about 200 million from 1973 to the present that gives 10,000 convictions per year or about 300,000 murder convictions from 1976 to present.

Then applying simple arithmentic to statistics provided by wiki results in about 242 death sentences being issued per year with 4.7% of these sentences being overturned via exoneration (much higher percentage are commuted to life for procedural reasons). Being extremely ungenerous to the justice system (intuitively, the following number should be lower), let us assume that 4.7% of executions are wrongful. Then 47 executions since 1976 would be wrongful.

Then r is given by 47/300,000 or 0.00016. Thus by the algebra given above, the death penalty in its current form is acceptable on a utilitarian basis if approximately 0.00016 of all murders are deterred.

That's an exceedingly low bar to satisfy. I suspect that its much higher than that. I actually estimate it to be at least 50%. Why? Because rational humans really do respond to changes in incentives and avoiding death is a pretty big incentive. That humans respond to lesser incentives
was recently noted by Kaus (scroll down to Friday Dec 2 - Kaus's permalinks suck) that with respect to post-Katrina gas prices it was

"almost as if insidious law was at work--as prices rise, demand declines!"

People changed their behavior just to save a few bucks. Surely they would do the same to save their own lives (except for pirates with booty - I'll let Thason explain that one). Surely, this deterent effect is greater than 0.00016, so surely the death penalty is acceptable on a utilitarian measure of innocent lives.

Now that being said, it is still worthwhile to utilize virtually every means available to ensure that we don't execute the innocent. Why? Because we typically assign a very high value to human life. While it is common to just say that a life has infinite value, we don't really mean it and economists can and do assign a finite value to a human life.

Regardless of what the exact value of life is, it's pretty high, and certainly more than the cost of running a DNA test. So it's to society's benefit to ensure that we take virtually every means available to get a death sentence right. Of course I say "virtually every means available" as some means seem likely to significantly reduce the deterrent effect and thus likely to be of net detriment to society.

Update
In the comments, Tom suggests that many people value the loss of human life differently when it is taken in different manners. Specific to this case, someone may value the loss of an innocent life via execution differently than the loss of an innocent life via murder.

So let's assume that you weight the loss of innocent life via murder a fraction 'f' as much as the loss of innocent life via execution. Then our equation becomes the following:


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The Onion breaks the story of the century: Voice of God Revealed to be Cheney on Intercom.

In a transcript of an intercom exchange recorded in March 2002, a voice positively identified as the vice president's identifies himself as "the Lord thy God" and promotes the invasion of Iraq, as well as the use of torture in prisoner interrogations.

Most influential Vice President in history.
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Just noticed Wonkette pointing out some surprisingly good news from Iraq; news the liberal mainstream media doesn't want you to hear because it casts a positive light on Bush. Here's the story. Although Iraq's still a mess and American casualties mount, there is a silver lining: the United States is building one hell of a Paralympics team. Money quote:

The unprecedented number of troops who are returning from Iraq with missing limbs has given the US Paralympic Team an unexpected recruitment boost and the chance to become “unbeatable” at the next Games in Beijing in 2008. More than 60 potential recruits have already been identified in sports as varied as powerlifting, archery and table tennis.

(And yes, I think the Paralympics are great, and yes, I know that the reason we have so many amputees is because doctors are able to save the lives of soldiers who would have died in earlier wars). On a similarly morbid note, did anyone see Homecoming? I haven't tracked down a copy yet but it sounds just about perfect. Joe Dante may be the most underrated director in Hollywood (check out Matinee, for instance).
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You've probably seen this by now, but here's Lise Olsen's Houston Chronicle piece about Ruben Cantu's 1993 execution for a crime he didn't commit. Cantu was 17 at the time he allegedly commited this crime; he was sentenced to death on the testimony of a single eyewitness, who identified Cantu only on the third try, possibly under police pressure. Now the eyewitness admits Cantu wasn't there. Too bad the state executed him twelve years ago.

I don't deny that some crimes are heinous enough to warrant execution. I just think that there will inevitably be mistakes made by our criminal justice system. Allowing executions inevitably means that people like Ruben Cantu will be killed, and I can't accept that. Even if capital punishment were a wonderful deterrent, even if it were colorblind, even if court-appointed attorneys were uniformly brilliant, one innocent death is one too many.
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This short film has more plot than most features. And while it's kind of a cheat to use as much voiceover as they do, I still think it more or less works. It's about a man who is addicted to faking his own death to escape responsibility, his son, a boxer who believes he is from the future, his daughter, the world's greatest swordfighter and champion viola player, and the totalitarian society that is created when the son invents a perpetual motion machine.
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Lord of the Flies, now at the Criterion Contraption.
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