Econstudentlog

Some stuff on lotteries

Let’s say you have a population of n (ex ante) identical individuals each making an income of w. Say you now decide to set up a simple voluntary tax-transfer type scheme, where all individuals who choose to participate are required to pay an amount (/tax), t. The contribution/tax t is used to finance a transfer T, which is equal to n*t (the sum of all contributions, i.e. there’s no administration or anything like that to start with). Each individual has a 1/n probability of receiving the transfer T, so that the expected payoff of this scheme is equal to the probability of receiving the transfer times the size of the transfer minus the contribution, or 1/n*(n*t)-t. Which is equal to 0 and independent of both t and n. The expected income of an agent participating in the scheme is w + EP = w.

A risk averse individual will always choose not to participate. A risk neutral is indifferent between participating and not participating given that the reservation utility is 0. Note that even if the expected payoff of the scheme is ‘mathematically’ zero, the way most people think about a scheme like this (..out of context at least, when talking pure math) is that you’re most likely to lose if you participate, especially if n is sufficiently high. If a million people participate and there’s one transfer each month, then the likelihood that you’ll have gotten your money from the contributions back after a year is not very big.

It’s probably even lower than you realize, if you’re not familiar with statistics. To illustrate why this is, let’s get a little more technical. There’s one transfer T each timeperiod. There are n people who participate in the scheme. Now assume that your likelihood of getting a transfer next period does not depend on who got it last period. You can think of it as an assumption stating that an individual can receive several transfers if he or she is very lucky. This assumption is important, but I also think it’s justified in the empirical framework I’m attempting to apply this to – it would be completely justified if the scheme was mandatory, but regarding lotteries we know that a) at least some lottery winners play on after they’ve won anyway and, far more important, b) that the number of participants in real world lotteries is pretty much independent of the behaviour of the winners ex post (1 marginal lottery winner does not translate to one less lottery participant in general) [where ‘behaviour’ here relates only to the decision as to whether to participate in future lotteries or not]. If you don’t like to think of it as an assumption about past winners playing along after they’ve won, you can think of it as new people entering the scheme after past winners decide to exit, keeping the probability of winning constant over time.

Now perhaps a not uncommon way to misunderstand how this works is for people who don’t know statistics to think/assume that if you have 52 participants and 52 weeks of contributions/transfers, then the probability that you receive a transfer is equal to 1 after one year. It’s not, it’s lower than that, because some lucky guy might win 2 times and get the transfer instead of you. The only case where you can be certain to have won after a year is in the case where nobody can win more than once. In that case, the conditional probability of winning is increasing over time – the chance of winning the first lottery is 1/52, if you don’t win the first lottery you have a 1 in 51 chance of winning the next lottery, ect. I’d like to instead look only at the case where the conditional probability of winning is constant over time.

The probability that an individual i will receive a transfer before period k, where k is equal to 1,2,3…, follows in that case what is called a geometric distribution, which is itself a negative binomial distribution (I know I’ve linked to that one not long ago here on the blog) with r = 1. The cumulative distribution function, which in this specific case can be thought of as a function telling us how likely we are to have gotten a transfer by the time we reach period k, is equal to 1 – (1 – p)^k. To make this a bit easier, think of throws with a die. After one attempt, the likelihood of rolling a 6 is 1 – (1 – 1/6)^1 = 1 – 5/6 = 1/6 (we knew that!). The likelihood of rolling a 6 after exactly two attempts is equal to: 1 – (1 – 1/6)^2 = 1 – (5/6)^2 = 1 – 25/36 = 11/36. Note that this is smaller than 1/3 (or 12/36) for reasons already mentioned; when outcomes are independent, you can’t just add the probabilities to get your estimate. Also note that the probability of getting that damn 6 is of course increasing in the number of attempts. Now what’s the probability that you will not have rolled a 6 after 10 throws? Probably higher than most people think: 1 – [1 – (1 – 1/6)^10] = 0,1615, which is a tiny bit lower than the probability of rolling a 6 in the first attempt. Note that here I take advantage of the fact that there are only two outcomes [roll 6 or don’t roll 6] and that the probability of not rolling 6 in a sequence is equal to 1 minus the probability of doing it (mutually exclusive & collective exhaustive and all that..).

Now if we have a lottery with 1 million people participating (p = 1/1.000.000) and one transfer handed out each week, what’s the probability that you’ve not gotten a transfer after 10 years of participation (k=520, 52 weeks in one year…)? Putting in the numbers we get 1 – {1 – (1 – 1/1.000.000)^520} = 0,99948 = 99,948%. The funny thing here is also that the transfer is uncertain but the contributions are not, so if you assume weekly contributions of value $5 over the 10 year period, the certain costs are $5 * 520 weeks = $2.600. So if you play along in this lottery, you pay $2,600 and get nothing with 99,9% certainty. The expected payout from the lottery is of course the same as the amount you pay, as the transfer is $5.000.000 and and the probability of getting the transfer each period is one in a million, so that expected payout is 520/1.000.000*5.000.000= 520*5 = 2600 and the expected total payoff is 0.

Now here’s a twist some of the people who participate in schemes such as these probably don’t fully understand: Assume you try to buy two lottery tickets instead of one to increase your chances of winning. How does that affect the expected payoff? We already know. By assumption it doesn’t, because EP = 0 in our model (see the beginning and above). It also doesn’t matter how many times (weeks) you play, you can’t increase your chances in expected terms by playing for a longer period. Another thing is that in the real world the expected payoff of participating in a lottery is of course always negative – because it takes work and effort to make lotteries work, the contributions need to cover the costs of selling the lottery tickets, tv ads, tax compliance and administration, ect. In the real world, when you buy another lottery ticket, your expected payoff goes down. So to return to our model, if you think it would be mad to participate in a lottery where you pay $2,600 ove a decade and end up with nothing with 99,9% certainty, you should be aware of the fact that these odds are better than the ones offered by real-world lotteries. In the real world, the deal offered is even worse.

People who claim to be in favour of income distribution from rich to poor who also participate in lotteries are kind of funny. They say they want one thing from the political system, then they voluntarily decide to participate in a redistribution mechanism which will always have the exact opposite result. When you have a lottery where the winner takes all or most of the money, you redistribute from everybody to one (/soon to be) very rich guy. I know that lotteries hand out both large transfers and small, but on net most of the small transfers probably cancel out because that’s part of what keep people playing.

20111204
(smbc)

May 31, 2011 Posted by | Economics, Psychology, Statistics | 2 Comments

Wikipedia articles of interest

1. Yardang.

“A yardang is a streamlined hill carved from bedrock or any consolidated or semiconsolidated material by the dual action of wind abrasion, dust and sand, and deflation.[1] Yardangs are elongate features typically three or more times longer than they are wide, and when viewed from above, resemble the hull of a boat. Facing the wind is a steep, blunt face that gradually gets lower and narrower toward the lee end.[2] Yardangs are formed by wind erosion, typically of an originally flat surface formed from areas of harder and softer material. The soft material is eroded and removed by the wind, and the harder material remains.”

See also this and this for related stuff.

2. T-34.

3. Endogamy. The Wiktionary says endogamy is: “The practice of marrying or requiring to marry within one’s own ethnic, religious, or social group.” The article has more. Didn’t know there was a name for this.

4. Factor analysis (somewhat study/exam-related).

5. History of paper.

“Toilet paper was used in China by at least the 6th century CE.” I had no idea it’s been around for that long! Also:

“The earliest recorded use of paper for packaging dates back to 1035, when a Persian traveler visiting markets in Cairo noted that vegetables, spices and hardware were wrapped in paper for the customers after they were sold.[20]”

Latest xkcd-strip which I thought I ought to add here:

Btw, I think Randall Munroe perhaps does not spend much time around people with average IQ’s, if the RHS is supposed to illustrate that 30 point drop. The average IQ of people who don’t know what a car is, well, it’s pretty damn low (most of them also probably can neither read nor write). The learned helplessness (‘why should I remember this when I can just look it up’) aspect of tech is important, but that comic was too much over the top to do it for me.

Incidentally, the drop (which is real and significant for me too) is part of why I almost prefer to interact with people online rather than in person. I have the impression that real-time face-to-face interaction is not exactly where I have my comparative advantage. Online interaction also makes discussions with a significant knowledge-component much easier to engage in, and the lag/delay between idea exchanges which is often a part of that interaction makes sure people like me, who perhaps aren’t really all that quick on the uptake, have time to think things more through. It goes both for ‘pure ideas’ and it goes for implicit social rules and norms which I sometimes have a hard time remembering implementing when doing the face-to-face stuff because there’s not enough time to both have the conversation and be aware of all that other stuff.

May 25, 2011 Posted by | Geology, History, Personal, Statistics, Wikipedia | 6 Comments

Quotes

1. “The trouble with our times is that the future is not what it used to be.”

A comment on this quote also worth quoting:

“Thanks to Historians, the past is also not what it used to be.”

Paul Valery and ‘RR’. Link.

2. “Science is a way of thinking much more than it is a body of knowledge.” (Carl Sagan)

Though the line is sometimes blurry, in general a scientist should never tell you what to think, rather he should tell you how to do it. People who are used to being told what to think often don’t think all that much. Thinking takes a lot of work and practise.

3. “economists can predict things very well unless something changes.” (John Emerson/maybe Galbraith said something similar – I’ve not been able to find this quote elsewhere online though).

4. “Ah, the life of a newspaper cartoonist — how I miss the groupies, drugs and trashed hotel rooms!” (Bill Watterson)

5. “Man is a credulous animal, and must believe something; in the absence of good ground for belief, he will be satisfied with bad ones.” (Bertrand Russell)

6. “Every murderer is probably somebody’s old friend.” (Agatha Christie)

7. “If you want to have good ideas you must have many ideas. Most of them will be wrong, and what you have to learn is which ones to throw away.” (Linus Pauling)

8. “The best way to remember your wife’s birthday is to forget it once.” (Joseph Cossman)

9. “It is impossible for someone to lie unless he thinks he knows the truth. Producing bullshit requires no such conviction. A person who lies is thereby responding to the truth, and he is to that extent respectful of it. When an honest man speaks, he says only what he believes to be true; and for the liar, it is correspondingly indispensable that he considers his statements to be false. For the bullshitter, however, all these bets are off: he is neither on the side of the true nor on the side of the false. His eye is not on the facts at all, as the eyes of the honest man and of the liar are, except insofar as they may be pertinent to his interest in getting away with what he says. He does not care whether the things he says describe reality correctly. He just picks them out, or makes them up, to suit his purpose.” (Harry Frankfurt, On Bullshit – found here)

May 24, 2011 Posted by | Quotes/aphorisms | Leave a comment

Special

Smbc.

May 23, 2011 Posted by | Cartoons, Psychology | 4 Comments

People are strange

“The fact is that there was never any Holocaust of Jews in “gas chambers”. This has even been proven by Jewish non-Zionist historians such as David Cole! It may hurt, but the Holocaust is the only after war time propaganda which stayed alive in order to etablish the state of Israel.

It is you who should read history!”

A youtube comment to this video:

You can jump to 46.08 and see the next couple of minutes and then ask yourself if the commenter has even seen the video he’s ‘responding’ to. If he had, why did he use those “…” around “gas chambers” in his comment? So did the Americans make all that stuff up we see in the video? What about the dead bodies?

The video is incidentally a video I can not recommend that you watch right after you’ve eaten. The Why We Fight episode of Band of Brothers was very well done and one of the highlights of that series IMO, but this is the real deal. I shouldn’t have to add this and perhaps it’s superflous, but my generation is so used to see people shoot at each other in the telly and people dying on tv shows and what have you, that it can sometimes be a little hard to not use the same implicit mental standards when evaluating material such as this as the ones you use when watching Ironman (or whatever, I’ve never seen Ironman, don’t know if it’s a bad example). What is really crucially important to remember when watching material like this is that every single one of those dead people in those mass graves was a real person, just like you and me, a real person – with family, friends, hopes and dreams – who was killed.

And again, if a small child is watching over your shoulder, you should either send him/her off to bed or close the browser. Also, you don’t need to watch all that much of it to figure out roughly what’s in the parts you elect not to see. The extant video documentation of the atrocities is much more extensive than I’d thought. And much of it is freely available.

May 19, 2011 Posted by | Random stuff | 2 Comments

Discrete Mathematical Structures

Here’s the link, below a few quotes to illustrate what kind of book this is:

1) “Theorem 3: Let A, B, and C be finite sets. Then |A∪B∪C| = |A|+|B|+|C|-|A∩B|-|B∩C|-|A∩C|+|A∩B∩C|.”

2) “Existential quantification may be applied to several variables in a predicate and the order in which the quantifications are considered does not affect the truth value. For a predicate with several variables we may apply both universal and existential quantification. In this case the order does matter.”

3) “Theorem 2 The Extended Pigeonholde Principle: If n pigeons are assigned to m pigeonholes, then one of the pigeonholes must contain at least ⌊(n-1)/m⌋ + 1 pigeons.

Proof ( by contradiction ) If each pigeonhole contains no more than ⌊(n-1)/m⌋ pigeons, then there are at most m * (n-1)/m = n-1 pigeons in all. This contradicts our hypothesis, so one of the pigeonholes must contain at least ⌊(n-1)/m⌋ + 1 pigeons.”

The above perhaps points to part of the reason why I haven’t quoted from the book before. Given that the exams are getting closer every day, it’s unlikely that I’ll do much more reading in this book (or perhaps any non-directly study-related book) in the next month’s time. The book contained a few remarks on ideas as to how to construct proofs in chapter 2, which though most of the ideas were familiar to me are not completely exam-irrelevant. Pretty sure most of the other stuff is. Though I’ll perhaps not get a lot of non-exam relevant reading done I’ll try to keep blogging over the coming weeks, I’ve almost returned to ‘one post/day’ and I like that very much though it’s uncertain if I can keep up that kind of activity level in the longer run.

May 19, 2011 Posted by | blogging, Books, Mathematics | Leave a comment

Timequake 2

I haven’t blogged a lot of book stuff in a while so thought I ought to give it another post. Finished it yesterday, same day I started it, it’s easily read and quite a bit of it is actually reasonably funny.

1. “The Bible may be the Greatest Story Ever Told, but the most popular story you can ever tell is about a good-looking couple having a really swell time copulating outside wedlock, and having to quit for one reason or another while doing it is still a novelty.”

2. “Just because you’re talented, that doesn’t mean you have to do something about it.” (‘Allie’, or Alice – Vonnegut’s sister, the same person behind the quote “If there is a God, He sure hates people…” in the first post. My type of girl)

3. “The point I want to make, though, is that one course I took required me to read and then be ready to discuss A Study of History by the English historian Arnold Toynbee, who is up in Heaven now. He wrote about challenges and responses, saying that various civilizations persisted or failed depending on whether or not the challenges they faced were just too much for them. He gave examples.”

When I’d finished the last sentence I laughed out loud.

4. (commenting on a reunion of a high school class of 1940:) “They and I were so old that we could remember when it didn’t matter all that much economically whether you did or didn’t go to college. You could still amount to something.”

To be fair, some people still manage to ‘amount to something’ without going to college today. A lot of college education taking place today has a negative ROI, both for the individual and society. But it’s worth remembering that our ideas and norms about education and its merits have changed a lot over the last two generations.

5. “I always had trouble ending short stories in ways that would satisfy a general public. In real life, as during a rerun following a timequake, people don’t change, don’t learn anything from their mistakes, and don’t apologize. In a short story they have to do at least two out of three of these things…”

6. “Even with military training, there is no way a man can accidentally blow his head off with a shotgun.”

7. “There is no way a beautiful woman can live up to what she looks like for any appreciable length of time.”

8. “Extenuating circumstance to be mentioned on Judgment Day: We never asked to be born in the first place.”

May 16, 2011 Posted by | Books, Quotes/aphorisms | 2 Comments

Yep, still awesome!

Yesterday I watched this:

A few links:

Khanacademy

Google.

Google scholar.

Google books.

Wikipedia

Mathworld

Some good blogs

ect. ect. ect.

Also, this and this.

May 16, 2011 Posted by | Khan Academy, Lectures, Mathematics, Random stuff | Leave a comment

Timequake

I’m currently reading Kurt Vonnegut’s Timequake. A few quotes:

1. “Now imagine this: A man creates a hydrogen bomb for a paranoid Soviet Union, makes sure it will work, and then wins a Nobel Peace Prize! This real-life character, worthy of a story by Kilgore Trout, was the late physicist Andrei Sakharov.
He won his Nobel in 1975 for demanding a halt to the testing of nuclear weapons. He, of course, had already tested his. His wife was a pediatrician! What sort of person could perfect a hydrogen bom while married to a child-care specialist? What sort of physician would stay with a mate that cracked?
“Anything interesting happen at work today, Honeybunch?”
“Yes. My bomb is going to work just great. And how are you doing with that kid with chicken pox?””

The next-to-last receiver of the Nobel Peace Prize was – and still is – the head of the largest military force in the world, a military force which at the time he received the Prize was engaged in two wars. But anyway, that last part of the quote is why I picked out the quote. Not long ago I had a conversation, touching upon the same theme, at the hospital with a guy who’d recently received a cancer diagnosis and was undergoing treatment. He told me how one day, while he was in dialysis, the sound of the tv in his hospital bed had malfunctioned. He couldn’t hear the comments, just watch the pictures. What he was watching made a lot of things seem downright absurd to him. They had been showing scenes of aircrafts attacking/bombing targets in Libya. Where he was at that moment doctors and nurses ran around trying so hard to stop people from dying – elsewhere different people worked very hard to kill each other.

Not that all wars are unnecessary or that people down there could just all stop fighting and everything would be nice and shiny. But your perspective on things like war is context-dependent and it’s conditional on a lot of things you aren’t even thinking about.

2. “I heard the poet Robert Pinsky give a reading this summer, in which he apologized didactically for having had a much nicer life than normal. I should do that, too.”

3. “They say the first thing to go when you’re old is your legs or your eyesight. It isn’t true. The first thing to go is parallel parking.”

4. “In A Streetcar Named Desire, Blanche DuBois said as she was taken away to a madhouse, after she was raped by her sister’s husband, “I have always depended on the kindness of strangers.”

5. “”Satan,” he said, “couldn’t undo anything God had done. She could at least try to make existence for His little toys less painful. She could see what He couldn’t: To be alive was to be either bored or scared stiff. So she filled an apple with all sorts of ideas that might at least relieve the boredom, such as rules for games with cards and dice, and how to fuck, and recipes for beer and wine and whiskey, and pictures of different plants that were smokable, and so on. And instructions on how to make music and sing and dance real crazy, real sexy. And how to spout blasphemy when they stubbed their toes.
“Satan had a serpent give Eve the apple. Eve took a bite and handed it to Adam. He took a bite, and they fucked.” […] “All Satan wanted to do was help, and she did in many cases,” he concluded.”

I like this book’s version more than the original. Or I think I do – it’s been a long time since I read the original.

6. “My mother was addicted to being rich, to servants and unlimited charge accounts, to giving lavish dinner parties, to taking frequent first-class trips to Europe. So one might say she was tormented by withdrawal symptoms all through the Great Depression.
She was acculturated!
Acculturated persons are those who find that they are no longer treated as the sort of people they thought they were, because the outside world has changed.”

I’ll try to remember that term.

7. “If there is a God, He sure hates people. That’s all I can say.”

8. “”In my entire career as a writer,” said Trout in the former Museum of the American Indian, “I created only one living, breathing, three-dimensional character. I did it with my ding-dong in a birth canal. Ting-a-ling!” He was referring to his son Leon, the deserter from the United States Marines in time of war, subsequently decapitated in a Swedish shipyard.”

May 15, 2011 Posted by | Books, Quotes/aphorisms | 2 Comments

A few papers

From the European Public Choice Society’s meeting this year. There’s a lot more stuff here.

1. Public Investment and Re-election Prospects in Developed Countries.

Last I was home I found out that the idea that managers might decide to deliberately ‘boost their numbers’ in various ways strategically some time before leaving for another job was something my parents had never even considered. I find it obvious that politicians from time to time decide to employ similar strategies by trying to make the important numbers look good up to the election and then take the hit a year or two later, once they’re in office.

2. The end of the news.

3. Econometric Estimates of Deterrence of the Death Penalty: Facts or Ideology? From the concluding remarks:

“Considering all these results, a critical and cautious examination of them leads to the conviction that we cannot draw any strong conclusion: while there is some evidence that a deterrent effect might exist, it is too fragile to be sure about it and the possible quantitative effect usually measured by the number of homicides prevented by each execution is so uncertain that it is difficult to conclude anything that would be relevant for policy purposes.”

4. Benefit Morale and Cross-Country Diversity in Sick Pay Insurance. From the abstract:

“We analyze the impact of benefit morale on sick pay entitlement levels in a political economy framework. Stronger benefit morale reduces the number of recipients. On one hand this reduces the probability of receiving benefits, on the other hand it makes insurance cheaper. Numerical simulations show that the probability effect can dominate the price effect and hence benefit morale might decrease insurance levels.”

The ‘benefit morale’ mentioned is a social norm against benefit fraud, so that you don’t claim benefits if you’re not sick. And yeah, I know I’ve linked to it before but I should probably leave a link to this every time I publish a post like this with multiple studies.

May 13, 2011 Posted by | Economics, health, Papers | Leave a comment

Tradeoffs som vi ikke ønsker at tænke over, afsnit 35123

I Danmark er der antageligt (det er overordnet set sådan folk stemmer) generel konsensus på samfundsplan om, at det er en god ide at bruge offentlige institutioner til at hjælpe svage individer ved at støtte dem økonomisk og på anden vis, hvis de har det svært. De gælder både nationalt, hvor en lang række ordninger er sat op for at fungere som et ud fra et internationalt perspektiv betragtet meget omfattende ‘socialt sikkerhedsnet’, og såmænd også internationalt, hvor vi sender adskillige milliarder ud af landet hvert år, med henblik på at hjælpe indbyggere i lande som er fattigere end os.

Selvom der bruges mange milliarder på ulandsbistand, udgør den dog stadig en meget lille andel af det offentlige budget. Vi bruger omkring 0,8 % af bruttonationalindkomsten og selvom det er meget i international sammenhæng er det faktisk ikke noget særligt i det store billede (især ikke givet at en ikke ubetydelig andel af midlerne er mere eller mindre direkte erhvervsstøtte til danske virksomheder eller støtte til mere eller mindre politiske interesseorganisationer funderet i Danmark – hvor alternativet kunne være mere direkte indkomstoverførsler til mennesker med færre midler som bor i andre lande). Det er lidt sjovt, hvis man tænker lidt over det; altså at beløbet ikke er meget større. En af grundene til, at man kan forundres over omfanget af støtten er, at den marginale effekt af et økonomisk bidrag til en dansker er meget, meget lavere end den effekt, der ville opnås såfremt bidraget i stedet blev givet til et individ i et andet land med en meget lavere indkomst.

Sidstnævnte pointe fortjener en et tal-eksempel, så folk er med på hvad der sigtes mod. Man kan tænke over det på denne måde: Hvis en rig dansker vælger at give en relativt fattigere dansker uden for arbejdsmarkedet 300 kroner, svarer til at give ham måske tre dages husleje, hvis han bor relativt billigt. At give 300 kroner til et individ med en indkomst på en dollar om dagen svarer til at give vedkommende omtrent 2 måneders indkomst. Sagt på en lidt anden måde kunne man for hver måneds husleje, der overføres til en dansk modtager af indkomsterstattende ydelser (som bor billigt) have fordoblet en fattig inders indkomst i vel over halvandet år. Eller hvis man anskuer situationen for en given transferydelse i et givet tidsinterval: For hver dansker som får huslejen dækket af det offentlige kunne man have fordoblet 20 inderes indkomst i den samme periode i stedet for.

Nu kunne man jo spørge sig selv, hvorfor der er bred enighed om, at det er en rigtig god ide at lade næsten alle vores offentligt indsamlede midler gå til folk som ligner os selv, bor tæt på, osv., hvis folk som bor langt væk ville have meget større glæde af at modtage pengene? Det interessante er især, at det i den politiske debat som foregår i landet tages for givet – og i mindre udstrækning tages for givet i de fleste øvrige rige lande, at vi først giver den fattige afrikaner en mulighed for at få en uddannelse efter at vi har betalt uddannelsen for vores egne, såvel som for husleje, mad, sundhed, mikroovn og internetforbindelse til alle de arbejdsløse danskere og deres børn, pensioner til de ældre og tidlig pension til de yngre, børnepenge, den nationale tv-kanal, subsidier til teaterbilleter… Også selvom vi kunne hjælpe mange, mange flere mennesker, hvis vi besluttede os for at bruge flere penge på at hjælpe den fattige pige fra Chad og færre penge på at hjælpe Søren.

Jeg har aldrig set en politisk plakat, som kritiserede at 9-årige Ajambo stadig arbejder i stenbruddet i stedet for at gå i skole, fordi vi har brugt de penge, der kunne gå til at betale for hendes skolebøger, til at betale for 37-årige Brians internetforbindelse. Det er ikke den kritik, der bliver rejst når eks. Enhedslisten rejser deres kritik af fordelingspolitikken; hvis Ajambo nævnes er ideen som regel at lade offentlige institutioner betale for både Brians internetforbindelse og Ajambos skolebøger. De anerkender heller ikke eksistensen af disse tradeoffs, de omgår dem bare ved at lade som om der er penge til det hele.

Ovenstående er ikke nødvendigvis et argument for at ændre praksis i fordelingspolitikken, man kan sagtens finde væsentlige argumenter imod at gøre det. Men det er interessant at den nationale norm er, at det er helt på sin plads at anskue tilhængeren af omfattende omfordeling af indkomst på nationalt plan og meget begrænset omfordeling af indkomst på internationalt plan som en form for ‘barmhjertig samaritaner’. Danmark er et af verdens mest lige lande. Hvis målet er at mindske uligheden, så findes der rent faktisk så godt som ingen dårligere lande at bruge pengene i end Danmark; alle andre landes ulighed ville mindskes mere end den danske pr. krone brugt på marginen. Ud fra et internationalt perspektiv svarer vores nationale fordelingspolitik til at omfordele fra de rigeste måske 2 % af verdens befolkning til de ‘fattige danskere’ der måske kun er i top 5%. Det kan godt være mange danskere er stolte af den omfordeling, der finder sted på nationalt plan, men set fra den fattige inders perspektiv…

Sidst: Naturligvis er høj omfordeling af indkomst til indbyggere i andre lande en politisk dødssejler, med mindre indbyggerne har meget stærke altruistiske præferencer. Naturligvis er en reform i den retning væk fra status quo umulig at gennemføre, fordi dem politikken primært gavner, de fattige udlændinge, ikke stemmer, hvorimod alle dem, som mister teaterbilletter og internet, gør. Og nej, for at komme i al fald et modargument i forkøbet: Det er ikke gratis at finde ud af, hvem der mangler pengene mest og sørge for, at de går til de rette, hvis modtageren bor i et fremmed land mange tusinde kilometer væk. Men tror du der ikke sker misbrug af det danske system? Tror du de danske sagsbehandlere arbejder gratis? Hvis pengene går til en af de forkerte i Chad, hvad er så sandsynligheden for at vedkommende har mindre brug for pengene end Brian?

Hvis Danmark er et land fyldt med altruistiske vælgere, som bekymrer sig en masse om andre menneskers kår og hvordan man kan hjælpe dem med politiske tiltag – et narrativ danskere traditionelt støtter op om – hvorfor er debat-emner som disse så ikke på den nationale dagsorden?

May 12, 2011 Posted by | politik, tradeoffs, velfærdsstaten | Leave a comment

Politics matters

“It turns out that people place more emphasis on finding a mate who is a kindred spirit with regard to politics, religion and social activity than they do on finding someone of like physique or personality,” said John Alford, associate professor of political science at Rice University and the study’s lead author.

On a scale of 0 to 1, where 1 means perfectly matched, physical traits (body shape, weight and height) only score between 0.1 and 0.2 among spouse pairs. Personality traits, such as extroversion or impulsivity, are also weak and fall within the 0 to 0.2 range. By comparison, the score for political ideology is more than 0.6, higher than any of the other measured traits except frequency of church attendance, which was just over 0.7.

Link, via Razib Khan. He’s written a lot of good stuff lately, the main reasons why I’ve not linked to him more is that a) I feel bad about linking to so much of his stuff all the time, b) I’ve not exactly tried to hide the fact that I think you people should be reading his stuff already. He has two posts on trust up at his discover gnxp blog which you should go read right away if you don’t already have (The slow decline of trust over time, The End of Trust: Hawk & Dove, maybe some of you’ll find the gender difference post interesting as well, I didn’t consider the main finding at all surprising).

In my mental model, people should ideally choose a mate where the disagreements which exist between the partners can be more or less ignored on a daily basis. If they can’t, the partners are more likely to run into problems in the long run. Politics is difficult to ignore on a daily basis because people spend a lot of time discussing it (I tend to think that this and gossip makes up a large percentage of total daily verbal communication for the average individual); it’s part of many people’s every day lives in some way or another, so choosing a mate with very different views is probably quite costly on average. I don’t think all of this is just politics, it’s also that politics correlates with other stuff that really matters a lot in the long term; like views on child rearing and loyalty/trust-aspects (‘if (/s)he does not agree with me on X, I can’t really trust him/her’) – remember that a lot of politics is about signalling that you belong to the ‘good tribe’, and people (especially females) who belong to the good tribe and have invested some in belonging to that tribe will be much less likely to partner up with one of the ‘bad guys’.

Like Razib, I’ve been unable to find the paper online. If I do, I’ll post a link here later.

May 11, 2011 Posted by | politics, Psychology, Random stuff, Religion | Leave a comment

Wikipedia articles of interest

1. Aposematism. You know that thing where poisonous animals have very brightly coloured skin to stop predators from eating them and die in the process?

I’ll have forgotten what it’s called next week, unless I reread this post multiple times. My tendency to forget all kinds of stuff I’ve supposedly learned is part of what separates me from high IQ-folks; my knowledge retention rate is much lower. Though I don’t care enough about it to do something about it, like trying to improve my memory.

2. Himalayas.

Interesting related fact: The highest of the ‘fatality to summit’-ratios of the eight-thousanders is that of Annapurna. Also: “Annapurna I holds the highest fatality rate among all 14 eight-thousanders. As of 2005, there have been only 103 successful summit attempts, and 56 lives have been lost on the mountain”. Half of all who climb that thing die yet people keep doing it. The best reason the first solo climber of that mountain could come up with when asked the question why? “I did it for my soul.”

3. Republic of Venice. The ‘history of…’ article has more.

4. Execution by elephant.. Exactly what it says on the tin. A few quotes:

“Hindu and Muslim rulers executed tax evaders, rebels and enemy soldiers alike “under the feet of elephants”.” Yes, tax evaders.

“Some monarchs also adopted this form of execution for their own entertainment.” (remember how it was before the tv? You have to do something to keep the boredom at bay…) […] “in the Mughal sultanate of Delhi, elephants were trained to slice prisoners to pieces “with pointed blades fitted to their tusks”.[1]”

“The use of elephants as executioners continued well into the latter half of the 19th century.”

5. Bergmann’s rule.

May 10, 2011 Posted by | Biology, Genetics, Geography, Geology, History, Wikipedia, Zoology | 1 Comment

Spring

An image post, I’ve put it all below the fold. Most of All of the images are back from April. Click any image to view it in a much higher resolution. You’re free to do whatever you like with them.

Continue reading

May 8, 2011 Posted by | Nature, pictures | Leave a comment

A question

Though I haven’t personally seen (m/?)any of them, I have the impression that the: ‘if you were told you had 24 hours left to live, what would you do in the time you had left?’-theme has been dealt with extensively in movies and pop culture. Now how about this related if still quite different question: “If you had the chance to be told at one point exactly when you were to die, when would you like to get that information?”

Not at all? Ten seconds before? A week before? A year before? Right now?

Of course this question is somewhat related to the fact that more information sometimes makes us worse off rather than better off. Knowing is not always better than not knowing. This is a well known fact in i.e. health economics. However the devil is in the details as well and uncertainty sometimes deceives us, makes us think things that aren’t true (and perhaps makes some states of uncertainty preferable to others to us). I’ll illustrate this in a model below. It’s a bit technical, but not too much and you needn’t know any fancy math to understand what’s going on. It’s pretty basic but a lot of people get stuff like this wrong. The “|” thing I’m using below should be read as ‘conditional on‘, that ought to be (if anything) the only thing you haven’t seen before. So let’s set up the following model:

Say you have a genetic test that will determine with 99,9% certainty whether you have terrible disease X. More precisely, assume 1 out of 1000 tests gives a false positive (let you think you have the disease even though you don’t) and that no false negatives ever happen (everybody with the disease will be caught by the test, you will never get a negative test result if you have the disease). X is incurable and deadly; think of it as a ticking time bomb version of the worst disease you can imagine (you don’t know you have it before it gets very bad). Say the background incidence of X is 0,001% (1 out of 100.000 people get it). This is low enough that ‘ordinary people’ would never worry about having the disease (it’s not genetic). Say a public screening protocol is implemented using the test mentioned above. The screening protocol is implemented solely with the purpose of giving people more information about their health status, as no cure exists. Now what would happen?

Let’s say a guy gets a positive test result. What’s the probability that he has the disease? Well, we know that the test is 99,9% accurate, so it should be pretty high, right? Wrong. People familiar with Bayes’ Rule probably know what I’m getting at.

There are six relevant probabilities here:

P(X) = 0,00001 (1/100.000; this is the probability that a random test taker has the disease)
P(not X) = 1 – 1/100.000 = 0,99999 (the -ll- does not have the disease)
P(negative test | X) = 0 (probability that a test taker has the disease but tests negative)
P(positive test | X) = 1 (-ll- and tests positive)
P(positive test | not X) = 0,001 (probability that the test is positive even though you don’t have the disease)
P(negative test | not X) = 0,999 (probability that the test is negative and you don’t have the disease).

Now we calculate P( X | positive test), i.e. the probability that you get a positive result and you actually have the disease. This is equal to

[ P(positive test | X) * P(X) ] / [ P(positive test | X)*P(X) + P(positive test | not X)*P(not X)] =

[ 1*0,00001 ] / [ 1*0,00001 + 0,001*0,99999 ] = 0,009901. Multiply by 100 and you realise that this amounts to less than 1%. The probability that you get a positive result but aren’t sick is of course 1 minus that number, so more than 99% of all people who are tested positive aren’t sick even though the test we’re talking about is 99,9% accurate.

Some information just can’t be unlearned, and people usually are very bad at interpreting probabilities and dealing with numbers like these. Even a lot of doctors get this stuff wrong and might never even have heard about Bayes Rule (or have forgotten all about it even if they have). Note that if people who are actually sick would prefer to know in advance, even a blunt screening process like the one above makes the sick people much better off; they have a far more accurate assessment of their probability of developing the disease than they did before the screening, as their estimate of having X changes from 1/100.000 to ~1/100. The other side of the coin is that some people who’re not sick will think they’re much more likely to be than they really are – perhaps some of them would have preferred never to have been screened.

Note also in the context of i.e. genetic testing that adding additional information to an insurance market can sometimes make that insurance market break down, because the uncertainty that made insurance a sensible move is no longer there. Insurance is about risk diversification and if you take away the risk and replace it with certainties, well there’s not much left. If a life insurance firm knows that you with probability p will die within the next 5 years, there’ll often exist some potential insurance contract making both the firm and you better off. But what’s the price (/premium) of such an insurance contract if p is suddenly no longer uncertain, but rather equal to 1 or 0? What if it’s not about the probability of dying but rather the probability of getting a horrible disease, say, 40 years down the line? Same thing. If uncertainty is replaced by certainty it often also might have some distributional consequences to the parties involved (insurance always involves some element of (statistical) cost sharing across individuals).

Going back to the beginning of the post, I find the “when would you prefer to get that information?”-question a much more interesting question than the “how would you react when you’d already gotten it?” It is not at all, in my mind, an easier question to answer.

May 3, 2011 Posted by | Medicine, Random stuff, Statistics | Leave a comment

(Fake) quotes

Megan McArdle has an article up where she wonders why someone would post and spread what might(?) be a fake quote by Martin Luther King. Here are some of the responses to the article:

1) “People believe anything they read on the internet if it fits their preconceived notions.” –Thomas Jefferson. (first comment in the thread, had me laughing loudly)

2) “First!” – ‘Adam’ (of course he’s actually fifth though he does come right after god…) – followed by the comment: “Dammit!” by ‘Eve’

3) “False attributions are cool!” — Megan McArdle

4) “Shit, got USA Troops knocking at my door” – O……..

5) “You can fool some of the people all of the time, all of the people some of the time, but you can’t lead a horse to water and make him a boat captain.” — Abe Lincoln.

6) “a small step for a man a giant leap for mankind” –genghis khan.

7) “The great thing about the internet is that you can make up anything and attribute it to anyone you want.” —George Washington

May 3, 2011 Posted by | fun, Quotes/aphorisms | 2 Comments