Imagine someone offered you a bet - you pay $1 and pick an integer between 1 and 100. An integer in that range is randomly chosen, and if it matches your choice you win $200. Do you take it?
If you do, it's probably because you do this calculation in your head (whether you realize it or not): $200*(1/100)=$2. Since the expectation of the game is greater than $1, you're better off taking the bet.
Conversely, imagine someone offers you a $1, but if they pick the right number (again out of 100), you owe them $200. Would you take that bet instead (presumably no one thinks it makes sense that you would take both)? Well, towards what I thought was the end of a discussion about economics, a friend of mine did take that bet. Three years later we're still talking about it, so it's time to share it with all of you.
A rational person is expected to undertake any action in which the person believes the marginal benefit outweighs the marginal cost. If someone offers you $2 for something you value at $1, you'd be wise to sell it to them. However, how do you value things that are not definite, but instead have some probability of having a certain value? The conventional explanation is to calculate the expectation. It is the sum over all outcomes of the chance of that outcome happening times the value of that outcome happening.
My friend claims that it is not only the expectation, but also the distribution, that is important in determining what the actual value is. In this case, 99% of the time he wins money. The expectation is closely approached only over a large number of trials, so if he plays only once he is quite likely to come out ahead. Needless to say, since we've argued about this for some time, but I disagree with his reasoning. While I realize that the added information about the distribution may be valuable, I fail to see how. In the end you must make a yes/no decision, and there has to be some point at which your decision changes based on the particular probabilities and payouts. I claim that point is when the total expectation becomes negative. I think it's a significant point that expectation has all sorts of nice properties like additivity.
I think the problem here is a cognitive bias: treating a small probability as if it were zero. I bet the calculation goes: 1/100 is approximately zero, so 0*$200=$0 which is less than $1. So he takes the bet. I wonder if there is some way to test this - at the very least it seems like there are some psych experiments in here somewhere.
If you agree with him, here's the question I'd most like answered: you must go through some decision making process - what's the formula you use to determine whether to play or not?
Friday, June 22, 2007
Wednesday, June 20, 2007
Genarlow Wilson ordered released
Before my highly anticipated post on the use of expectation in decision making, I thought I'd pass along what I think is some great news (if a bit old) - last week a Superior court judge ordered the release of Genarlow Wilson. For those of you who are not familiar, Wilson was sentenced to ten years in a Georgia prison for having consensual oral sex with a 15 year old girl when he was 17. After his trial, the Georgia legislature changed the penalty for his crime to a misdemeanor, and at the time consensual intercourse was also a misdemeanor. The law was applied so harshly in part because he was accused of raping another girl and refused to plea to that charge. He was aquitted of rape but convicted of statutory rape and the jury was not allowed to know that a mandatory 10 year sentence was required.
Understandably there was a great deal of outrage over this case, and he got coverage in ESPN, the New York Times and even from Mark Cuban. He is still in jail pending the Attorney General's appeal, but this decision is a big step towards his freedom. This Volkh Conspiracy post discusses the legal reasoning and chances of it being upheld on appeal.
Understandably there was a great deal of outrage over this case, and he got coverage in ESPN, the New York Times and even from Mark Cuban. He is still in jail pending the Attorney General's appeal, but this decision is a big step towards his freedom. This Volkh Conspiracy post discusses the legal reasoning and chances of it being upheld on appeal.
Thursday, June 14, 2007
Blatant self-promotion
As some of you know, I've decided to take the rest of the year off to travel. If you want to keep track of where I am and what I'm up to, take a look at my travel blog.
Hodgepodge
Some things I've seen in recent weeks that I found interesting but weren't blog-worthy
on their own:
Stopping Menstration with the Pill (Slate): One thing I found interesting was the argument that menstruation was actually somewhat unnatural because for much of human history women spent most of their fertile years either pregnant or breastfeeding.
Reverse Contact Lenses (The Independent): Lenses you wear at night which squish your eyes back to the right shape, restoring perfect vision for up to 48 hrs.
Living Streets (itofd.com): An interesting article (and a cool site by the way) about how to get people to drive carefully on residential streets. One neat idea is to make the street environment more vague, forcing the driver to slow down to figure out what's going on. I can't explain it as well as he can, so just read the article.
AT&T and the NSA (arstechnica.com): Recently published documents show that AT&T has installed sophisticated NSA equipment into its internet backbone which an expert claims has the capacity to filter through up to 10% of all traffic passing through it. I'm sure this isn't a shock to many, but it's pretty disturbing that there is now evidence.
on their own:
Stopping Menstration with the Pill (Slate): One thing I found interesting was the argument that menstruation was actually somewhat unnatural because for much of human history women spent most of their fertile years either pregnant or breastfeeding.
Reverse Contact Lenses (The Independent): Lenses you wear at night which squish your eyes back to the right shape, restoring perfect vision for up to 48 hrs.
Living Streets (itofd.com): An interesting article (and a cool site by the way) about how to get people to drive carefully on residential streets. One neat idea is to make the street environment more vague, forcing the driver to slow down to figure out what's going on. I can't explain it as well as he can, so just read the article.
AT&T and the NSA (arstechnica.com): Recently published documents show that AT&T has installed sophisticated NSA equipment into its internet backbone which an expert claims has the capacity to filter through up to 10% of all traffic passing through it. I'm sure this isn't a shock to many, but it's pretty disturbing that there is now evidence.
Wednesday, June 13, 2007
Avandia and the "New-Media Man"
In all honesty, I don't give a @$#@ (that's French for rat's ass) about the diabetes drug Avandia. While this article in the New York Times is ostensibly about the recent news that Avandia has been associated with an elevated risk of heart disease, the author spends much of his time discussing his research for the article. He refers* to himself as a "new-media man", meaning that rather than trust the headlines, he utilizes the "entire niche of blogs and digital news sources on relevant subjects — drug risks, Big Pharma, diabetes". I was pretty impressed. This guy was going to do a little digging and come up with a nice take-home message, empowering his reader to use the internet to look past the headlines and scrutinize what they are reading. So what was his take-home message?
"And here is what I found: everything, except insight."
What a disappointment! Maybe I should have guessed as much, after all the title of the article is "Call the Doctor". But this was a gimme! The take-home message is so simple, yet the author got caught up trying to weigh opinions of others when he would have been far better off just reading the study and forming his own. To me, the value of so-called "new-media" is unprecedented access to primary sources, allowing the people (as in "we the") to form their own opinions rather than simply selecting between those of politicians and journalists. (The Durham-In-Wonderland blog is a fantastic example, to which I've linked to multiple times before.)
A quick skim of the actual study in the New England Journal of Medicine given a pretty simple take-home message:
There is a 95% that the increase in risk of heart attack due to the use of Avandia for 24 months is between 3% and 98%, the best estimate being 43%. In other words, Avandia does seem to increase the risk of heart disease, but the studies have been small so the precise magnitude is unknown until larger studies are conducted. This result should be taken very seriously because Diabetics are at higher risk for heart disease to begin with, so even a relatively small percent increase in risk is significant, in the same way that doubling your chances of getting in a car accident is more significant than doubling your chances of being hit by lightning.
* in reference to Jaideep's comment, formerly "refferse"
"And here is what I found: everything, except insight."
What a disappointment! Maybe I should have guessed as much, after all the title of the article is "Call the Doctor". But this was a gimme! The take-home message is so simple, yet the author got caught up trying to weigh opinions of others when he would have been far better off just reading the study and forming his own. To me, the value of so-called "new-media" is unprecedented access to primary sources, allowing the people (as in "we the") to form their own opinions rather than simply selecting between those of politicians and journalists. (The Durham-In-Wonderland blog is a fantastic example, to which I've linked to multiple times before.)
A quick skim of the actual study in the New England Journal of Medicine given a pretty simple take-home message:
There is a 95% that the increase in risk of heart attack due to the use of Avandia for 24 months is between 3% and 98%, the best estimate being 43%. In other words, Avandia does seem to increase the risk of heart disease, but the studies have been small so the precise magnitude is unknown until larger studies are conducted. This result should be taken very seriously because Diabetics are at higher risk for heart disease to begin with, so even a relatively small percent increase in risk is significant, in the same way that doubling your chances of getting in a car accident is more significant than doubling your chances of being hit by lightning.
* in reference to Jaideep's comment, formerly "refferse"
Sunday, June 10, 2007
Choose Responsibility
Five years ago, near Charlottesville, a woman threw a birthday party for her son. To insure that none of the guests drove home drunk, she insisted that (1) the guests not drive to the party and (2) that they spend the night. No one at the party drank above the legal limit for driving and no one left the house as agreed...until the police showed up. For their good faith efforts, Elisa Kelly and her now ex-husband were sentenced to over 2 yrs in jail a piece on 9 counts of providing alcohol to a minor.
In fairness, Kelly definitely screwed up for "[misleading] parents who called to ask about alcohol [and for trying] to get the kids to cover it up after police got there." There are certainly different ways of looking at this case: Radley Balko of Reason (here) and Charlottesville's Daily Progress (here). Along these lines, Balko has also written about a group called Choose Responsibility headed by John McCardell, a former college president. As first reported in this article of the Chronicle of Higher Education, McCardell argues for a plan which would lower the drinking age to 18 with a "catch." People between the ages of 18 and 20 would be given a provisional license to drink alcohol, but it would be revoked if they screwed up. People under the age of 18 would lose access to the provisional license if they screwed up before turning 18. The idea is that this gives kids under 18 an incentive not to drink until they turned 18. It also gives people between 18 and 20 an incentive to drink responsibly. Some Q&A here.
In fairness, Kelly definitely screwed up for "[misleading] parents who called to ask about alcohol [and for trying] to get the kids to cover it up after police got there." There are certainly different ways of looking at this case: Radley Balko of Reason (here) and Charlottesville's Daily Progress (here). Along these lines, Balko has also written about a group called Choose Responsibility headed by John McCardell, a former college president. As first reported in this article of the Chronicle of Higher Education, McCardell argues for a plan which would lower the drinking age to 18 with a "catch." People between the ages of 18 and 20 would be given a provisional license to drink alcohol, but it would be revoked if they screwed up. People under the age of 18 would lose access to the provisional license if they screwed up before turning 18. The idea is that this gives kids under 18 an incentive not to drink until they turned 18. It also gives people between 18 and 20 an incentive to drink responsibly. Some Q&A here.
Monday, June 4, 2007
Test Your Ethics (or Lack Thereof)
Did I just plagiarize that title? Anyway, John Tierney at NYT has posted this about a survey on ethics administered by Carnegie-Mellon. It takes about 10 mins, so try it out if you want, and then read the rest of this post.
The survey presents certain actions in different scenarios and you're asked to specify (a) how ethical it is and (b) how often you do it. You're also given a chance to specify whether it is even an ethical issue at all. I found myself answering that, very generally speaking, most of the things listed were not ethical issues. (Though, there were some definite exceptions.) On the other hand, I also answered that I almost never do most of those things. This is profoundly confusing: "If those things aren't even ethical issues, then why don't I do more of those things?" At first I thought, "Oh, those aren't ethical issues, they're moral issues." But I don't feel comfortable with that distinction either. When taking the survey, my reasoning often went something like this:
For "big" situations, a person has probably thought about it beforehand. Therefore, their response has probably been orchestrated based on a personal "worldview." However, I suspect that, in the heat of the moment and in a split second, for scenarios that haven't been thought about ("small stuff"), one probably tries unconciously to minimize the future potential for feeling guilt. To do this well, one probably has to have some sense of whether a particular action will lead to guilt. If so, presumably one get "better" with time after accumulating more experience. Maybe it's like muscle memory? Does feeling guilt and/or regret have anything to do with things that are considered wrong/evil/not okay/etc.? Is there a relationship or mapping among right/wrong, good/evil, and okay/not okay?
Does the degree of an action even play a role in whether it's okay or not? For example, kicking one ugly, loud, obnoxious, anti-social, disfigured puppy into the middle of an empty road late at night when you're drunk can, from a certain point of view, be rather funny (i.e. it's okay). On the other hand, throwing a box of cute puppies into a busy intersection during rush hour is probably not cool (i.e. it's not okay). Maybe that's not the best example, but hopefully it gets the point across. (note: I don't kick dogs of any kind.) How much weight should be given to the motivation of an action versus the consequences of the action? What, if any, are the moral/ethical absolutes? (Never kick puppies...) In other words, is it always possible to cook up a realistic situation that presents mitigating circumstances for any kind of action? (...unless it's for self-defense) Personally, I can think of only one thing that you should never do under any realistic circumstances (which I'll leave unsaid to encourage discussion); but there could certainly be others. (I know, I know: define "realistic"...)
The survey presents certain actions in different scenarios and you're asked to specify (a) how ethical it is and (b) how often you do it. You're also given a chance to specify whether it is even an ethical issue at all. I found myself answering that, very generally speaking, most of the things listed were not ethical issues. (Though, there were some definite exceptions.) On the other hand, I also answered that I almost never do most of those things. This is profoundly confusing: "If those things aren't even ethical issues, then why don't I do more of those things?" At first I thought, "Oh, those aren't ethical issues, they're moral issues." But I don't feel comfortable with that distinction either. When taking the survey, my reasoning often went something like this:
Only a dick would do that and I'm usually not a dick, so I wouldn't do that/haven't done that....but it's not like it's a moral or ethical question. If I saw someone doing those things, I would think, "they're probably dicks, but you never know, maybe they're having a bad day."Since I probably don't know what they mean, I looked up morals and ethics in wikipedia. Even though the entries were different, I really can't tell the two apart. Is there any difference? If so, what it is? (This is straight out of Election.) For whatever reason, I associate morality with big (traditionally) religious questions of good and evil (should i steal/kill/etc.) and ethics with professional/business questions of right and wrong (should i give that person credit for their ideas/steal my work computer/etc.). Are these kinds of questions completely separate or are they different applications of one larger abstract fundamental concept? Is there a word for the "smalller" stuff? In other words, does there exist a concept for actions for which the consequences aren't really that big of a deal, but if you do it, you're a dick/douche/appropriate slang?
For "big" situations, a person has probably thought about it beforehand. Therefore, their response has probably been orchestrated based on a personal "worldview." However, I suspect that, in the heat of the moment and in a split second, for scenarios that haven't been thought about ("small stuff"), one probably tries unconciously to minimize the future potential for feeling guilt. To do this well, one probably has to have some sense of whether a particular action will lead to guilt. If so, presumably one get "better" with time after accumulating more experience. Maybe it's like muscle memory? Does feeling guilt and/or regret have anything to do with things that are considered wrong/evil/not okay/etc.? Is there a relationship or mapping among right/wrong, good/evil, and okay/not okay?
Does the degree of an action even play a role in whether it's okay or not? For example, kicking one ugly, loud, obnoxious, anti-social, disfigured puppy into the middle of an empty road late at night when you're drunk can, from a certain point of view, be rather funny (i.e. it's okay). On the other hand, throwing a box of cute puppies into a busy intersection during rush hour is probably not cool (i.e. it's not okay). Maybe that's not the best example, but hopefully it gets the point across. (note: I don't kick dogs of any kind.) How much weight should be given to the motivation of an action versus the consequences of the action? What, if any, are the moral/ethical absolutes? (Never kick puppies...) In other words, is it always possible to cook up a realistic situation that presents mitigating circumstances for any kind of action? (...unless it's for self-defense) Personally, I can think of only one thing that you should never do under any realistic circumstances (which I'll leave unsaid to encourage discussion); but there could certainly be others. (I know, I know: define "realistic"...)
Saturday, June 2, 2007
Hard Sudoku Puzzle (and Solver Website)
I was trying to do this Sudoku puzzle without writing down anything other than the correct solution. That failed miserably, and even after I gave up on my "no scratchwork" rule, it still wasn't easy. I wondered if there was an website that would solve it for me, and of course there is. How difficult do you think this one is? Got a harder one for me to try?
Puzzle 136 from "Sudoku to go" by Will Shortz (the NYT crossword guy)
| 2 | 7 | 1 | 4 | 3 | ||||
| 3 | 4 | 5 | 2 | |||||
| 8 | 2 | |||||||
| 3 | 6 | 2 | 4 | |||||
| 5 | 6 | 1 | ||||||
| 6 | 3 | |||||||
| 8 | ||||||||
| 4 | 1 | 8 |
Puzzle 136 from "Sudoku to go" by Will Shortz (the NYT crossword guy)
Wasteful-but-Wonderful Fruit Salad
It's summertime again, and you know what that means? Alan's wasteful-but-wonderful fruit salad.
Ingredients:
2 large ripe watermelons
1/4 cup chopped mint leaves
1 lime
4 ripe bananas
1 ripe cantaloupe
Refrigerate the watermelon and cantaloupe over night. This is essential! If the melon is room temperature when mixed with the banana, you'll either have warm melon or mushy banana at the end.
Once the melons are cold, cut out the hearts of each of the watermelons and toss out the rest. The heart is the middle part that has no seeds. (In a seedless, use your best judgment) Cut the watermelon hearts and your cantaloupe into about 1 inch cubes. Add mint. Cut the bananas into bite-sized slices and juice the lime over them. This will keep them from turning brown. Mix it all together and let rest in the fridge for 1 hr. Serve COLD!
Notes:
1. Other fruits can be added (blueberries would be my next choice) but avoid oranges and grapefruits; They don't play well with others.
2. If you REALLY like sweets, you can shake 3 tablespoons of splenda over the salad. Spenda is better that sugar here because of its high solubility in cold water.
Ingredients:
2 large ripe watermelons
1/4 cup chopped mint leaves
1 lime
4 ripe bananas
1 ripe cantaloupe
Refrigerate the watermelon and cantaloupe over night. This is essential! If the melon is room temperature when mixed with the banana, you'll either have warm melon or mushy banana at the end.
Once the melons are cold, cut out the hearts of each of the watermelons and toss out the rest. The heart is the middle part that has no seeds. (In a seedless, use your best judgment) Cut the watermelon hearts and your cantaloupe into about 1 inch cubes. Add mint. Cut the bananas into bite-sized slices and juice the lime over them. This will keep them from turning brown. Mix it all together and let rest in the fridge for 1 hr. Serve COLD!
Notes:
1. Other fruits can be added (blueberries would be my next choice) but avoid oranges and grapefruits; They don't play well with others.
2. If you REALLY like sweets, you can shake 3 tablespoons of splenda over the salad. Spenda is better that sugar here because of its high solubility in cold water.
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