Monday, November 28, 2011

More Charity Auctions

Check out the post over at This Young Economist for some interesting additional facets of charity auctions.

I wonder if more value typically flows to the charity through the initial donation of items or through subsequent inflated bidding on those items.

Meteors and Gender Differences

A meteor falls out of the sky and destroys your house.  "Why me? Life isn't fair!" you might be heard to cry.  There would probably be a lot of nodding from all directions.

Well yeah, it's pretty unfair from the perspective of after the meteor hit your house.  Everyone on the face of the planet has a non-meteor-kablooeyed house except you!  But on the other hand, before it happened, everyone had an equal chance of destruction.  From the perspective of beforehand, everyone is in the exact same situation, so it is in some sense fair.

The basic idea of fairness is something like "equality between people."  But equality from what perspective?


To accommodate randomness, let's say a situation is fair if two people are drawing from the same distribution. The question is: which distribution are we requiring to be the same?  The distribution of outcomes conditional on what point in time, or more generally what facts about the world?  What do we take as given, and what is still up in the air?  Fairness depends entirely on what you condition on.

Disagreement here is widespread.  That's okay.  But once in a while, it's nice to step back and notice what we're conditioning on, and perhaps question it.



To that end, here's a thought exercise: Why do we worry so much about unequal outcomes between groups of people?  Let's take a step back.

Consider a world where each person simply has a life outcome and a label.  You can think of the life outcome as income or any other measure of "success," and the label could be something like race or sex.  Our moral starting point is that the label shouldn't matter; skin color or gender should be irrelevant to how much we care about a person.

Now, there is a joint distribution over outcome and label.  Associated with it, we have densities for outcome and label alone, as well as conditional densities for each given the other.

Now consider these two scenarios:
  • Scenario 1: The label is drawn first, and then the outcome is drawn from the conditional distribution (conditional on the label that was already drawn).
  • Scenario 2: Life outcome is drawn first, and then the label is drawn conditional on the outcome.  
Mathematically, of course, the end product is the same in either case, namely (outcome, label) pairs drawn from the joint distribution.  (Or, if we are label-blind, we just see a bunch of people drawn from the same outcome distribution in each case).  But to most people, I think scenario 1 seems potentially much less fair than scenario 2.  Why?

Because fairness depends on what you condition on. In the first scenario it seems sensible to condition on the label, and say: The label shouldn't matter, so the distribution of outcomes conditional on the label should be the same for different labels. But in the second scenario, everyone draws from the same distribution of outcomes, and afterward there is an irrelevant draw from a label distribution. (In this world, people don't care about the label per se, so once their outcome is drawn, nothing else matters).

But here's the kicker.  Should the scenario we're in really make any difference to fairness?  Do we really want our notions of fairness to depend on things like the order events actually unfold?  If the outcome is what matters, and the outcome is the same in each scenario, what does it matter how we got there?

Personally, I don't want to care about anything I don't care about!  I care about the pool of realized outcomes, not labels, and to be label-blind means to have no preference over how labels are split among those realizations.  I don't want to get sucked into finding differences between scenarios 1 and 2; I want my notion of fairness to be robust to the order of irrelevant events such as the assignment of irrelevant labels.



Is it unfair to women that there aren't so many good athletic career opportunities?  As a point of fairness, how do they compare to the 99.99% of men who just aren't good enough at sports?  Is there a difference between a woman who can't be an NBA all-star because she's drawing from a distribution that doesn't have support over the upper tail of the rankings, versus a man who can't be an NBA all-star because he happens to just not be awesome at basketball?


Tell me, what do you think?  Is there a coherent way to argue that labels should and shouldn't matter at the same time?


[Discrimination, by the way, is orthogonal to this post.  To the extent that unequal outcomes across groups is evidence of discrimination, you might be upset indeed, the above notwithstanding!  But even putting discrimination aside, many people will still observe the unfairness of inequality across groups.  Is there something else going on here?]

Saturday, November 26, 2011

Charity Auctions

Why are charity auctions insanely successful?  A few possibilities:

  1. They attract people who aren't regular auction-goers.  (These people don't know to correct for the winner's curse and so forth, where applicable).  
  2. People are happy to give some money to charity (and so will bid higher than they would have).  
  3. Charity auctions give people an excuse to bid the way they're really dying to bid in a normal auction, without fear of reprisal (from themselves or others) that they were being irrational.
Now, I wonder how efficient the outcomes of charity auctions turn out to be.  That is, do the people who value the items the most tend to end up with them?  Or do the items go to those who are most willing to give to charity?  The answer would tell us something interesting about which of the reasons above is playing the bigger role.

Monday, November 21, 2011

Perspective

I'm sure this is going to be linked from all over the place, but if you haven't seen today's xkcd comic...

I might have to buy the poster.

Monday, November 14, 2011

Strong feelings undeserved and overserved

I had a good friend in elementary school who went away to Israel and came back poisoned with hatred for The Enemy.  It doesn't really matter which side he was on.  If my memory is to be trusted, I didn't much care about the situation in the middle east at the time.  I just remember being sad that my friend had been changed in such an overt and terrible way.

I have a big problem with blind hatred, which unfortunately seems to describe most hatred.  It is possible to understand something and still hate it.  But it's much easier -- and so more common -- to hate something you don't understand.  Because, though the world is a pretty ordered place, we often fail to see that order, and then we tend to assume it isn't there.  And if something makes no sense, we don't have to take it seriously.  We can drop it in the mud and walk all over it without a second thought, because it has no right to exist, making so little sense and all.  And the people who believe it are just as easily dismissed.

We try not to execute people without being pretty sure they're guilty.  Hatred is, I think, a sort of mental execution that we shouldn't be so hasty to dole out in advance of understanding.  How can hatred be so firmly buttressed by the conviction that the enemy is being unreasonable, when we don't even understand why the enemy is behaving in such a manner?  Extreme reactions should require a high degree of confidence.

So, what bothers me is hatred in advance of understanding.  What bothers me is the depressingly default assumption that the burden of understanding falls on the person (or thing) to be understood.  That it is their job to be understood by us, not our job to understand them.  That if we do not understand them, it must be that their position doesn't make sense, not that we are failing to make sense of their position.

Let me inject a little perspective.  Since the dawn of man, we have looked upon the world and seen no shortage of black boxes.  The world was impossibly mysterious at first.  We just didn't understand its workings.  In retrospect, this lack of understanding was a property of our brains, not the world.  But instead of recognizing that, we took our inability to explain things as strong evidence that they were, in fact, inexplicable.  There was no underlying order that we just hadn't discovered yet; rather, things were inherently mysterious.  Of course we gave names to the mysterious things -- called them "magic" and so forth -- but you can't actually demystify a cat by calling it Mittens.  Cats are complicated, you know.

Of course there are still many black boxes to be cracked open, although by now, in the realm of science at least, we've pretty much got the idea that the boxes have stuff in them even before they're opened.  We understand that discovering an unopened black box should probably weaken our confidence in our understanding of the world, not readily convince us that the world actually makes no sense.

But it seems we haven't quite absorbed the analogous moral on the topic of why people do what they do.

Suppose half the world believes A and the other half believes not-A.  Quite apart from the question of whether A or not-A is the truth, there is the question of why a person might think one or the other is true.  And if we can't understand why people on the other side of the table think what they think, our brains have failed.  It should weaken our confidence in our true understanding of the situation, not convince us that those people actually make no sense.

And when we fail to understand the other side, we are in no position to make a legitimate judgment about what ought to happen, or to hate anyone for supporting an outcome we don't even know how to reasonably evaluate.

Of course, transactions and debates and negotiations and wars can occur without either side understanding the other.   And I don't mean to say that's inherently wrong; it will sometimes be optimal to go to war in advance of full understanding.  But confusion should make us uncomfortable, not somehow magically bolster (!) our eagerness.

[This post inspired by a depressing display of blind hatred in a Facebook debate between several people from different countries in the middle east.]

Tuesday, November 8, 2011

Punkin Chunkin

Via MR, a progress report on the pumpkin launching ability of our great nation.  Why has the max distance launched leveled off at about 4000 feet in recent years?

I'm not exactly sure why, but I once actually attended the Punkin Chunkin event.  There were several classes of competition, from catapults and trebuchets all the way up to pneumatic cannons.  If memory serves, the cannons were arrayed at one end of a large field, and would take turns firing these white pumpkins.  Someone would rush to where the pumpkin asploded, and the distance would be measured, possibly with some type of laser device.

Only, the field wasn't long enough.  Some of the pumpkins went so far that they were lost in the woods at the other end of the field.  They didn't count, sadly.

So maybe 4000 feet is just the length of the field.  Or maybe this high school memory has decayed way beyond the point of trustworthiness.