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31 January, 2004

Bring on the Draft

Allan Hazlett recommends replacing the current search procedures with an NFL style draft. He says one of the big advantages of this procedure is that we could replace all the costs of interviews etc with one big draft day extravaganza. But surely this is a mistake – the NFL draft has just as many expenses pre draft day as we have. The ‘exhibition’ games like the Senior Bowl, the combines, private workouts and so on are just as expensive as campus interviews etc.

That got me thinking, why don’t we have combines in philosophy? That is, why don’t we have somewhere where every student on the market can turn up and present a paper and field questions and generally show what they’re made of? Well, you might say, how could we arrange such a thing, and wouldn’t it be expensive and so on? Maybe, but I have an idea.

Why not replace all the papers, or at least all the colloquium papers, at the APA Eastern with papers by new candidates? One problem is that this would require making the conference a little bigger – or at least require more papers being on simultaneously. This year there were a little under 100 colloquium papers, but there are more than 100 new PhD students going on the market. Still, with only a small expansion of the colloquium program (and perhaps cutting back on the symposiums) we could give every new candidate a chance to present a paper. Ideally these would be commentator-free. Even more ideally the candidate would present a short summary of a pre-posted paper and the bulk of the hour could be spent responding to questions as at BSPC. This would mean hiring departments would have to send scouts as well as interviewers (if they are interviewing) but I think it could be really useful. For one thing, departments could have different scouts go to different papers and so get a chance to have a look in person at many more candidates than they do now.

Note this is not like my wild suggestion that the APA Central go unrefereed. That’s a good idea that I don’t think will ever happen. I think going the whole way and making the APA Eastern entirely a hiring conference, with the papers being hiring related just like everything else, really could happen. And I think it could be a good change.

This isn’t mean to be an endorsement of the draft idea. Allan’s 5th point, that drafts stop dynasties forming, strikes me as a really bad feature of the draft. I like dynasties. When I think about just how nasty good [insert name of department I’ll be in next year here] could be over the next few years, I start to …

Sorry. Got carried away there. It’s Superbowl week, it’s too easy to get excited. Too much time reading Bill Simmons’s Superbowl blog gives me too many big ideas. Back to normal now.

Posted by Brian Weatherson at 11:17 pm

10 Comments »

30 January, 2004

Supacrush

Will blogging help you finish your thesis? Watch Supacrush to find out. (Well, watch Supacrush to find out one data point that may or may not be anomolous.) In the meantime, will blogging help me read a pile of grad school applications, or prepare classes, or write papers, or decide where I’m going to live next year? Stay tuned…

UPDATE: Some of Kaye Trammell’s advice about secret blogging may (have been) relevant here. I have toyed with setting up a secret blog at various times, in recent times largely because I felt like writing down my job-choice-related deliberations. If I do I’ll have to keep various of these tips in mind.

Posted by Brian Weatherson at 12:33 pm

3 Comments »

State Considers Banning ‘Evolution’

Via CNN.

The state’s school superintendent has proposed striking the word evolution from Georgia’s science curriculum and replacing it with the phrase “biological changes over time.”

From the details it looks like this is repeating the Kansan tragedy as farce, and since the proposal has bipartisan opposition this farce probably won’t go far. But don’t you just love a country where scientific theories that are accepted universally within the relevant scientific community are the subject of partisan disagreements? If this were happening in a tiny unimportant country it would be the stuff of late-night comedy. Instead, well it probably is a little tragic.

Posted by Brian Weatherson at 10:55 am

1 Comment »

Bayesianism, Infinite Decisions, and Binding

Frank Arntzenius, Adam Elga and John Hawthorne have a paper up with that title on the PhilSci Archive. (I had not noticed this previously because my browser was still checking the 2003 PhilSci Archive. Must remember the new year changes things!) It’s well worth reading, though I still prefer my solution to the Banker’s Paradox.

By the way, for a pleasant little morning brain challenge, find a non-recursive definition of the payouts in their Bill Gates in St Petersburg game. It took me a little while to figure it out, but I think I know at least one simple answer now.

Posted by Brian Weatherson at 10:48 am

2 Comments »

Weird Google Hits

I’ve really got no idea how this happened, but Nedstat assures me that someone made it to TAR from this search. It doesn’t say how long that searcher stayed. I also got pinged via this search, which I guess is a little more relevant to TAR’s content.

Posted by Brian Weatherson at 1:32 am

2 Comments »

He Wanna Be Adored

That last post made me think about wanna, and now I’m a little confused. How grammatical do each of the following seem to you?

(3) a. I want to be adored
      b. I wanna be adored
(4) a. You want to be adored
      b. You wanna be adored
(5) a. He wants to be adored
      b. He wanna be adored
(6) a. She wants to be adored
      b. She wanna be adored
(7) a. They want to be adored
      b. They wanna be adored

My intuitive judgments are that all the a sentences are OK, while 5b and 6b are very bad, and 7b is pretty bad. It turns out Google agrees that 5b and 6b are much worse than 3b and 4b, but it also thinks 7b is bad. But all the forms are used widely enough that they seem kinda acceptable at least to some. Here are the counts for searching for pronoun followed by “want to” or “wanna”.

want to
wanna
Ratio
I
10,600,000
2,390,000
4.4
You
16,400,000
1,510,000
10.9
He
1,760,000
11,800
149.2
She
816,000
16,500
49.5
They
4,030,000
79,400
50.8

79,400 is many more hits than I expected for a phrasing I regard as marginal, an 28,300 between ‘he’ and ‘she’ is way more than I expected for a phrasing I regard as clearly bad. At least the ratios were way down than from ‘I’ and ‘You’.

Posted by Brian Weatherson at 12:38 am

2 Comments »

De Se Desire Reports

Europa Malynicz sent me the following case, which it turns out we have different intuitions about.

Brian is running for election on the Monster Raving Loony Party ticket. He did not want to win when he entered, because he’s just smart enough to know that Monster Raving Loonies are bad for government. But, being a bit of a Monster Raving Loony himself, he’s now forgotten that he’s in the contest. While watching nightly news he sees himself dressed up as a Teletubby disguised as a teacup campaigning for votes. Not recognising who he is, but being very impressed with the hat he’s wearing, he forms the desire that that guy wins the election. In this context, which of (1) and (2) are true?

(1) Brian wants Brian to win the election.
(2) Brian wants to win the election.

I think that (1) is probably true, although it might be misleading. But I think (2) is false. (Europa thinks it is also true but misleading, which is where the difference arises.) So the first reason I’m posting this is to check what your intuitions are. Could (2) really be true in this context? Could (1)?

The second reason I’m posting this is because I like drawing wild hypotheses on the basis of remarkably little data. Here’s two that look promising.

De Se Hypothesis
(2) is only true if Brian has a de se desire, a desire that is essentially self-directed. It’s false in the case described because he has a de re desire that that guy wins, a desire that is directed at the guy on TV, which just happens to be him.

PRO Hypothesis
It’s really hard to explain the difference between (1) and (2), i.e. that one of them is true and the other false, if there is a hidden pronoun PRO between ‘wants’ and ‘to’ in (2). So here’s some evidence that there isn’t one. (I make no claims to originality here – debates about hidden pronouns are very well worked over so I suspect someone has made this point before.)

Posted by Brian Weatherson at 12:22 am

9 Comments »

29 January, 2004

A Really Bizarre Two-Envelope Paradox

This could get complicated. I wanted to create a two-envelope paradox where the expected utility of receiving either envelope was not infinite. It’s impossible to create a paradox when the utility is finite, but it turns out it is possible to devise one where the utility is undefined. What’s the difference between an infinite utility and an undefined utility? Well, if X is infinitely valuable, it is irrational to prefer any good with finite utility to it, whereas if its utility is undefined, such a preference would be rationally acceptable. For a simple example, consider a situation like the following.

Eris tosses a fair coin repeatedly until it falls heads. She counts how many throws that took, call that n, and then places something worth (-2)n utils in an envelope. How much is the envelope worth?

If you try and work this out, it comes to -1+1-1+1-1+1-…, which is obviously undefined. I think (and I could be wrong about this) that for any good with finite utility, it is rationally permissible to be indifferent between Eris’s envelope and that good.

That isn’t the two envelope paradox I have in mind though. It works something like this. Eris takes three fair coins, A, B and C. She tosses A repeatedly until it falls heads. Let n be the number of tosses this takes. She then tosses B and C. The amount of utility put into the two envelopes is determined as follows:

 Larger Smaller
Heads3n+13n
Tails5-g(n)5-g(n+1)

where Heads means B lands heads, Tails means B lands tails, and g is the function recursively defined as follows:

g(1) = 2
g(n+1) = 2 * g(n) – n/4

If coin C lands heads she puts the larger amount into the blue envelope, and the smaller amount into the red envelope. If it lands tails she puts the larger amount into the red envelope, and the smaller amount into the blue envelope. She then gives you the blue envelope.

Question: How much is the blue envelope worth?
Answer (I hope): It’s undefined.

Question: Should you pay to swap envelopes?
Answer: Er, no.

Question: If you see how much is in the blue envelope, will you want to swap?
Answer (I hope): Yes – whatever you see the expected utility of swapping is at least 1/12.

Question: Was this whole thing just an attempt to get fewer readers?
Answer: No – some people find this stuff genuinely interesting. Well, at least I find it genuinely interesting and I can project.

Posted by Brian Weatherson at 11:57 pm

2 Comments »

Linguistic Amusement

A quick illustration of the fixity of clichéd expressions. H. R. Block (a tax return company) currently is running a promotion that if you don’t get the maximum possible tax return using them, the tax return is free. Here’s the slogan they use (at least on bus shelters in downtown Providence.)

Get every penny you deserve, or don’t pay a dime

I was sort of stunned to notice how much more natural that sounds, even to my foreign ears, than

Get every nickel you deserve, or don’t pay a quarter

While on this theme, a couple of Google spellchecks that don’t really help.

judgment: 8,190,000
judgement: 2,760,000

busses: 417,000
buses: 3,660,000

The last one of these amuses me every time I walk past the corner in downtown Providence where there are two signs opposite each other with a word for more than one bus, and no other word containing ‘s’, and five ‘s’s between them. (Disclaimer: At least there were such signs last I looked – they might have been replaced/repaired by now.)

Posted by Brian Weatherson at 2:01 am

1 Comment »

How Surprising is the Two Envelope Paradox

Matt Weiner writes:

I don’t think we want it to be the case that, once you open the first envelope, you have a reason to switch. Now, one issue here is the mathematical impossibility of defining a probability distribution on which every rational number is equally likely—probabilities are supposed to be countably additive, which makes it impossible to assign the same value to an infinite number of different ones. [Afterthought: Anyone know if non-standard analysis can do any work here?]

Actually you don’t even need non-standard analysis. As John Broome (1995) pointed out you can get just the result that Matt doesn’t want within standard probability theory. To be sure, you can’t get the result that whatever you see in the envelope it is equally likely that there is twice as much in the other envelope as half as much. But we can get the result that whatever you see, you should switch. Here’s one way. (It could be Broome’s exact method for all I remember – I don’t have the paper in front of me. And the numbers feel familiar from what I remember of Broome’s paper.)

Let’s assume we have a red and blue envelope, a currency denominated in utils, and a God, Eris seems appropriate, who chooses how much to put in the envelopes as follows. She takes a coin that has a 2/3 probability of falling tails, and tosses it repeatedly until it falls heads. Let n be the number of tosses this takes. (If it falls tails infinitely often, stipulate that n=1.) She then takes a fair coin and tosses it once to determine what goes in the envelopes by the following rules.

If heads, then 2n utils in the red envelope and 2n+1 utils in the blue envelope.

If tails, then 2n utils in the blue envelope and 2n+1 utils in the red envelope.

Let’s assume she now gives you the red envelope and you somehow (presumably with the help of another God – this part sort of defeats Eris’s purposes) get to see what’s in it. It turns out there are only two cases worth considering.

Case 1: You see 2 utils. In this case you know that there are 4 utils in the other envelope, so the expected gain from switching is 2.

Case 2: You see 4 utils. In this case you know that there are either 2 utils in the other envelope or 8. The prior probability (i.e. before Eris tosses any coins, which we can assume is when she stops telling you what happens) that the red envelope would end up with 4 and the blue envelope with 2 is 1/9. The prior probability that the red envelope would end up with 4 and the blue envelope with 8 is 2/27. So by a quick application of Bayes’s theorem, the posterior probability that the blue envelope has 2 is 0.6, and that it has 8 is 0.4. So the expected value of the blue envelope is 2 * 0.6 + 8 * 0.4 = 4.4. So the expected gain from swapping is 0.4.

What about all the other cases you ask? Well I won’t try doing the algebra in HTML, but it isn’t too hard to prove that for any x larger than 2 that you see, the expected gain from swapping is x/10. So whatever you see, you should not only prefer to swap, you should be prepared to pay at least 0.4 to swap. And note that we’ve only used standard (countably additive) probability functions here and standard reasoning.

By the way, although I’ll leave the proof for another day, I’m pretty sure that the expected utility of receiving one of the envelopes does not have to be infinite for a two-envelope paradox style situation to arise, i.e. a situation where you will want to swap whatever you see in your envelope, whichever envelope you are given. (No one I know of has ever said that it has to be, but it’s easy to misread David Chalmers as saying that it must be.) In the case here, the expected value of Eris’s gift is infinite. (Well, until she starts getting you to pay to switch envelopes.) But I’m pretty sure that by mixing positive and negative payouts in the distribution it’s possible to produce a paradoxical distribution with each envelope having a strictly undefined expected utility.

Posted by Brian Weatherson at 1:42 am

5 Comments »

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