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I hope this isn't your homework! This condition, "Sen's property alpha", is often called "independence or irrelevant alternatives". Another way to say this is that "if an alternative a chosen from a set B is an element of a subset A of B, then a must be chosen from A." Let's show that WARP implies Sen's alpha. Let a \in A \subset B and a \in C(B). We want to show that a \in C(A). Suppose on the contrary that a \not \in C(A). By assumption, C(A) is nonempty, so there exists some b \in C(A). Since A \subset B, we know that A = A \cap B. (intersection) Now you can apply WARP, which says "if x,y \in B \cap A, and x \in C(B), and y \in C(A), then x \in C(A)". (I just changed the letters.) Take x=a, y=b. We stated in the first line that a \in A, and b \in C(A) implies b \in A. Since x,y \in A = B \cap A, and x \in C(B), and y \in C(A), by WARP we must have x \in C(A), i.e. a \in C(A), which contradicts our assumption that a \not \in C(A). Hence we conclude that the assumption is false, so we have a \in C(A).

Sorry about the off-topic question, but do you mind going into a bit more detail about which results from complex analysis you used? I've seen comments on this forum about how complex analysis is not useful for economics, so I would think that if it is used at all it would be for some obscure theory field. I'm curious about how you used it, this sounds interesting. Thanks!

Thanks to all who responded! @Economists: I'm not sure if I should mention names, but a few Harvard grad students could be used as examples (YY has 6, JG has 4, SH has 6, and YK has 2 plus 9 submitted). @santacanyon: Your comment seems consistent with my observations, but why is it the case that theory students are more likely to publish?

After looking at the websites of some current grad students, I have noticed that some of them have already published papers. A few have even published more than three. I'm not completely familiar with the system, but from my understanding, a doctoral thesis / dissertation essentially consists of 3 loosely related papers (hence titles such as "Essays in ..."), of which one is condensed to form the "job market paper". And not every chapter in every dissertation gets published, so I would think that getting a paper accepted or R&R while in grad school would be more than enough to have a dissertation chapter. Why would these students still be in grad school, if they have already done more than enough research for a dissertation? Is a dissertation more than just 3 (publishable) papers?

The Powerprep practice test gives us a score range and tells us the number of questions that we answered correctly in each section. Rachel and factorial have confirmed that the actual revised test reports the score ranges. Does it also tell you the number of questions that you get right, or is that information omitted? Thanks!

I have seen people here discuss whether it is better to have a good, personal letter from someone who is not famous or a less personal letter from someone who is well-known. The consensus seems to be that the former is preferable. My question is the following: Assuming that both writers know the applicant equally well and that both letters are equally well-written, is it better to have a letter of recommendation from a famous professor from a completely different area or a less famous professor from the field that the applicant is interested in? For example, if you want to study micro theory, is it better to have a letter from the not-so-well known micro theorist or the famous macro empiricist? Thanks!

I think this would be a great idea. Have you heard of stack exchange? The original one (stackexchange.com) is for programming, but there are many derivatives such as Mathematics - Stack Exchange. There's also MathOverflow, which encourages people to use their real names, and you can find undergrads, grad students, and professors here having great discussions with no trolling. There is a process for getting new stackexchanges created. In fact, there already exist proposals for economics. See Research Economics - Area 51 - Stack Exchange and Economics - Area 51 - Stack Exchange. The latter currently has more followers, so it has a better chance. There is also one for game theory: Game Theory - Area 51 - Stack Exchange. Just to see what this could turn in to, here is one for philosophy which was created last week: Philosophy - Stack Exchange. I hope that we can get something like this going because it would be great to have more discussion of research.

I've done some searches, but I can't really find a complete story about getting a phd from business schools. First some general questions: 1. Most research at b-schools is applied, but they have people doing theory as well. In which areas of economic theory are each business school considered strong compared to the respective econ department? 2. Is it common for b-school phds get jobs at econ departments? vice versa? Which b-schools have better placement relative to the respective econ program? 3. Which schools allow / don't allow applicants to apply to both business school and regular econ? Lastly, if I am interested in welfare economics, public economics/finance, game theory, decision theory, and social choice theory, should I apply to b-school econ or econ? Which programs in particular do you recommend? Thank you for all the help!

Ideally, your letter writer should already know your name, right?

Thanks everybody, I appreciate the advice!

Thank you rthunder27 and zeno for the suggestions! Perhaps I should add more information about my background: I'm a math major, but I want to get a PhD in economics. I've taken standard econ courses so far (intermediate micro, macro, metrics, game theory). For math, I've taken several semesters of undergrad analysis (measure theory, complex, functional). I had wanted to take both, but that will not be possible. For alternatives, I was thinking if I don't do real this year, I could take complex along with micro; or if I don't do micro, I could take metrics along with real. At the moment, I'm indifferent between the two paths, so any further comments are welcome. Thank you!

Assuming you could only take one, either grad micro or grad real analysis, which one would it be? They are offered at the same time next fall, so I have to pick one (and I can do the other one the following year). I have enjoyed both subjects so far, making it hard to make a decision based on which interests me more, so I thought perhaps 'signaling' value could be a tiebreaker. Any suggestions? Thanks!

Thanks to those who replied. So at schools that do not have quals, is it not possible to place out of first year courses?

On the "Sample Prelims and Requirements" sticky, it says that Berkeley doesn't have any prelims. I know that some other schools let students place out of first year core courses if they can pass the prelims. Does anyone know what the procedure for this is at Berkeley (if it is even allowed)? Also, are there any other schools that don't have prelims or that have a different placement system from the one described? Thanks!

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