Much depends on the country you're in. You have better prospects in the US, I think, than elsewhere because the US has no mandatory retirement age, holds people responsible for their own retirement savings, and has rules against age discrimination. (In many other countries, when a university hires someone at 45, it gets burdened with the obligation to pay her/him a pension after age 65 or so.) I think that, if you go on the job market at 45 or so with a really good dissertation and perhaps two published articles, you stand a fair chance of landing a job, especially if you also have a track record as a good teacher or teaching assistant. At least your prospects won't be substantially inferior to those of younger, equally qualified candidates.
There are some technical issues with your formula. You need to decide whether you want to understand L as a constant (80 years), thus assigning equal value to each year of human life, or whether you want to understand L as a variable that varies from person to person, thus assigning greater value to life years of persons whose lives are short. There are plausible arguments on both sides.
You might also rethink your reliance on percentage increase in the goodness of a person's life/time. Do you conceive of goodness as being always a positive number? And do you assume there to be some upper bound such that goodness can vary, say, between zero and one? Assuming all this, your formula is prioritarian: you give greater weight to those who are worse off. Thus, according to your formula, getting someone from 0.01 to o.11 is 50 times more valuable than getting someone else from 0.5 to 0.6 (+1000 percent versus +20 percent). Prioritarians often use a different formula, measuring down from the top or from some sufficiency threshold and then tagging on some exponent greater than 1. If the exponent is 2, then this formula yields a value of 0.99^2-0.89^2=0.188 for the first improvement and a value of 0.5^2-0.4^2=0.11 for the second improvement. Here the first improvement is not even twice as valuable as the first.
Leaving these technicalities aside, it seems plainly false to me to assume that "anything really important will eventually be achieved". There are, to use your own example, billions of ways of organizing education in the United States. Do you really think the best of these will eventually be achieved? In many ways, the last thirty years have been the opposite of progress: there have been more chronically undernourished people in the last two years than ever before in human history, for example, and similarly for environmental degradation, resource depletion, and the rapidity of climate change. So I think there are real opportunities not merely to accelerate progress but also to stave off retrogression or to turn retrogression into progress.
The fact that there are so many possible futures (billions of ways of organizing education in the United States, etc.) also saddles you with a baseline problem. If you devote your life to improving the US education system, how will you know how this system would have evolved without your efforts? I believe that such impacts of persons are next to impossible to ascertain with any precision, even long after the fact. For example, how would the world have evolved if Immanuel Kant had died in his crib? I doubt anyone can provide anything like a solidly grounded answer to this question.
This thought of Kant suggests two further points. First, even if you devote your life to the improvement of the US education system, the effects of your life will reverberate throughout the entire human world (witness the "non-identity problem" as one example of such reverberation -- how you decide to live will likely affect who (in terms of DNA) will be born in the future). Second, the effects of your life will last into the distant future, quite possibly making much more of a difference in the fourth millennium than in our 21st century.
The upshot of these last three paragraphs is that, even if you're well on your way toward a reasonable formula, it will be next to impossible to obtain the empirical data and -- especially -- the predictions that the formula requires. In the end, you'll have to make an intelligent guess about how you can sustainably add the most to the collective effort to make this world better. (Here "sustainably" alludes to yet another uncertainty: concerning your adherence to your original plan. It makes sense to choose a path that you will find interesting and challenging so that you will be happy and productive in its pursuit and will want to stick with it rather than switch out before you can really achieve much.)
Yes, there surely are (just look through the list on the right), though it's probably also true that women are better represented in practical philosophy than in philosophy generally. Outside practical philosophy, among the earliest in this country was Ruth Marcus who taught Saul Kripke, among many others, and had a very distinguished career at Yale. Leigh Cauman (even earlier) studied with Quine, taught logic, and was the managing editor of the Journal of Philosophy for many years. Women are very strongly represented in ancient philosophy, with Gisela Striker (Harvard) a good example. In the history of modern philosophy there's Beatrice Longueness (NYU) . If you look through the various departments -- www.philosophicalgourmet.com/overall.asp -- you'll find that most of them have one or more female philosophers outside practical philosophy, so examples could be multiplied. While the profession is still a long way from where we should and want to be, further progress is made likely by there already being a substantial female presence in most areas of philosophy.
Nearly all the unbearable suffering in this world occurs among the poorer half of humankind which, collectively, accounts for about 2.4 percent of global consumption and 1.1 percent of global wealth. Are doctors lining up to relieve this suffering? Actually, the opposite is the case. Many physicians trained at great expense in poor countries are lured away to rich countries after their training is completed, sometimes by very active recruitment efforts. So, if you became a doctor to relieve this unbearable suffering, you would be one of a tiny number of doctors, each of whom is -- as best as he or she can --replacing hundreds of doctors migrating in the opposite direction. Check out Partners in Health (PIH) for some more information.
If you do not become a doctor, the person taking your place in medical school is very likely to choose what indeed is a replacable job: caring for affluent patients in an affluent country. How many GP's in this country don't even open their practice to Medicaid and Medicare patients?
As for bankers, most money they give to charity goes to affluent domestic religious communities, universities, opera houses, museums, and the like. So there, too, you can make a contribution to relieving unbearable suffering that, but for you, would not be made.
This depends on the university as well as on your specific interests in this field. You might apply especially to universities that have both: a law school with a real interest in legal theory as well as a philosophy department with strength in philosophy of law, ethics, and political philosophy. Such universities also typically offer a joint JD/PhD program, which may be just right for your interests and would allow you to keep more career options open.
If you are really mainly interested in "the philosophical underpinnings of research in political science," then one plausible solution is to apply to political science doctoral programs after all. Look for a program that has strength in political theory/philosophy and/or is located at a university with a strong political philosophy presence in its philosophy department. This way you can take courses in political (and moral) philosophy and can later, when it comes time to write a dissertation, invite a philosopher to be on your committee. This sort of collaboration is quite common -- for example, as a philosopher I have supervised four political science dissertations at my institution.
Should prolonged exposure get you interested in other areas of philosophy and make you eager to write a dissertation on a topic that does not fit into political science, then you'll be in a very good position to switch departments at that point. Doing so is usually much easier than getting admitted from the outside (because by then you're known to the philosophy faculty and already on the university's budget).
Ranking these dimensions is impossible, I believe. You cannotcompare dimensions as such, but at best only specific differencesacross dimensions. Consider, for example, whether teaching experienceis moreimportant than awards. Well, a large advantage in teaching experiencewill outweigh some small advantage in awards, and a large advantage inawards will outweigh some small advantage in teaching experience. Inorderto compare advantages across dimensions, we would need a metric withineach dimension as well as a standard of comparison across thesedimensions. We might then be able to conclude that, say, teachingexperience is more important than awards in the sense that a smalleradvantage in teaching experience outweighs a larger advantage inawards. But such a conclusion presupposes cross-dimensional comparisons ofmagnitudes.
There are two further difficulties. First, dimensions that receive a lot of attention from some mayreceive very little attention from others or none at all. Employers have quite diverse needs, interests, preferences, andpredilections -- a small liberal arts college will give greater weight to teaching relative to publications than a major research university. In the same vein, hiring decisions are often made by acollective consisting of people who vary greatly in what they pay attention to and in how they then form theirjudgments.
Thesecond further difficulty is that someone on a hiring committee will adjust the weight sheassigns to specific pieces of evidence according to the other evidenceshe has. The weight she will give to an applicant's grades may dependon how she assesses the school he attended, for example, and the weightshe will give to his conference appearances may depend on how pushy shetakes him to be. Like a juror in a criminal trial: One assigns acertain initial credibility to the various witness testimonies andpieces of evidence; but one then adjusts such initial assignments up ordown depending upon how each testimony or other evidence fits with therest. These adjustments are case-specific.
This brings me to your question whether there are criteria youhave failed to mention. Yes! You have failed to mention what (for me atleast) is of the greatest interest: the quality of the applicant'swriting sample(s). If the applicant's writing shows that s/he cannotwrite philosophy or think philosophically, then all the rest of therecord cannot really make up for that. (By contrast, if the writing issuperb and the rest of the record mediocre, one might suspect that theapplicant got rather too much outside help with his/her essay.) You also fail tomention the content of the references. It's not the name and fame ofyour referees that will get you a job, but their assessments of you inconjunction with their reputation for honesty and good judgment. (Somevery famous people are well known for their grotesque exaggerations, andreferences from them consequently carry very little weight.)
The answer depends a bit on the country you're in. I answer on the assumption that you are an undergraduate student in the US.
Finding a job as a professional philosopher after completing a PhD in this field is a good bit harder than the average for all careers. Still, the odds are not against success. There are somewhere around 25,000 professional philosophers in the US and only about 75 philosophy departments producing PhDs. So, much of the selection takes place already at the stage where people apply to graduate schools. Those who get the PhD normally find a job. In this job search, the quality and prestige of the university, of its philosophy department, and of the student's supervisor do indeed play a major role. You can find lots of information about these matters on www.philosophicalgourmet.com and elsewhere.
All this suggests that a philosophy major aiming to be an academic philosopher should think seriously about other careers if s/he cannot get into a philosophy department that is in the top half, at least in his/her intended specialty. Choosing another career goal at this stage does not mean that the undergraduate study of philosophy was wasted. There are alternative careers in which undergraduate philosophy training is highly useful. A career in the law is one: many philosophy majors go on to law schools and do quite well there. But philosophy is good preparation for a wide variety of careers, and may well be the best major to choose for those whose career choice is still quite unsettled. Moreover, studying philosophy and learning to think philosophically has its own rewards which often last a lifetime (as I have been told many times when meeting people in other careers who had majored in philosophy).
In conclusion, if you are attracted to a career in biology, you should probably stay with it and satisfy your philosophical curiosity through an occasional course in philosophy. If you feel that a career in biology (or a related area) is probably not for you, then career worries should not keep you from majoring in philosophy.
There are all sorts of regulations about this in different jurisdictions, but I assume you are interested in the moral prohibition and the reasons for it.
I don't think it's wrong in general for teachers and students to become romantically involved with each other. It is wrong only when they also have a student-teacher relationship, or a potential student-teacher relationship. I believe that, in such cases, becoming romantically involved is always wrong.
This belief is plausible only if the word "potential" is understood in a robust sense. Otherwise any romantic relationship involving a teacher would be wrong (because it is always possible for the other party to become this teacher's student). So I mean it in a robust sense: You are potentially my teacher only if I am a registered student in a unit of a university in which you teach -- a graduate student in your department, say, or an undergraduate in your college -- even if I have not taken a class with you.
Such student-teacher romantic relationships are wrong, because they subvert the educational environment. When such relationships are regarded as acceptable, then many teachers will try to convert their authority and power over their student's educational success into romantic and sexual affairs, and many students will try to convert their sexual attractiveness into special attention and better grades from their teachers.
Much thought has been given to how such conversion attempts (esp. on the part of teachers) can be blocked without proscribing all romantic involvements by teachers with their students. But such intermediate solutions are bound to fail. To see this, suppose there are widely accepted constraints on how teachers may approach students they hope to become romantically involved with. With these constraints known, teachers will seek creative ways of signaling their interest in a constraint-abiding way. The offensive conversions will not be blocked, but will merely play out a bit differently. And such constraints have a further draw-back: Students, knowing that teachers trying to pick them up must find a creative approach, will often suspect romantic intentions where there are none. And teachers who do not want to be suspected of romantic intentions must then avoid any interactions with their students that the latter might conceivably interpret as a creative but constraint-abiding romantic approach. This is a great loss to the student-teacher relation which, at its best, goes well beyond the classroom by involving mentoring, conversations, even friendship. In an environment in which romantic relations between teachers and their students are simply out of the question, you can take your student for an intensive intellectual discussion on a walk through the park. You can watch a play together, or a movie. In an environment in which such romantic relations are viewed as acceptable so long as they came about "in the right way," the discussion will take place in your office with the door wide open and with some effort at mutual reassurance of the strictly professional character of the proceedings. You'll have a hard time discussing Freud or the Symposium.
I have suggested that romantic relationships between teachers and their students are wrong because of the great damage they can do to the student. Such damage can be enormous. Just imagine the situation of a third-year graduate student under romantic pressure from her or his thesis adviser who, typically, is the only person in the department, or by far the best, for supervising this thesis. If the student falls in love with this teacher and their romantic relationship lasts happily till the thesis defense, then there is little harm to the student. But what if not? Unbelievable numbers of esp. women graduate students have been very severely harmed by such pressures and failed romantic relationships, often finding themselves compelled to quit halfway through graduate school.
I have made the further point that such relationships -- when widely viewed as an acceptable practice within colleges and universities -- also harm other students and teachers. Under this heading of third-party harms one should also mention the discomfort of students who know or suspect that their teacher is having an affair with one of their peers. Such students must assume that everything their teacher knows about them will be passed on to their fellow student, and they will also often suspect that their teacher's lover will be unfairly favored (also by this teacher's colleagues) not just in terms of face time and advice, but also in terms of grades, teaching assignments, funding opportunities, letters of recommendation, and much else.
I am not denying that a teacher and his/her student may fall in love with each other in the most perfect way, nor that something magnificent would then be lost if they could not become romantically involved. But I think that, rather than realize their wonderful gain at others' expense, they should then bear the cost themselves: by waiting until the student graduates, or by one of them moving to another school.