Let’s distinguish the knowledge from the degree first. The average skill requirement of jobs (measured in years of education for example) is rising over time, so people need more knowledge before entering the labour market. What is obsolete is the packaging of that knowledge into degrees and perhaps its teaching in universities.
The PhD takes six years on average (http://gsa.yale.edu/sites/default/files/Improving%20Graduate%20Education%20at%20Yale%20University.pdf) and during that time the student is guided by one or at most a few advisors. Working on the same topic on years is often necessary to become an expert, so unavoidable. But being tied to the same advisor is a throwback to the medieval guild system where the apprentice and journeyman work years for the master. It means seeing only one viewpoint or set of techniques. Most importantly, the topic of the thesis is limited to what the advisor is competent in (sometimes a laissez-faire advisor allows a dissertation on an unfamiliar subject, which is even worse – incompetent advising follows). Taking courses from other faculty in the same department or university broadens the horizons a bit, but there may be an institutional culture that introduces biases, or expertise in some fields may simply be missing from the university. Attending conferences again broadens the mind, but conferences are few and far between. Suggestions that run counter to the advisor’s views may be interpreted as wrong by a novice graduate student.
Ideally, a trainee researcher would be advised by the whole world’s scientific community, mostly but not exclusively by people in the same discipline. Electronic communication makes this easy. Many different viewpoints would be explained to the graduate student, interpersonal issues would be easier to resolve by changing advisors (no lock-in to one person who determines one’s career prospects). People who just use students as free labour without providing much in return would suddenly become lonely. The problem is moral hazard – if no specific person has responsibility for a student, indefinite postponement of advising effort may occur. Credit for useful advice would be spread between many people, which dilutes incentives. In short, advising is a public good.
Still, public goods are sometimes provided, despite the difficulty of explaining this with a rational agent model. People write free software, answer questions from strangers in forums, upload advice and instructions on many topics. This suggests some volunteer advisors would step forward under a shared responsibility system. The advisor pool may become more ideologically biased than now, because people who want to spread propaganda on their strong views have a greater incentive to volunteer advice. They do this on the internet, after all. Similar incentives for shrill prophets operate in universities, but if each faculty member is required to advise some students or if there is a cap on how many disciples one can take, there is less scope for indoctrinating the masses. Such restrictions can be imposed online to some extent. There could be a reputation mechanism among the advisors, so the crackpots are labelled as such. The larger pool of opinions may balance the biases.
The economies of scale in advising one student are reduced with sharing. A single advisor per student means that during most of the PhD program, the advisor is already familiar with the student’s work and only needs to read the new part each week. With many advisors, each would need to devote time to the same material. Some sharing of responsibilities (one reads the introduction, another the conclusion) is possible, but the interdependence of the parts of the research does not permit full splitting.
Another medieval aspect of the PhD is paying for the received teaching in labour, not money. Graduate students may be free from tuition and may even get a scholarship, but in return have to work as teaching assistants or do the advisor’s research in their lab. Less ethical help also occurs, such as reviewing papers the advisor is officially the referee of. Inefficiencies of a barter economy are introduced. Instead of paying for the program with money earned in the job the student is the most productive or happy in, the student is forced to work as a teaching assistant and essentially pay the difference between a fair market wage and the teaching assistant wage to the university. Further, the teaching work is restricted to the university of the PhD program, even if other universities need teachers more and offer higher wages. This gives the university market power and allows it to depress grad student salaries.
A doctoral program may lose money directly, in the sense that teaching the grad students is more expensive (due to small classes, advanced material, so more professor time per student) than their TA work. The fact that universities still keep the PhD programs suggests the existence of indirect benefits. One is reputation – attracting paying undergraduate and Master’s students. In some countries, an institution is not allowed to call itself a university if it does not teach at the doctoral level. Altruism by the higher education sector is possible, even if John Quiggin’s quote “never stand between a Vice-Chancellor and a bucket of money” suggests otherwise.
One utopic proposal is an online system where graduate students and advisors sign up and can talk over video calls, send emails etc. It keeps a record who communicated with whom and how much. Later, data on the academic achievement and job market performance of students can be added, so advisors can be rewarded for their students’ success. There may also be some popularity index, meaning students rate their advisors and vice versa. But in the end, an advisor’s contribution should matter more than popularity, so the latter is optional. Advisors may look at and rate each other’s advising sessions to limit the spread of bad advice. Students can collaborate and may decide to meet in person.
For experimental science, lab space can be rented by student cooperatives. Instruction in the use of equipment can be given via video. Classroom space can also be rented directly by groups of students if needed. The students may pay advisors. Some people may only advise conditional on payment. Students may teach other students (including TA jobs), whether for money or pro bono. The system would cut out the middlemen – university administrators – making education cheaper for society. Of course, in the lab and classroom rental business, other middlemen would appear and take their share.