A model of any academic department in the UK

Memo to possible colleagues

(1. The basic set-up) Academic members of staff in the department have three types of task to achieve to fulfil their contractual obligations:

Research (r)

Teaching (p; pedagogy)

Administration (a)

Such that:

[(r+p+a=T) & (T=1)]

Where T is the total time allocation of a generic contract, irrespective of its FTE status[i].

Various values of r, p and a can lead to T.  To this end we might usefully approximate different roles within the department as follows:

r>p>a          (research post; T_r)

(r=p)>a        (lecturing post; T_p)

r<p<a          (managerial post; T_a)

The research and managerial post abstractions are transitive, but not symmetrical (clearly), such that r>a and r<a respectively.

These abstractions capture expected time allocation to the component tasks of the generic academic post (T).  Within each of these specific posts, then, we might say that r, p and a are differently valued in terms of the expected effort for each.  It is possible that one or more of these constituent components can have a zero value.  In both T_r and T_p, a can equal zero.  In T_a, r can equal zero.  Technically the middle term of any abstraction cannot be zero as there is no established equality between that term and the third.  Under this model this means that p always has a positive value.

It is a policy of the university that r≠0.

Note that T_a is the only post where a holds the highest value.  In the other two posts, a is always the lowest value.  Thus far we have held the nature of a (and r and p) constant because we have been dealing with kinds or types of task.  Administration is a large set of tasks that can be organized into subsets and tokens of administrative activity.  To this end we must think about the utility of administration and its architecture.

Administration might be broken down into the following subsets:

Whole organism administration (a₁)

Systems administration (a₂)

Organ administration (a₃)

Here I am using biological organization as a metaphor to clarify the hierarchical and embedded nature of the tasks, such that we can group the administrative types as follows:

{a₁[a₂(a₃)]}=a

Organ level administration refers to administration of tasks that are functionally specific to immediate concerns of the role holder.  For example, lecture organization, research planning, and module leadership.  Systems refer to oversight of multiple organs, for example programme leadership, research leadership; and, whole organism refers to oversight of all, typically the work of a Head of Department and her team[ii].

We now have a refinement such that we might wish to change our initial academic post abstractions[iii]:

r>p>a₃=T_r

(r=p)>(a₂Va₃)=T_p

r<p<a₁=T_a

Furthermore, given the set structure, we can assume that:

a₁>a₂>a₃

Such that a₃ should never exceed the amount of time allocated to either of the other administrative categories, which in turn means that those pursuing T_r should have the most amount of time available for r, holding p constant.

Administration as a whole (a) is comprised of dependent tasks, as outlined.  All of the activities are essential to the survival of the department for they facilitate the delivery of r and p, and the embedding of those products within the university and the wider community.  This means that there is a dependent relationship not just within a, but also between r & a, and p & a.

It is possible that we might be able make the following conditional argument for ideal overall departmental activity, which can be denoted by T_d[iv]:

[(r & a) & (p & a)] à T_d

This does depend upon two assumptions.  First, that p is essential to the existence of the department.  Second, that r is.  This second is embodied in the ruling that r≠0 (see above).  I assume the first is embedded somewhere within the statutes of the university as a core existential claim.

(2. Utilities) The tasks that fall under r, p and a are essential to the existence of the department.  The existential qualities of all three are not equal, however.  Administration (a) is essential for any activity to be maintained, but is not a self-contained activity in its own right (although there are benefits to meta-administration that leads to efficiencies).  Therefore, without r and p there would be no need for a.  Administration has the intentional property of always being about either (r V p) V (r & p).

Teaching (p) can be determined by three factors: a desire to impart knowledge (k), external curriculum designation (such as that from the professional bodies; e), and market forces (such as how much money the university can make from the existing population of possible students; m, markets).  A reasonable assumption about the weighting of these components would be that:

m>>e>k

The logical relationship, from the perspective of the university, might be:

{m à [(e & k) V (e ¬ k)] à p}

such that k is not regarded as essential.  For departments without e the abstraction may be as simple as (m à p) thereby giving primacy to only one causal component.

Research (r) is an open-ended task with no precise market structure and may well be driven by something such as curiosity (c) in the first instance.  However, the sector reality now is that research must make money (f, finance, fiscal, funding), if only to sustain itself, and achieve socioeconomic impact (i).  More generally, both money and impact are packaged into a compound variable of status (s) such that[v]:

s=f+i

So the utilities that the department seeks to maximize are p and r, which can be further broken down into specific opportunities to make money and gain status.  All of this is supported by the total set of a, which by default must also be maximized.

(3. Dynamics) Individual members of staff will have preferences for p, r and a.  It is possible that the order of those preferences more or less reflects the structure of their specific roles, such that:

T_r à (r>p>a₃)

T_p à [(r=p)>(a₂Va₃)]

T_a à (r<p<a₁)

But it is also possible that preferences do not match the roles, as described.  Given this there might be a temptation to reduce effort in low preference areas and divert effort to high preference areas.

As an example, imagine a T_p colleague who is engaged only in a₃ activity but detests this form of administration.  Her preference structure might be like this:

T_p à [(r=p)>>>(a₃)]

If she were to divert investment from a₃ to r and/or p at some point either or both of those activities would suffer as a result.  Initially this will impact upon the colleague, as this level of administration is concerned with the immediate functions surrounding their p and r tasks.  However, if p and r begin to decrease in value (which is equivalent to a decrease in quality) then the overall departmental activity and therefore utility (T_d) is reduced.

To this end, a₃ activity contributes to a public good for the department as it acts to maintain, or even increase, departmental utility. Note also, that any diminution in a₃ effort will cause increased a₂ and a₁ work further up the administrative hierarchy as others seek to maintain the departmental utilities.  This is freeriding – the original colleague getting some of her work picked up by others because it is essential.  A certain amount of freeriding can be tolerated by the system, but there will be a threshold point which once passed will lead to a departmental catastrophe. 

Regulations and disciplinary procedures operated by the third party of Human Resources exist to avoid total catastrophe, but these are not without cost.  We must therefore rely on internal regulation and trust to avoid reaching that position.  In general this works very well.

Administration and teaching are straightforward activities, considered in this way.  Effort is expended and utilities maximized.  Courses are well run and continue to recruit, money flows into the university and then the department.  Research is different because of the pursuit of status such that:

s=f+i

The f parameter is fulfilled through grant capture and return from the government through REF.  Part of grant capture is based upon forecasting i, and part of REF is based upon assessing past i, so these parameters are not wholly independent.  Status (s) is the university level utility for research (r), such that:

r à s

But to sustain and grow r, f is required (see footnote 5):

f à r

This forlorn abstraction needs to be put into context.  The university level, and to some extent department level utility is to increase status through funding and socioeconomic impact[vi].  At this level these are collective actions.  At the individual level a given colleague can simply be driven by curiosity, and that can be capped by available resource to pursue ideas.  For example, existing experimental equipment in the department can be used for new work.  Underlying costs of maintaining a lab to run that work are not trivial, but there is sufficient latitude in the system to enable some such work to continue virtually cost free.

Colleagues cannot operate in this way at all times.  At various points in time some colleagues will need to acquire grant income and make socioeconomic impact in order to fulfil the departmental utilities.  This will enable new equipment to enter the department, and for new research possibilities.  The more this is done the better, as it increases the probability of some income given the almost below chance nature of any one person receiving funding at any given application point.  Again, there is the potential for freeriding, but here things are different.

Administration is rule and regulation bound.  There are specific tasks that are generic across all three levels of administration, and to some extent they are all independent of content.  Administration is there to support teaching and research.  Research is content specific.  If a colleague acquires funding, and achieves socioeconomic impact, that will be within a very defined domain.  It will be difficult for another colleague, with different interests, to gain anything from this effort.  If another colleague has the same interests the less effortful approach is to collaborate and share[vii]. 

The only real opportunity for freeriding is in terms of access to REF income.  REF income is typically based on a sample of work from the department, and therefore not all colleagues contribute.  But this is an administrative decision at the a₂/a₁ level.  One simple way to make this equitable is to have a department where all members of staff could be submitted to the REF audit, but for strategic reasons only some are.  This maximizes income whilst no one can be accused of not making a contribution[viii].  REF income is therefore treated as a public good.

(4. Summary)  This memo has presented a toy model, in semi-formal terms, of a generic academic department.  The only really specific issues were some quantitative scientific examples, but they can be suitably generalized for all aspects of scholarship.

The purpose of the memo was to clarify the parameters we work within and expose their interdependence and the public good nature of our work.  On this latter point I have only focused upon members of the department as the public, and occasionally on the wider university.  There is a public beyond the department, and beyond the university, whom we also serve.  Our research activities lead to new understanding and the potential for change.  It is the nebulous, and probabilistic nature of this public investment that has increasingly led to research and teaching quality audits and an inward focus on the component variables of T.

We should not lose track of the nebulous and probabilistic, nor of our curiosity.  But we need to understand how working together to deliver T_d can in fact buffer those activities.

(5. Slides) The video below contains slides to accompany a short talk picking up on the key points above.  The film moves rather fast so pause on each slide if you wish to take in the detail. There is no sound, but the sense of the slides should be clear given the above argument.

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[i] Once the model is established and finessed then T can take on fractional values in order to usefully relativize contributions within the population.  At this stage this is a statement about the generic individual member of academic staff.

[ii] These examples are designed to clarify the basic abstraction.  They are not absolute or definitive statements.  Sets will overlap and individuals will make transitions between the simple post structures in the model.

[iii] Note: V means or.

[iv] Such that, ∑ (T_r,T_p,T_a) = T_d, when looking at the total population of roles within the department.

[v] One reason to focus upon the status concerns is because research money and growth lead to a vicious circle problem.  As research grows, and grant income increases, projects also expand and in turn demand more infrastructure, captured by a.  This increase in a means more money is needed.  One possible rational choice is not to pursue money and cap research growth.  But this means capping curiosity (c), the sustenance of which is still regarded as a moral obligation of universities.  Focusing upon status, a relative property, enables choice over competitors that absolutes, driven by real costs, do not.  The onset of socioeconomic impact (i) is also potentially free and can offset reductions in f whilst leading to an increase in s.  How sustainable this in the long term is, to a large extent, an empirical matter. But true formal modelling would help.

[vi] For ease of exposition I have not discussed reputation, which is separate from the kind of league table driven status I am modelling here.  It would be easily added as a publication variable with two slightly ephemeral components, readership and intellectual impact.

[vii] This can lead to territorial disputes over ownership of the research, which can be modelled using the Bourgeois game, a variant of Hawk-Dove.

[viii] Note that I am deliberately ignoring developmental aspects of these decisions.  Not all staff are at the same point in their research careers and some need investment to increase their future yield on r, including f and i.  In general, this just extends the time sample of the public good assessment: something I have also not discussed.