Arrow’s impossibility theorem – for academics

I’m reading John Cassidy’s remarkable book How Markets Fail (2009), which includes a brief aside on economist Kenneth Arrow‘s fundamental work on “‘social’ ordering” – the problem of “converting individual preferences over a set of [possibilities]…into a consistent ordering for society as a whole” (p. 62, in Cassidy’s paperback edition).

To paraphrase Cassidy’s eloquent summary, imagine you’re asked to rank A, B & C things according to your personal preference (first, second, third). Here, A, B & C could be outcomes (as on a ballot), activities (the run/bike/swim of a triathlon), or things (apples, pears, bananas). If you asked a random sample of people for their rankings, you could reasonably expect a third of them to respond with ABC, a third with BCA, and a third with CAB. Taken together, a majority of people would prefer A to B, a majority would prefer B to C, and a majority would prefer C to A.

Upshot? There is no dominant social ranking (or “ordering”) – hence, Arrow’s impossibility theorem.

For the past year – more than in other years – I’ve been preoccupied (typically late at night, staring at the ceiling, wanting to be asleep) by the triple-header of demands on my (and others’) academic time: grant proposals, peer-reviewed papers, and teaching. (There’s other stuff, but a three-body problem is thorny enough.)

I just finished (well, “finished”) a major grant proposal. I’ve been doing that instead of working on papers, which is a writing process that I much prefer. And both the grant-smithing and the article-knitting (because I’ve still managed to do some) have played out during maybe the heaviest teaching year I’ve ever handled. Nearly everyone I know in this line of work contends with the same wobbly spinning plates.

Enter Arrow’s impossibility theorem for academics. The impossibility of a social ranking of (A) grants, (B) papers, and (C) teaching is never in sharper contrast than during annual appraisals and the rhetoric of all-hands departmental meetings. There is a majority preference for each ranked combination, and it’s impossible to reconcile (1) my own preferences with (2) the priorities I might be told I should have, with (3) the priorities the institution regularly lays out in official strategery. (Indeed, I have yet to see an institution fazed by this or any other variant of Arrow’s impossibility. Ever the optimists, I guess.)

Prior to rediscovering Arrow through Cassidy, I had been thinking about these three activities – grants, papers, teaching – in terms of a zero-sum game. Given a finite amount of available time, it’s difficult to find a way of working on one thing that doesn’t come at the expense of the others. The thinking and imaginative spaces associated with grants, papers, and teaching are not mutually exclusive – and a good thing, too. (I am a firm believer that teaching improves one’s research.) But, at the nuts & bolts level, you’re not moving a manuscript any closer to an editor’s desk if you’re re-re-rewriting your grant’s “Aims & Objectives” section, and both those documents are on ice if your lecture slides for tomorrow’s class aren’t done. There are rare occasions – non-zero-sum outcomes – when a grant proposal (funded or not) becomes a paper, or when the syllabus for a class becomes the material for a research effort (paper or grant). But if the basis for a paper requires intensive data collection and analysis or a few months of model simulations (which maybe only a grant will enable), then zero-sumness is hard to escape – it’s the grant or the paper or teaching prep.

But hold that thought – I gotta go pick up my daughter.

– EDL