External membership of unions

The ostensible reason for the violent crackdown on protesting students at Alighar Muslim University and Jamia Millia Islamia last month was the involvement of “outsiders” in these protests. In both cases, campus authorities claimed that student protestors had been joined by “outsiders” who had gone violent, which forced them to call in the cops.

And then the cops did what cops do – making the protest more violent and increasing the damage all round, both physically and otherwise.

I’m reminded of this case from a few years ago from some automobile company – possibly Maruti. The company had refused to recognise an employee’s union at a new plant they were starting, because of an argument on the membership of non-employees in the unions.

The unions’ argument in that case was that external (non-employee) membership was necessary to provide the organisational and union skills to the union. If I remember correctly, they wanted one third of the union to consist of members who were not employees of the firm. The firm contended that they wouldn’t want to negotiate with outsiders, and so they wouldn’t recognise the union with external members.

I don’t remember how that story played out but this issue of external membership of unions, whether student or employees, is pertinent.

At the fundamental level, unions need to exist because of the balance of power – the dominance in favour of an institution over an individual employee or student is too great to always produce rational outcomes in the short term (in the long term it evens out, but you know what Keynes is supposed to have said). The formation of unions corrects this imbalance since the collection of employees or students can have significant bargaining power vis-a-vis the institution, and negotiations can result in more rational decisions in the short term.

The problem I have is with external membership of unions. The problem there is that external members (who usually provide leadership and “organisation” to the unions) lack skin in the game, and the union’s incentives need not always be aligned with the incentives of the employees or students.

Consider, for example, the protests in the universities last month which became violent. The incentive of the protests would have been to peacefully protest (to register their dissatisfaction with a recent law), and then get back to their business of being students. The students themselves have no incentive to be violent and damage stuff in their own institution, since that will negatively impact their own futures and studies at the institution.

External members of the unions don’t share this incentive – their incentive is in making the union activities (the protest in this case) more impactful. And if the protest creates damage, that can make it more impactful. The external members don’t particularly care about damage to the institution (physical and otherwise), as long as the union’s show of strength is successful.

It is similar in organisations. It is in the interest of both the employees and the management that the company does well, since that means a larger pie that can be split among them. The reason employees organise themselves, and sometimes go on limited strikes, is to ensure that they get what they think is a fair share of the pie.

The problem, of course, is that negotiations aren’t that simple, and they frequently break down. The question is about what to do when that inevitably happens. Each employee has his own threshold in terms of how long to strike, and at what point it makes sense to back down and accept the deal on the table.

In an employee-only union, the average view of the employees (effectively) guides when the strike gets called off and the negotiations end. External members of the union lack skin in the game, and they have a really long threshold on when to back down from the strike. And this makes strikes longer than employees want them to be, which can make the strikes counterproductive for the employees.

One infamous example is of the textile mills in Mumbai in the late 70s, and early 80s. There was massive union action there in those times, with strikes going on for months together. Ultimately the mills packed up and relocated to Gujarat and other places. The employees were the ultimate losers there, either losing their jobs or having to move to another city. If the employees themselves had controlled the union it is likely that they might have come to a settlement sooner or later, and managed to keep their jobs.

In the automobile case I mentioned earlier, if I remember correctly, the union demanded that up to 33% of the membership of the union be comprised of outsiders – a demand the company flatly refused to entertain. Now think about it – if external members control a third of the union, all it takes is one fourth of the employees, acting in concert with the union, for something to happen. And there is a real agency problem there!

Deranging groups

Ok so this is a mathematical problem. I plan to give three group assignments to my IIMB class. Let’s assume that there are 60 kids and for each assignment I want them to form groups of four members each. For the first assignment I’ve let them form the groups themselves.

For the second assignment, though, I want to create a “derangement” of these groups – in the sense that I want to form a different set of 15 groups of 4 members each such that no pair of students who are in the same group for assignment 1 will be in the same group for assignment 2. And I’m looking for an algorithm to thus “derange” my students. And whether it is possible at all to derange students thus.

My inclination is that this might have a solution in graph theory – in terms of graph colouring or something? Take the students from the first group and join every pair of students that are in the same group with an edge. Then colour the nodes of the graph. Pick nodes of the same colour (these are students that haven’t been in groups together) and randomly assign them to new groups. Repeat for all colours.

Question is how many colours we need to colour the graph. If it’s planar, we’ll need only 4 colours! And considering that the first assignment has 4 students per group, the maximum degree of a node is 3. If the maximum degree of an edge is 3, does that say anything about the planarity of the graph? If I derange the students once for assignment 2, can I do it again for assignment 3 (now each node has a degree of 6!) ? How do I think about this mathematically? Can you help?