Isn't this a statistical catch-22? If being in a union increases the odds of getting fired… well, then there's nothing to discuss because that's illegal. And if it should decrease it because of fear of legal retaliation, wouldn't that make it less likely that this happened randomly.

This feels like the wrong conclusion to draw (especially the second part), but I suck at statistics so someone please explain where I'm off.

> Isn't this a statistical catch-22? If being in a union increases the odds of getting fired… well, then there's nothing to discuss because that's illegal.

Extreme example: suppose a company has 100 employees. Four of them are in the union bargaining team and they just happen to all work for the widgets department because of an accident of history or randomness etc. The widgets department has 10 people overall.

Now the company decides for business reasons entirely unrelated to unions, that thanks to GPT they don't need so many people in the widgets department. So they fire 8 people from widgets. Assume further that they went out of their way to protect the union bargainers: of those 8 people fired, only 2 are in the union bargaining team. (That means that the remaining 2 widgets people are both union bargainers.)

Even though the company went out of their way to protect the union bargainers, statistically they only laid off 8% of the company, but 50% of union bargainers. Would that be illegal or even unfair?

(In the real world, I am fairly sure that union bargainers are concentrated in some departments. Mostly because it attracts certain kinds of people, and different departments also attract certain kinds of people.

But, of course, I have no clue what the reality inside of Bandcamp was like. I'm just speculating about hypothetical examples.)

You've given a really clear example of confusing probabilities! Would this be an instance of Simpson's Paradox?

I'm not sure. Simpson's Paradox is even more confusing, if I remember right.

My example crucially hinges on the company being able to convincingly argue that they singled out that particular widget department for reasons unrelated to the union. If they can't make that argument, or someone even manages to proof that they fired from the widget department _because_ of the union people, then they would be in deep trouble.

You can characterize it that way:

    P(lose job | bargainer): 50%
    P(lose job | not bargainer): 6.25%

but

    -----widgets team-----
      P(lose job | bargainer) 50%
      P(lose job | not bargainer) 100%
    -----everyone else----
      P(lose job | bargainer) NaN
      P(lose job | not bargainer) 0%
    ----------------------

Simpson's paradox in its prototypical form occurs when the comparison drawn in the top table (of just one cell) is reversed in every cell of the bottom table. (Which has two cells, here.)

This isn't the cleanest example, since the comparison at the bottom can't be drawn at all. But the way the problem is narrated, it would counterfactually have exhibited the paradox.

It would not be illegal if that was the genuine business reasoning. If they quickly rehired people to those roles it would likely not hold up as legal.

One thing you might not have considered is that some notion of "dissatisfaction w/ job" would increase both the likelihood of you wanting to join a union and your employer wanting to fire you or lay you off.

Edit: also, another confounding factor that hasn't been discussed is job role/department. Layoffs and union membership are definitely not evenly distributed across role/department, but there is not enough info in the article to know if the layoffs were targeting specific roles or uniform across the company.

Higher odds of getting fired increase the odds that you will seek to join a union. So you'd always expect layoffs to hit proto-unions especially hard regardless of whether proto-union membership is considered at all. It's not a catch-22.

And also that the union employees were identical to others -- which is kinda demonstrably false. People who self-select as union leaders are likely to be different from the other employees in various relevant ways.

Modelling any of these assumptions yields an arbitrary probability of your own choosing.

Are you saying anything I didn't already point out in this paragraph?

>> You might want to ask yourself "Do I really believe that, if I thought I might be about to get fired, that would have no influence on whether I tried to join a union?"

Being a union bargainer is different from just being a member of a union? I would assume it takes more lead time than most people in the 'about to get fired' scenario have?

Ah, fair enough.

I think that's probably true in general, but if the whole union movement at the company is fairly new I don't think it necessarily applies (or is at least severely tempered).