> the employer side should also be numerous enough to establish an employer organisation.

They are and they have; see US v. Adobe Systems Inc., et al. From the wiki article:

"DOJ alleged in their Complaint that the companies had reached "facially anticompetitive" agreements that "eliminated a significant form of competition...to the detriment of the affected employees who were likely deprived of competitively important information and access to better job opportunities."

https://en.wikipedia.org/wiki/High-Tech_Employee_Antitrust_L...

Unions organize in public, employers collude in secret. The fact that the companies proposed a settlement the day the suit was filed indicates they simply priced that into their cost-benefit analysis when they were colluding.

I meant a formal employers' union, not a secret agreement.

What would be the remit of such a union? These companies likely compete with each other; Adobe and Apple for example have competing video editing products, and Jobs's letter sent Flash, another popular Adobe product to an early grave.

So what would this employers' union do exactly?

The whole point of unionization is the employer side has the advantage of being way less numerous.

Employer organisations also consist of multiple employers. In a fully unionised bargaining, both employer and employee unions attend bargaining process.

There are sufficient number of software and database companies to establish an employer organisation for software.

Fairness depends on the ratio of employee employer monopoly power. There may be enough tech companies to form a union, but that just means employees need to be more consolidated to match. Your "fully unionized bargaining" case is just one point in the blanced subspace. A many-to-many relationship where the employers per employee matched the employees per employer (along with other hierarchical symmetries) would be an (outlandish) other such point.

Historically anti trust laws in the united states considered unions as potential trusts that the government would be able to break up. However, they later repealed that piece because it's completely absurd. Even the most powerful union is unable to form a trust in the way that companies can do in order to systemically underpay workers.