What would happen if a law was passed that said all content determined via algorithms had to be open source?

What do you think an algorithm is?

I'm not sure I understand the intent of your question. What do you mean "determined" via algorithms?

This would be a significant change to the intellectual property laws that govern most western countries currently. Not all algorithms are electronic in nature. For instance, manufacturers, stock trading firms, and banks may all use algorithms that are proprietary to perform manual or mechanical processes. Requiring these to be open sourced to the public would likely result in many trade secrets being leaked. There would also be a question of rather a recipe constitutes an algorithm as it really is just a set of processes at the end of the day. If so, Coca-Cola and a bunch of other countries are screwed.

Apart from the less obvious cases, there is also every software company in the world to consider. If they were forced to make their code public, we would see a lot of effects, some good and some not. To begin with, anyone would be able to compile and spin up any software at any time, making paid software a much less profitable business. Microsoft's only customers in the software world would be the less tech savvy among us, and even then, they would be severely undercut by other companies as well as the neighborhood kid down the street who could volunteer to compile the OS code on your behalf for significantly less money. Specific INSTANCES of software, including the databases and information inside, as well as physical infrastructure would not be put at risk by this change, so the giants like Microsoft and Amazon would still be poised to win. However; they would have a lot more competition and would need to pivot away from software licensing as a business model all together.

Much more interesting to consider is the financial impact that such a change would have on society. I suspect the stocks for the major tech companies like Microsoft and Amazon would plummet. Apple in particular, who highly values secrecy and proprietary software, and who is not in the cloud computing business just yet, would be impacted more than anyone, as their closed down ecosystem would become a lot more open. If the law was passed in a particularly large market like the US or the EU, Apple and other tech companies would almost definitely sue that government, but the case would take years to resolve and would go to the highest level of the courts before being resolved. Open sourced code is technically still protected by copyright laws according to the terms of the open source license, so you would definitely see a lot of IP lawyers going after businesses for the slightest violation of those terms. You would also see a ton of trademark cases in response to people blatantly ripping off the Microsoft logo. The end result would probably be that their brand would get some limited protection from becoming all together irrelevant, but they would still be unable to stop individuals who are fully compliant with the open source license from downloading and compiling code themselves, severely cutting into Microsoft's profits.

Likely, these big software companies would then realize that they must move from a product based model to a service based model when it comes to software. I don't care if you can see the code for Netflix's sorting algorithms -- that doesn't necessarily mean you have access to their video content. Products like Microsoft Word would become valueless while Microsoft Teams would potentially skyrocket in value. Data and files in general would become highly prized by these tech giants as they would allow for content to be fed by their programs that distinguishes their instance of a service from the one you are running on your local machine.

However; this would ultimately not be enough to starve off the sudden loss of revenue from such a change. Consider less flashy examples like insurance companies and banks that have business rules hidden in their algorithms. If someone found out the "rules" to get an insurance claim approved by automated systems, they would surely take advantage of it. You would see a massive amount of insurance fraud, financial fraud, and just general chaos as the rules that have powered these institutions for the last 40 years or so suddenly became irrelevant. We would quite likely see a total collapse of the stock market, and at such a scale that governments would not be able to fix the problem. Of course, if the government passing this law gave companies more time to respond... Five years... A decade... Many of the problems could be mitigated, as could the impact. You might see a recession instead of a depression after implementation.

As far as what would happen afterwards? Open source would do what open source is supposed to do. It would point out the flaws in software, allow for creativity to bloom, and ultimately make the digital world a brighter, safer, more creative space. Innovation would bloom. Security algorithms would improve. People would be able to make more informed choices about where they do business. These learnings would come at a high cost for companies slow to respond to public comments on their Git repos. You would expect to hear about a lot more high-profile exploits and data leaks in the news. It might even cause an even deepening financial crisis similar to the one explored on "Mr. Robot" if, say, a major credit card processing company's data was intercepted, or if financial loans for some of the world's biggest financers were erased. However; new models would take the place of the old ones. The economy would eventually recover, and be rebuilt from the ashes on much more stable ground.

Or maybe Elliot would regret his decision and undo it. I don't know. (spoilers ahead for those of you who still haven't seen Mr. Robot)

Oh that's easy. Corporations would pick up and move to a jurisdiction without that law, and then just not comply. Or I'd make a lot of money running obfuscations services to technically meet publication requirements.

Personally, I'd try to find a way to use it to compel speech in the USA (I don't live in the USA but recall compelled speech being protected by the First Amendment). For example, your mind contains an algorithm that uses your phone to push content to your friends. In many cases, that algorithm contains a PIN code to your phone. Now publish it as open-source so the police can have it. Hopefully the pushback from this will result in the law quickly being repealed, but who knows.

One of the reasons for not disclosing content recommendation algorithms is to combat spam or generally exploitation of the algo.

You’d be exclusively recommended content from whoever is trying the hardest to game the algorithms, and not however the algo was actually intended to work.

There is a law in the EU that is similar, you can't have systems making automated decisions about people without the decision being explained to the people you make them about.

This is part of the reason EU companies don't use crappy automated filtering in their ATS systems.

So anything that was compressed and uncompressed, ie zip, rar, tar, would have to be open sourced? I honestly can't see that happening.

It would change nothing for us. Most of it is all black box and they could leave any number of "dials" and not tell us what they are set to.

I'd much rather see restrictions on using algorithms to recommend content, period. I have yet to be grateful for any algorithmically generated feed. It comes across as useless and annoying at worst, creepy and intrusive at best.

Better to have a forum with humans recommending things to each other that can be searched and sorted according to keywords and direct input from the users, according to our preferences.