> This is why I think we need a new way of identifying market abuse because you can make anyone a/not a monopoly based on what definition you use.

Which is why it matters if there are close substitutes or not.

> IOS device software distribution -> apple has a monopoly

There are no good substitutes for this. There is no viable alternative for distributing apps to the people with iOS devices. Distributing apps to people with Android devices isn't a substitute because they're different people, in the same way that distribution in the Northeast is not a substitute for distribution in the Southwest.

> High end phones -> apple probably has a monopoly

There are high end Android phones that are probably adequate substitutes. But if there weren't (or you think they aren't adequate substitutes) then sure.

> Total revenue of phones sold -> apple probably has a monopoly

The market you've specified is "phones" which is obviously not something Apple has a monopoly on. Whole Foods doesn't have a monopoly on food just because they have high margins. There are tons of non-Apple phones if all you need to satisfy to be part of the market is to be a phone.

It may even be a weak market definition because it's too broad -- a feature phone isn't a very good substitute for an iPhone. A better market definition might be smartphones, but even then they still don't have a monopoly. It's not about revenue or margins, it's a question of whether the consumer has a reasonable alternative supplier of something sufficiently equivalent.

> Number of phones (in use?) by OS -> android has a monopoly

The market in that case is would be "phone OS" but then Android has the obvious competition from iOS. Also, Android isn't a company, it's a product. It's nearly impossible for a piece of open source software to have "a monopoly" when literally everyone is allowed to supply it and anyone can do so at trivial cost. All the Android phone manufacturers are each independent suppliers of it.

> Number of computers by OS -> nobody has a monopoly

The market in that case is "computer OS" which is a poor market definition because desktop and phone operating systems are poor substitutes for each other.

I agree that there are substitutes for everything except the IOS distribution one. I also agree that most of these metrics are not true monopolies. However, I'm using the term "monopoly" in the way the EU sees it when enacting antitrust fines to curtail this type of behavior because what they basically use is >50% in some arbitrarily chosen metric (percent of of smartphones running an OS used for the EUs recent 5 billion dollar android fine on google) as that is what the EU is currently using to fine companies into "behaving" despite IOS being a much more abusive platform IMO.

This is why I think we need a new way of identifying market abuse.

The problem with what the EU is doing is that they aren't interested in applying a rigorous standard. It's perfectly possible to define markets or abuse in various ways, but if all they're really doing is to backfill reasoning to justify enormous fines on American businesses there is no point in arguing about what is in practice a rationalization, and the response if they continue to use such ambiguous rules probably ought to be something like lobbying the US government to negotiate a truce (or retaliate in kind against EU businesses).

Wow, I cannot upvote you enough.

> The problem with what the EU is doing is that they aren't interested in applying a rigorous standard.

Yeah, this is what I and a lot of other people have a problem with these EU antitrust laws and even GDPR . In the google case, they literally had the android play clauses set from day 1 when they had 0% market share and instead of telling google that they could no longer bundle chrome/search to the play store now that they reached 50% market share in mobile OS (their magic antitrust metric), they waited 7 years and then threw a ridiculous fine at them. If the laws were clear, this wouldn't be a problem.