I think that arrogance can be measured by how much a company pays attention to what is being said about it in the mediasphere.
By mediasphere I mean the entire landscape of traditional media through to social networks, blogs, Twitter and anywhere else there is a conversation about that company.
My recent experience with Apple's AppleCare was not good. I wrote about it here [RantWatch: Shoddy AppleCare - arrogant Apple]and got a tremendous amount of talkbacks, 90 at last count and more than 4,000 people read the post and this number continues to rise. I also wrote about it on my SiliconValleyWatcher site, which has a wide distribution.
Lots about Apple and AppleCare but nothing from Apple. To me this means that Apple can't be bothered. All it would take would be for an Apple representative to leave a comment along the lines, of "sorry, we always try to do our best but in this case we couldn't fix it. But we have a tremendous service and our feedback shows xx% satisfaction which is the highest in the industry, blah, blah, blah."
It doesn't fix my problem but, hey, it at least shows Apple is paying attention and it cares about what people say about its products and services.
But Apple clearly isn't paying attention. That comes across as being arrogant, imho. So while Apple fanboys foam at the mouth when someone criticizes Apple, Apple doesn't care. It doesn't $24-billion-in-cash (adding $1bn/quarter) care.