I can only go off the expert opinions, but most people her don't commit petty crimes. Now there is still lots of white collar crime and gangster activity (as in most places) but most people don't think to commit theft at any level. Lots of people, for example, park their bikes in places and don't chain them up. The odds of someone taking your bike are slim to none. Same for being pick pocketed or having an iPhone stolen if you leave it on a table for a minute.
I think it has to do with education. Those kinds of things are done by low-class people with a sense of entitlement, and who feel they are owed something by society. With that comes a sense that they have been wronged somehow (whether real or just perceived). Some people make the argument that America has so much crime and violence because of the sheer number of different races, nationalities and religions clashing together in the less-than-idyllic melting pot. But crime and violence happen in plenty of homogenous countries too. There's also the glorification of gangster culture in America, which leads to impressionable young people doing things like theft and taking drugs to fit in and appear "cool". We don't have that sort of gangster worship here, where you see people wearing Scarface shirts and whatnot.
These are also small islands, where it's perceived to be harder to disappear. Look at China: their crime rates are much higher than Taiwan, Japan or Korea's, because it's easier for someone to disappear. Even though we're densely populated in some areas here, Taipei is the biggest little city I've ever been to. I'm constantly seeing or running into the same people, and if someone were to be caught for grabbing a phone on the subway, they'd be shamed on the news and would likely have to move to another city.
