This is where devices that run iOS and Windows 8 RT stand out. Not as open but if your goal is to not look at permissions and we can't answer with "forget those apps" then you need to change to a closed system.
Permissions on apps often change over time. For instance, Field Trip has added a permission that would allow it to create new bluetooth connections and to make and accept connections with paired devices. This app can also make changes to Wi-Fi networks. How does a user avoid downloading an app that can be used maliciously? How can a user evaluate the permissions on apps?