uninstall globally (use sudo if needed)
sudo npm uninstall -g ionic
sudo npm uninstall -g ionic@beta
sudo npm uninstall -g cordova
fix permissions like this: https://docs.npmjs.com/getting-started/fixing-npm-permissions
this worked for me:
sudo chown -R $(whoami) $(npm config get prefix)/{lib/node_modules,bin,share}
reinstall (without sudo)
npm install -g ionic
npm install -g ionic@beta
I also installed the Android SDK