I'm not certain I understand what the real problem is, but see if this fiddle is what you want. (I obtained a list of preferred_genres from your other post.)
The controller scope property preferred_genres is being updated based on the checkbox state:
<li ng-repeat="(genre, checked) in preferred_genres">
<input type="checkbox" ng-model="preferred_genres[genre]"
id="genre-{{$index + 1}}">
As @dnc253 mentioned in your other post, you probably don't need ng-checked since each item has its own ng-model.
