If you want the submit button disabled if no choice is selected the easiest way is to check the length of the array in the ng-disabled attribute, without setting the required attribute
<input type="submit" value="Send" ng-click="submitSurvey(survey)"
ng-disabled="value.length==0" />
See here for updated fiddle
Another way to do this would be to check the array length in the ng-required attribute of the checkboxes
<input type="checkbox" value="{{choice.id}}" ng-click="updateQuestionValue(choice)"
ng-model="choice.checked" name="group-one" id="{{choice.id}}"
ng-required="value.length==0" />
Second fiddle