This should work for you:
Controller:
function MyCntrl($scope) {
$scope.obj ={"selected":null};
$scope.objects = [{id: 1, value: "Yes"}, {id: 0, value: "No"}]
}
Template:
<div ng-controller="MyCntrl">
<select ng-model="obj.selected"
ng-options="value.id as value.value for value in objects">
<option value="">Unknown</option>
</select>
<br/>
{{obj}}
</div>
You should use ng-options with select.