if i wrap your array to a scope variable it works just fine
html
<ion-nav-view>
<ion-view>
<ion-content>
<ion-radio ng-model="data.sort" ng-value="someValue" ng-click="closeSortPopover();">['-timestamp','model']</ion-radio>
<ion-radio ng-model="data.sort" ng-value="'brand'" ng-click="closeSortPopover()">Brand</ion-radio>
<br/><br/>
<button id="resetbutton" class="button icon-left ion-ios-reload button-dark" ng-click='data.sort=someValue;'>Set to data.sort to ['-timestamp','model']</button>
<br/><br/>
data.sort = {{data.sort}}
</ion-content>
</ion-view>
</ion-nav-view>
controller
angular.module('ionicApp', ['ionic'])
.controller('MyCtrl', function($scope) {
$scope.myTitle = 'This header hides the content below';
$scope.someValue = ["-timestamp","model"];
$scope.data={};
$scope.data.sort = $scope.someValue;
});