Select with model property binding updating in v2

I’d like to have a select where someone can change a setting (without a save button). If I’m correct this can be done with model property binding in v2, but I can’t get it to work.

view:

<select wire:model="post.is_public">
  <option value="0">No</option>
   <option value="1">Yes</option>
</select>

component:

    class Test extends Component
    {
        public $post;

        protected $rules = [
            'post.is_public' => 'boolean'
        ];

        public function render()
        {
            $this->post->save();

            // session()->flash('saved', true);

            return view('livewire.public-toggle');
        }
    }

I have commented out the session part, but I’d like this to be included eventually so I can display message to the user that this was saved.