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You need to add CSRF token:
https://laravel.com/docs/5.4/helpers#method-csrf-token
For example in the view
<script>
var csrf = '{{csrf_token()}}';
</script>
And in your script
var formData = new FormData();
formData.append('_token', csrf);
formData.append('input', this.newUserVoted);
this.$http.post('http://www.nmdad2-05-elector.local/api/v1/electionuser', formData)
Source:stackexchange.com