Because the bootstrap-select is a bootstrap component and therefore you need to include it in your code as you did for your V3
NOTE: this component only works in boostrap-4 since version 1.13.0
$('select').selectpicker();
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<link rel="stylesheet" href="https://stackpath.bootstrapcdn.com/bootstrap/4.1.1/css/bootstrap.min.css">_x000D_
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/bootstrap-select/1.13.1/css/bootstrap-select.css" />_x000D_
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>_x000D_
<script src="https://stackpath.bootstrapcdn.com/bootstrap/4.1.1/js/bootstrap.bundle.min.js"></script>_x000D_
<script src="https://cdnjs.cloudflare.com/ajax/libs/bootstrap-select/1.13.1/js/bootstrap-select.min.js"></script>_x000D_
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<select class="selectpicker" multiple data-live-search="true">_x000D_
<option>Mustard</option>_x000D_
<option>Ketchup</option>_x000D_
<option>Relish</option>_x000D_
</select>
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