select2 is not showing arrow down icon

For Select2 version 4.0.5+, this code exactly duplicates the single-select arrow.

.select2-selection--multiple:before {
    content: "";
    position: absolute;
    right: 7px;
    top: 42%;
    border-top: 5px solid #888;
    border-left: 4px solid transparent;
    border-right: 4px solid transparent;
}

You have used multi-select dropdown and used plugin(Select2) don't add dropdown arrow in multi-select dropdown. So if you want to add dropdown arrow, you have to add some custom CSS like below.

ul.select2-choices {
    padding-right: 30px !important;
}

ul.select2-choices:after {
    content: "";
    position: absolute;
    right: 10px;
    top: 50%;
    transform: translateY(-50%);
    border-top: 5px solid #333;
    border-left: 5px solid transparent;
    border-right: 5px solid transparent;
}

$(function () {
  $("#select1").select2();
});
.select2-container--default .select2-selection--multiple:before {
    content: ' ';
    display: block;
    position: absolute;
    border-color: #888 transparent transparent transparent;
    border-style: solid;
    border-width: 5px 4px 0 4px;
    height: 0;
    right: 6px;
    margin-left: -4px;
    margin-top: -2px;top: 50%;
    width: 0;cursor: pointer
}

.select2-container--open .select2-selection--multiple:before {
    content: ' ';
    display: block;
    position: absolute;
    border-color: transparent transparent #888 transparent;
    border-width: 0 4px 5px 4px;
    height: 0;
    right: 6px;
    margin-left: -4px;
    margin-top: -2px;top: 50%;
    width: 0;cursor: pointer
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<link href="https://cdnjs.cloudflare.com/ajax/libs/select2/4.0.6-rc.0/css/select2.min.css" rel="stylesheet" />
<script src="https://cdnjs.cloudflare.com/ajax/libs/select2/4.0.6-rc.0/js/select2.min.js"></script>

<select multiple id="select1" style="width: 300px">
  <option value="AL">Alabama</option>
  <option value="Am">Amalapuram</option>
  <option value="An">Anakapalli</option>
  <option value="Ak">Akkayapalem</option>
  <option value="WY">Wyoming</option>
</select>

Source: https://github.com/select2/select2/issues/167#issuecomment-322461384


Based on Adam Love's answer, this code uses the FontAwesome chevron down icon (although you could easily swap it for a different icon):

.select2-container--default .select2-selection--multiple {
    padding-right: 20px;
}
.select2-container--default .select2-selection--multiple::after {
    position: absolute;
    right: 5px;
    top: 42%;
    font-family: 'Font Awesome 5 Free';
    font-weight: 900;
    -webkit-font-smoothing: antialiased;
    display: inline-block;
    font-style: normal;
    font-variant: normal;
    text-rendering: auto;
    line-height: 1;
    content: "\f078";
    font-size: 0.7rem;
}

$("#e1").select2();
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css">
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.1.1/jquery.min.js"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js"></script>
<script src="http://cdnjs.cloudflare.com/ajax/libs/select2/3.2/select2.min.js"></script>
<link rel="stylesheet" href="http://cdnjs.cloudflare.com/ajax/libs/select2/3.2/select2.css">

<select multiple id="e1" style="width:300px">
  <option value="AL">Alabama</option>
  <option value="Am">Amalapuram</option>
  <option value="An">Anakapalli</option>
  <option value="Ak">Akkayapalem</option>
  <option value="WY">Wyoming</option>
</select>