If you want to validate this element with the jQuery Validate plugin, there are two problems with its markup...
<select id="BusinessDistrictId">
    <option value="-1">Select one...</option>
    //other options...
</select>
1)  As per the requirements of the jQuery Validate plugin, every element must have a unique name attribute.  When rules are declared within .validate(), they are identified by their name.  However, no matter how rules are declared, every element must still have a unique name attribute because that's how the plugin keeps track of the form elements.
2)  Your min: 0 rule is only a workaround for a broken required rule.  In order to use required: true on a <select> element, you must have the value="" attribute on the first <option> element;  so  in your case, the required rule will always be ignored.  And since you have the min: 0 rule, you are getting a similar validation result that requires an item to be selected.  Even with the value="" attribute on the first option, having both the required and min rules on a select element makes no logical sense.
Here is the correct code...
HTML:
<select id="BusinessDistrictId" name="BusinessDistrictId">
    <option value="">Select one...</option> <!-- first option contains value="" -->
    //other options...
</select>
jQuery:
rules: {
    BusinessDistrictId: {  // <-- this is the name attribute
        required: true
    }
},
DEMO:  http://jsfiddle.net/y82dV/