Я создал простую jsFiddle Demo .Это не идеально, просто иллюстрирует идею.
HTML:
<select id="first">
<option value="0" selected>No</option>
<option value="1">Yes</option>
</select>
<select id="second">
<option value="0">No</option>
<option value="1" selected>Yes</option>
</select>
Javascript:
//find the selects in the DOM
var first = document.getElementById('first');
var second = document.getElementById('second');
//this is the handler function we will run when change event occurs
var handler = function () {
//inside the handler, "this" should be the select
//whose change event we are currently handling
//get the current value and invert it (0 -> 1, 1 -> 0)
var invertedValue = this.value === '0' ? 1 : 0;
//check which select's change we are currently handling
//and set the inverted value as the other select's value
if (this === first) {
second.value = invertedValue;
} else {
first.value = invertedValue;
}
};
//add handler function to run on change event on both selects
first.addEventListener('change', handler, false);
second.addEventListener('change', handler, false);