Recently I faced the problem with using Knockout.js binding with jQuery Chosen plugin.

There was a problem when changing the selection of multiple choice control - the view model was not being updated. I've found a help with this StackOverflow question:  Knockout JS and Chosen multiselect not working.

I was struggling with the solution for a while but finally I've found the source of my problem. When binding view model to single-choice select, you should use

data-bind="value: selectedValue"
while for multiple-choice you should use
data-bind="selectedOptions: selectedOptions"

Here is the complete example.