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Add a label to the combobox
Set all datasource elements visible to initially be false

Something screwy is going on with kendoComboBox when it starts out with
a non-empty dataSource and you call data() on its dataSource passing
empty array. The dataSource is indeed empty but the options aren't
filtered. They just revert to whatever was initially loaded.
Rename dataSource elements' value property to id
Rename filteredDataSource() to visibleValues()
On this simple example, don't change the color of k-state-selected items
Clear the current selection if it's no longer visible
Rename dataSource to visibleDataSource
Make visibility a function of a separate key of the state map instead of mutable model property
Add a grid picker to represent another view on the visible people
Add a readOnly text box showing the currently selected person
Clarify Checkbox and Grid labels
Add some padding to top & bottom as well as left & right