Your binding should return true, so change it to this -
<input type="checkbox" data-bind="attr: { value: person.id}, checked: $root.chosenPerson() === $data">
Where chosenPerson is equal to the context of the input element. If the element is not within the context of a person, just do
<input type="checkbox" data-bind="attr: { value: person.id}, checked: $root.chosenPerson() === person()">