I'm not sure if you can do this with a rule on the form. I will do this with a workflow but this means update only after you saved the form.
The workflow will kick off with a start when modified expression comparing current value for person control with previous value for person control. If it changed, update the value to yes (if it was no) or no (if it was yes).
Let me know if you need more information.
following code should toggle yes/no control value within form based on people picker change
NWF$('#' + jsvarYesNo).prop('checked',!NWF$('#' + jsvarYesNo).prop('checked'));
var PPObj = new NF.PeoplePickerApi('#' + jsvarPP);