when selection change event pass in every option, so got more then one event. but you got $event.source.selected is true in one event which is you selected. so you can manage it.
your html should be like
{{ person.name }}
ID: {{person.id}}
{{person}}
your component function should be like
selectedPersonsInDialog(isSelected: boolean,person){
if(isSelected){
this.selectedPerson=person;
alert(this.selectedPerson);
let dialogRef = this.dialog.open(AddListOfPersonDialog, {
width: '500px',
data: { person:this.selectedPerson}
});
}
}