You need to set traditional: true when serializing arrays.
$.ajax({
type: "POST",
traditional: true,
url: "../BookOrder/MyMethod2",
data: { function_param: SelectedIDs}
});
Found this good explanation on what traditional: true does: http://stackoverflow.com/a/5497151/2419531https://stackoverflow.com/a/5497151/2419531
If you don't want to use traditional: true, you can pass the data as string using JSON.stringify and specifying the contentType:
$.ajax({
type: "POST",
url: "../BookOrder/MyMethod2",
contentType: 'application/json',
data: JSON.stringify({function_param: SelectedIDs}),
});