This is always the problem I find with things like this... Is the island the cartoon one palm island, something more realistic like Castaways' Island or something more substantial like Gilligans Island, or much bigger like Carusos' Island.
I think that if its a smaller island with no or limited resources your list would be a lot different then if you have a larger island with some or great resources.
For instance if you had Gilligans' or Carusos' Island there are enough resources that you might drop the cordage for another item and get to work makeing your own cordage from things found on the island.
On the other hand if you find your on the other two islands it might be better to have three or four items to cover food/water/shelter then have a solar panel with a PLB and/or satphone.
But then if they are going to be less then specific about what they are going to drop you on, you can be less then realistic about what 'things' you want with you.. Ask for a nuclear sub and a desalination plant... other then food, your set.