You assume that any pizza can be reliably sliced into four more or less even parts. Also you assume that cutter is interested in getting the best share. That is not always the case.
Imagine that slicer makes 1 huge and 3 tiny pieces. He obviously won't get the biggest one, but the second chooser will be mistreated too. Thus, evil divider can starve the second chooser to death.
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You assume that any pizza can be reliably sliced into four more or less even parts. Also you assume that cutter is interested in getting the best share. That is not always the case.
Imagine that slicer makes 1 huge and 3 tiny pieces. He obviously won't get the biggest one, but the second chooser will be mistreated too. Thus, evil divider can starve the second chooser to death.