I want to use a HiDPI resolution that is half the native size of the monitor, but this doesn't work
In some cases, you will see a resolution that is half the size of the native resolution of the screen. Selecting it will not work.
If you look in the Console (/Applications/Console), you'll observe a message like this one:
11/11/14 10:35:56,465 WindowServer: CGXCompleteDisplayConfiguration: Monitor 4304241; Mode -1569958512 not available
11/11/14 10:35:56,465 SwitchResX Control: CGSCompleteDisplayConfigurationWithOption
This is a bug within macOS
reports this resolution as available when building the resolution list, but doesn't let you select it.
You can try to work around it by creating a custom scaled resolution that would be one pixel less than native. That is, if your monitor is 3840x2160, try to create a scaled resolution like 3839x2160, this should create the same HiDPI 1920x1080, the pixel that has been removed will not be visible.