Voting lists: Alphabetic or Random?

Should the name of candidate Aardvark, Al always come before Zizovic, Jo on the ballot paper?

Not in Wallingford, Connecticut, where the names of the candidates are in random order:

There is a twist to this procedure: Republicans and Democrats alternate on the ballot paper.

Q. (for our US readers) Is the randomization of ballot order used widely in the US?

Q. (for the rest of us) Should we copy this practice?