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The vote means each ballot paper for the election will list candidates in a random order.
The unanimous vote was preceded by a speech from Mayor Dave Cull, in which he intimated those who voted for any other option could be perceived as voting for their own advantage.
''If anyone were to vote for the continuation of alphabetical listing they would have to be voting for a lack of evidence, putting perceived convenience above fairness, or possibly acting in self-interest.''
He said the council had stuck with alphabetical lists in the past because it had no evidence any other way would be fairer.
It now had evidence, after council staff sought advice from University of Otago political studies lecturer Associate Prof Janine Hayward, that randomly-ordered ballot papers would be fairer.
Prof Hayward advised that New Zealand and international studies confirmed a name-order effect, giving better results to candidates higher up in alphabetically ordered ballot papers.
The same effect, though to a lesser extent, would still occur in pseudo-random ballot papers, where candidates' surnames were not listed alphabetically, but in the same order on each voting paper.
Before the vote, Cr Bill Acklin raised a concern that voters might find it difficult to find the name they wanted to vote for on random ballot papers.
Mr Cull said that might be the case, ''but you can't put that above fairness''.
Cr Acklin said if it was perceived there were advantages to being at the top of the list he ''wouldn't want that'', and voted for the change.
''I just hope the voters don't come back and say this was a stupid thing to do.''
Cr Fliss Butcher said she would ''follow the evidence'' too, although she preferred alphabetical ballot papers so she could find names more easily. Cr Richard Thomson said fairness was
as important in an election as issues such as avoiding corruption.
''I do accept [voters] might have to look a little harder to find a name on a ballot paper, but the information about each candidate will be easy to find, and if you have to try a bit harder to vote, well, that does not strike me as being a bad thing.''
He said on alphabetical ballot papers 49% of candidates with surnames A to D were elected and on random ballot papers the figure was 24%.
Cr John Bezett said he had no doubt voters would cope with the change.
Cr Jinty MacTavish said it was ''incredibly important'' people trusted the voting system and random ballot papers were another step towards a more equitable and robust election process.