As soon as a candidate has enough first preference votes to be elected, their excess votes are transferred to voters' second preference and so on till enough people have been elected.
In May a 30-signature petition from "community leaders" asking council to change to STV was presented to councillors by unsuccessful 2016 election candidate Steve Baron.
He said STV was a much fairer system, didn't waste votes and elected a more diverse council.
On Tuesday councillor Philippa Baker-Hogan wanted council to indicate its preference to change to STV before it sought feedback and said council should have been consulting much earlier.
In indicating a preference first before seeking public feedback, Ms Baker-Hogan was only backed by councillors Josh Chandulal-Mackay and Helen Craig.
Instead council will seek feedback from a neutral position.
"I fear that if council indicated its support for change then it skews what should be some very open, public feedback," mayor Hamish McDouall said.
Mr McDouall said he would commit to holding a public meeting to discuss the two voting systems and answer questions.
Mr Chandulal-Mackay supported STV as it meant "more votes counted rather than wasted" but he wanted to the public to have a say.
Mrs Craig supported STV too and hoped a month of public consultation would avoid an expensive referendum.
"I believe (STV) delivers better community representation and that's we should be trying to achieve."
But councillor Rob Vinsen said STV was complex and many people couldn't understand it.
"Even Bill Gates wouldn't be able to work this one out on the counting system," he said.
"If we're going to change our system of voting we need to be pretty well guaranteed two things. One is increased participation and the other is increased diversity."
After Tuesday's meeting Mr Baron said he was pleased STV hadn't been ruled out and felt there seemed to be growing support for change among councillors.
"You'd have to take that as a positive."
A decision must be made in September.
A binding referendum can be triggered by council or five per cent of electors via a petition.
In 2013 Hamilton City Council held a referendum on its voting system with 70 per cent preferring to retain FPP.
Horizons Regional Council also recently decided to retain FPP.