FPP elects people by the total number of votes they receive.
STV allows voters to rank each of the candidates in their order of preference.
In 2011 councillors decided to go with FPP, but yesterday councillor Karen Hunt introduced a motion to change to the STV system.
She said STV was much fairer and was not as confusing at it looked.
"The difference for the community would be they would actually have to think about who they want to vote for.
"FPP is outdated and is little more than a popularity contest."
She said the Lakes District Health Board, by law, had to use the STV system and it would be sensible for the council to use the same system.
Councillor Charles Sturt was vigorous in his opposition to STV.
"I will challenge this at full council if you go ahead with this change," he said.
"Every election there has been change in this council, the ranking of people is just an absolute shambles, just look at how many votes were incorrect at the DHB election."
In the 2013 election there were 762 informal or blank votes received for the mayoral and council election.
In the same election there were 6243 informal or blank votes received for the Lakes District Health Board election.
Councillor Janet Wepa said she had not heard any calls for change.
"Keep it simple, stupid, we make things far too complicated," she said.
But, as councillor Mark Gould pointed out, the council only had until tomorrow to call an extraordinary meeting to ratify any changes and would end up not meeting the quorum due to most councillors not being able to attend an extraordinary meeting at short notice.
Ms Hunt then conceded the motion would be lost.
"We have run out of time and snookered ourselves," she said.
Deputy mayor Dave Donaldson and councillors Mike McVicker and Ms Hunt voted to change to STV. Councillors Charles Sturt, Mark Gould, Tania Tapsell, Rob Kent and Mrs Wepa voted to stick with FPP.
Three councillors were absent - Peter Bentley, Trevor Maxwell and Glenys Searancke and mayor Steve Chadwick is in Morocco.
