For those who want more on how to vote under STV, and a different view from mine posted yesterday, see Graeme Edgeler's guide to STV.
Of the many illuminating comments on Graeme's post one from Steve Todd stands out for interest to Wellingtonians
While it is perfectly valid to vote, simply by placing a unique first preference beside the name of the candidate you most wish to see elected, by doing so, you are, as Graeme has already pointed out, risking your vote being wasted, in whole or in part.
A classic example of votes being wasted (in whole) was seen at the 2010 Wellington City mayoral election, at which Celia Wade-Brown came from behind to defeat the incumbent, Kerry Prendergast. At the end of the count, 3,783 votes (7.09% of the 53,369 valid votes cast) had dropped out of the count; had become non-transferable. In other words, astonishingly (to me, at least), those 3,783 voters declined the opportunity to indicate a preference between the two *main* candidates; the only two candidates with a chance of winning.
Given that Celia won the election by just 176 votes, had 177+ of those voters carried on and indicated a final preference for Kerry over Celia, Kerry would have retained the mayoralty.
At iteration 4, when the third-placed candidate, Jack Yan, was excluded from the count, his 7,426 votes were distributed 1,806 to Kerry, 3,459 to Celia, and 2,161 went to the total of non-transferable votes. It seems to me that the great majority of the sort of people who would have supported Jack (generally speaking: young, educated, switched-on, socially/politically aware), would have had a preference for one or other of the last two remaining candidates, even if they didn't particularly like either of them. Yet, amazingly, 29.10% of them chose not to express that preference.
Given that the preferences for the previously-excluded candidates transferred about 2 to 1 to Celia, it is probable that about 700 of those 2,161 voters would have preferred Kerry to Celia, but didn't say so. As I say, if 177+ *had* said so, Kerry would have hung on, to win. By not saying so, those 700 or so voters allowed their lesser-preferred candidate (of the remaining two) to come through and snatch the prize.
That is why it is important for voters to express as many preferences for the candidates as they are able. The more preferences that are expressed, the more likely it is for voters to have a direct effect on the final outcome