Tag Archives: STV voting system

In defence of STV

“or How I learned to stop living the past and learned to love the vote.”

This posting is in response to the submission of Jeremy Belcher and Calvin Oaten to the DCC Electoral Review Committee, in February 2005, in which they criticise “Meeks NZ STV” and put forward their own Belcher/Oaten Method, which they claim is better than STV in several ways. A comment from Mr Oaten (with a link to the submission) was posted by Elizabeth Kerr on 22 August.

In his submission, Mr Oaten attacks single-seat STV, on the basis that it is the second preference votes of the least successful candidates that determine the outcome, and that the second preference votes of the highest polling candidates play no part in determining the final result. He calls this a “travesty of representation”.

What he fails to understand is that, under STV (in both the single- and multi-seat cases), second and subsequent preferences are merely contingency choices only; they are not additional votes having the same value (the value of unity) as first-preference votes. The system is called the single transferable vote for a reason – everyone has just one vote, which is transferable if necessary. If second preferences given for all the candidates were taken into account, i.e. if each voter had two votes, of equal value, even though only one vacancy was being filled (that were then merely tallied and the candidate with the highest combined total of first and second preferences was declared the winner), many voters would discover, too late, that their second preferences had served only to help defeat the candidate they had actually voted for, being the candidate for whom they had given their first preference. Now that would be a travesty of representation.

Mr Oaten then launches into multi-seat STV, again not realising that second and subsequent preferences are contingency choices only, not additional votes. He is critical of the fact that, in a three-seat ward, voters do not have three votes (of equal value) under STV, completely overlooking the reason why – if voters had three votes, in a worst-case scenario, the largest minority grouping (perhaps comprising only 35% of all voters), could use their three votes to elect the three candidates they wanted, with the remaining 65% of voters getting nothing. Clearly, Mr Oaten wants STV to, in effect, be the system it replaced – multiple-FPP.

Mr Oaten proposes his Belcher-Oaten Method, that he claims would correct NZ STV’s deficiencies. It is, in fact, a clumsy version of multiple-FPP. In a 3-seat ward, he wants the first three preferences to have the same weight, being the value of unity. As previously stated, this would enable the largest minority grouping to use their three votes to elect the three candidates they want, with everyone else missing out. Taking his example of Cargill 2004 on page 6 of his paper, he has determined that the total number of first, second and third preferences is 5210 + 5178+ 5127 = 15,515. To him, this is the number of valid votes. His Quota formula (on page 5) is 15515 / 3 = 5171.67 times 4 (the number of vacancies, plus 1) divided by 10 (the number of candidates), i.e. 40%, which equals 2068.668, which he has rounded up to 2069.

If the required three candidates have not attained this quota, then the total number of fourth preferences are assigned to the candidates on a pro rata basis according to his formula (on page 7). For Teresa Stevenson, therefore, the calculation is 327 / 4927 = 0.0663689 times 327 = 21.702, which he has rounded up to 22. In other words, voters have multiple votes (value 1), equal to the number of vacancies, plus further votes, if necessary, assigned on a pro rata basis, i.e. at less than the value of unity (327 votes, that he now calls preference votes, become 22 votes).

He calls his method “Proportional STV that reveals the true will of the People”. Surely he jests. First, it is not STV – it is a multiple-vote system (not a single vote system), and no votes are transferred; preferences are merely tallied.

Second, it is not proportional representation, because it is essentially multiple-FPP (with additional pro rata votes beyond the nth preference in a n-seat ward). Taking his example, three people he dislikes, because they share “political, social, lifestyle, or cultural associations or sympathies” (page 4, fourth bullet point), being Stevenson, Doug Hall and Paul McMullen, fill the three seats. In Cargill 2004, under STV, the three winners each obtained 25% of the votes, meaning 75% of the total of votes were effective in helping to elect a candidate, and they were quite different from each other. Under the Belcher-Oaten Method, the three winners are politically / socially aligned (according to him), but are elected with a total of only 7216 votes (plus 217 pro rata votes [22 + 195]) out of a total of 15,515 votes (plus 217 pro rata votes), i.e. on only 46.51% of the total of votes!! This means his Quota formula has no rational electoral basis, which leads to a concomitant conclusion that his method is well short of being mathematically rigorous.

Consequently, third, far from revealing the true will of the people, his method grotesquely distorts that will. He simply hasn’t clicked to the fact that the 987 voters who gave a second preference, and the 876 voters who gave a third preference, to McMullen (for example), would have, in many cases, helped to defeat their most preferred candidate, such as Paul Hudson or Michael Guest. Although it would be transparent, it is hardly fair, accurate or democratic. And once those voters see what they’ve done (because of the transparency), they’ll never express second or subsequent preferences again, and then we’ll be back to FPP – actually, we would have, by default, a close approximation of the Single NON-Transferable Vote in a multi-seat ward (a system, previously used in Japan, that produces unequal representation, or no representation at all, for voters).

Mr Oaten states that the first preferences of the highest polling candidates are never looked at (page 3, paragraph immediately above the table, and in a posting dated 22 August (at 11.35 a.m.)). That is simply not true. For example, once Stevenson attained the quota, her keep value was recalculated (at iteration 3) as 0.98857…, and was recalculated as the count progressed. Her final keep value was 0.66775… That means, at the conclusion of the count, she had kept 66.78% of all her votes, and the remaining 33.22% had been transferred to the second and subsequent preferences on her votes (both her first-preference votes, and those votes she acquired along the way), to help elect other candidates.

I suspect Mr Oaten laments the fact that, in Cargill in 2004, he was excluded from the count at the same time Stevenson was elected (at iteration 2), which meant he was unable to benefit from any second preferences given for him on her 1,313 papers. But, at iteration 3, Alan McDonald only received 104 papers from her (value 1.89 votes), Steve Young only received 156 papers from her (value 1.78 votes) and even Jo Galer and Nicola Holman only received 202 and 200 papers, respectively, from her (value 2.31 votes and 2.28 votes, respectively). The simple fact of the matter is, Mr Oaten was always destined for an early exit, because only 142 people (out of 5,210) voted for him. Not even the Belcher-Oaten Method would have saved him.

In conclusion, I commend the DCC for creating the 11-seat Central Ward. What this means is that any candidate who receives one-twelfth (8.33%) of all votes cast [45% of (say) 65,000 electors = 29,250 x 0.833 = (say) 2,400 votes] will be elected. Any group of voters, comprising 8.33% of all voters, will elect a candidate to represent them, regardless of who larger groups of voters may want.

Click here for a paper that explains how single-seat STV works, and the rationale behind the system. (PDF)

Click here to see a paper that describes multi-seat STV, and the rationale hehind the system. (PDF)

Click here to see a paper that describes how single transferable votes are counted, and how individual voters can work out how their vote was used. (PDF)

Click here to see a paper that explains STV to voters (PDF).

Click here to see a paper that reconstructs in meticulous detail how the votes cast in the Cargill Ward in 2004 were counted. (PDF)

Click here to see the guide prepared for the Department of Internal Affairs, the Society of Local Government Managers Electoral Working Party and Local Government New Zealand (PDF)

Author: Steve.

Posted by Paul Le Comte

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