In issue 3 of Chalkdust, Alex Bolton wrote an article about the maths of voting systems. In this week’s blog post, Alex looks at some interesting referenda relating to changing the status quo, and some difficulties in designing the system used.
In 2011, New Zealand was asked whether it would like to change its voting system. Voters were asked two questions:
- Should New Zealand keep the current voting system?
- If New Zealand were to change to another voting system, which voting system would you choose? (4 options were given)
If a majority were in favour of changing the voting system then the new system would be chosen using the alternative vote on the alternatives. This system has a clear problem: if both
- 49.9% of the electorate think the status quo is the best system, and
- the status quo would beat any alternative in a one-on-one contest,
A similar system was used in the 2003 California governor recall election. Voters were simultaneously asked whether they wanted to recall the current governor Gray Davies, and who they would like to replace Davies. 55% of voters chose to remove Davies on the first ballot, and he did not appear on the second ballot. The Republican Arnold Schwarzenegger won the second ballot. It was very easy to be nominated as a candidate for the second ballot, and Arnold Schwarzenegger was one of 136 candidates, including former child actor Gary Coleman and 46 other Republicans.A different system was used for the 2015-16 New Zealand referendums on changing the country’s flag. Many alternative flags were submitted and five were chosen for people to vote on. An alternative vote contest was held to choose which of the five alternatives would compete against the status quo. This system is preferable to the first system because people vote on the status quo with knowledge about what the alternative would be, and people have no extra incentive to vote against the status quo when it is put on the ballot. Of course the disadvantage of this system is that the votes have to be held separately, increasing the cost of running the ballot for both the government and the electorate. Indeed, after the first vote to choose an alternative, 57% of New Zealanders chose to keep the original flag.
The design of a referendum on the status quo is critical to ensuring that the wishes of the electorate are understood. Care needs to be taken to ensure that the electorate have a good idea of what the alternative to the status quo is in order for voters to articulate their true preferences without unintended incentives to do the contrary.
Header image: Flag referendum candidates flying above Albatross Fountain on Wellington Waterfront, Flickr user glasnevinz, CC BY-SA 2.0.
Flags: (1) Public domain. (2) Kyle Lockwood, CC BY 3.0. (3) Kyle Lockwood, CC BY 3.0. (4) Public domain. (5) Alofi Kanter, CC By 3.0. (6) Andrew Fyfe CC BY 3.0
More from Chalkdust
- I like my towns like I like my Alex: Bolton
- Alex Bolton plays noughts and crosses on unusual surfaces
- Chalkdust descends upon the UK's largest pop maths gathering and tells you what you missed
- How to win a game when your expected score is 0
- Why voting systems can never be fair
- A selection of our favourite mathematical blogs