S59 referendum: a game theory approach

datePosted on 22:25, June 17th, 2009 by Lew

How* to vote: Yes, [null] or !#gh$u%WfG?

What’s a body to do, who thinks the S59 referendum question is absurd and yet supports the rights of children to be free from violence, even that perpetrated by their well-meaning parents?

Russell Brown asks the question, and elaborates on the options, but doesn’t provide an answer. Essentially, the question is about principle against pragmatism. This approach is pretty elementary (game theory isn’t a speciality) but it does enough to demonstrate my views on the matter. (It looks to me like a weird sort of Stag Hunt with a third quarry thrown in). There are also a few assumptions and assessments as to how the results will play, which I’m happy to argue. I apologise if it all seems a bit bleedin’ obvious.

mehStarting with the worst response, the third quarry or null vote. An argument of principle, advocated by Denis Welch, it holds that people should treat the s59 referendum with utter contempt and dispose of their share of the $9m expense in the circular file. This is possibly best characterised as the Ostrich Strategy, viz. “ignore it and it’ll go away”. Unfortunately, no cause which attracts signatures from the 10% of the electorate required to trigger a CIR will ever just go away on its own. Given that there are a hard core of people who are strongly motivated to vote “no” in this referendum, the adoption of this strategy will send the (incorrect) message that the bulk of the electorate doesn’t care either way, ceding the field to the “no” voters (hereafter “anti-anti-smacking” or “AAS”). We can call this “Lose For Sure”, because no matter what happens, the strategy can’t win.

chadThe main argument of principle, made most forcefully in the PAS thread by Craig Ranapia and Tom Semmens, is that the question is so badly worded that reading meaning into it and voting on the basis of that interpretation accords the question too much respect, and devalues the CIR system which should insist on properly-formed questions. This argument holds that one should respond to a meaningless question with a meaningless answer by invalidating the ballot and submitting it anyway, which I have characterised above as “!#gh$u%WfG”; in other words, leaving the chad hanging or writing something to the effect of “This question is meaningless” on the ballot and returning it. This has some history in previous referenda, and in principle if enough informal ballots were returned, could serve to discredit the question and the questioning lobby group. Which is what we want. We can call this “Win Big”, because if enough people take this approach, the anti-anti-smackers will be roundly shamed in a more thorough manner than simply losing the referendum. On the other hand, if not enough people do this and the votes are split between “yes” and “informal” the AASers will claim victory. We’ll call this “Lose”.

yesThe argument in pragmatic terms is most eloquently put by Judy Callingham: “I’m going to vote “yes” – as I see it if the bastards don’t lose we’ll never hear the end of them”. This illuminates a key aspect of the matter: the AAS lobby doesn’t have to win big, they just have to not lose in order to demonstrate that they represent the “average kiwi”. This means the primary goal of those opposed to the question or what it represents should be to win, regardless of the magnitude of the victory. Put like that it seems obvious, doesn’t it? This position is most strongly put by The Yes Vote, whose banners are currently up all around the progressive NZ blogosphere. Essentially, if enough people interpret the question in the way in which the AAS want people to interpret it and vote “yes” anyway, they will lose, and the outcome will be positive, viz. parents not being allowed to claim correction as a defence for beating their children. We’ll call this “Win”. Those so voting will have favoured the AAS with a formal answer to their ballot, thus granting them some sort of legitimacy, and if insufficient people vote this way such that it boosts turnout and the AAS still win, they will rightly be able to claim that they have a public mandate for their policy of allowing parents to assault children with legal protection. We’ll call this “Lose Big”.

So, how do things stack up? I’ve established five notional outcomes, as follows:

  • Lose For Sure: %No > %Yes > %Informal (low turnout). This would be caused by people who object to the question refusing to vote.
  • Win Big: %Informal > (%Yes or %No) > (%Yes or %No). This would be caused by enough people voting informally to outnumber those who vote any other way, rendering the referendum a public farce. This requires a great deal of work to convince those who would instinctively vote “yes” despite disagreeing with the question, out of native respect for the democratic process or for other reasons.
  • Lose: %No > (%Yes or % Informal) > (%Yes or % Informal). This would be caused by those objecting to the question being split between “yes” and “informal” such that “no” snuck through the gap, allowing the AAS to claim a plurality and thus victory. There would remain some defence in that the cumulative “yes” and “informal” votes might add up to a majority, but I don’t think this would be worth much.
  • Win: %Yes > (%No or %Informal) > (%No or %Informal). This would be caused by enough people voting “yes” to demonstrate that the AAS does not represent the “average Kiwi” as they claim. It seems likely that those who consider the question an affront to the democratic process and are inclined to vote informally or not vote at all would need to be convinced to vote “yes” instead.
  • Lose Big: %No > %Yes > %Informal (high turnout). This would be caused by enough people voting “yes” to demonstrate that those opposed to the AAS were taking them seriously, but were outnumbered by the AAS itself, thereby justifying the claim that they represent the “average kiwi” with the assertion having been properly tested. If some (but not enough) people are convinced that voting “yes” is the right idea, this will be the result. Thus there is danger in an incomplete adoption of the strategy.

So how should one vote? Well, it obviously rests on what other voters will do. Clearly the best outcome in the case of a split requires collusion – members of one group (either the “informal” voters or the “yes” voters) changing their vote. It looks to me like this:

  • Fail to vote: Many people will do this, but it won’t have any positive effect for anyone other than the AAS. P(Lose For Sure) > *
  • Vote informally: Some people will do this, but probably not enough to Win Big, and if the result isn’t Win Big, it’s more likely to be Lose. This rests on your judgement of whether the number of informal voters will be greater than the number of “no” voters. I don’t think they will. Thus in my assessment P(Lose) > P(Win Big) > *
  • Vote yes: If enough people do this, it will result in Win. If nearly enough people do this it will result in Lose Big. I think the natural tendency of voters is to vote according to what they think something means, rather than what it actually means in cold hard terms. In addition, I think voters are generally reluctant to vote informally out of respect for the institutions of democracy. In addition, I think The Yes Vote has been running a fairly good campaign – they’ve had a few mentions in the mainstream media, and their message is clear and forthright. Therefore in my assessment P(Win) > P(Lose Big) > *

So, essentially, my argument based on this is “vote yes, support campaigns to convince others to vote yes, and all those of you who are considering not voting or voting informally in protest – don’t, just vote yes, because the main danger of losing is in splitting the vote. And hope like hell the yes vote doesn’t fall short, because trying and failing will mean a worse loss than just plain old failing.”


* I have omitted the “no” vote. People who are going to vote thus have no need to consider the questions I raise in this post.

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10 Responses to “S59 referendum: a game theory approach”

  1. Thomas Beagle on June 18th, 2009 at 08:40

    I know it’s not a valid response, but I loved the suggestion of a friend that it’s such a stupid referendum and such a stupid question, that we need to write in our own question and then answer that:

    “And the results are in for the so-called pro-smacking referendum and…. yes folks, marijuana is now legal!”

  2. lyndon on June 18th, 2009 at 10:12

    It’s so strange that the question arises; in a the kind of questions you’d hope for in a national referendum, the political issues would identify more closely with the actual meaning of the question.

    On the other hand, there’s a certain amount of auto-non-lose in the way the question, as written, is leading and in itself provides no guidance to legislators as to how to behave.

  3. roger nome on June 18th, 2009 at 13:48

    hmmm – how to re-word the question:

    Should it be legal for parents to inflict physical punishments on children, which have been proven to psychologically damage people?

    heh …

  4. BK Drinkwater on June 19th, 2009 at 11:38

    Hi Lew. Good post; sorry it took me a little while to get to it. I respond over here.

  5. chris on June 19th, 2009 at 17:39

    How about getting your own referendum started?
    Good luck with getting the numbers – you will need to phrase it even more carefully that the current one. After all it has not mattered if the word good have been in any of the polls. Most people are sensible enough to know that the law change was needed BUT IT WENT TOO FAR. The referendum is trying to fix this so good parents (and it is up to the government to interpret what an appropriate smack is) don’t become criminalised. Yes, if you break the law you are a criminal (unless it is a contract or civil law – and this is not).

  6. Lew on June 19th, 2009 at 20:09


    How about getting your own referendum started?

    Why? We already have the law the way we want it.

    In any case, this isn’t about the question, or the merits of the law – it’s about the voting strategy for the referendum. Do you have any views on that?

    (If you want to discuss the referendum question or the politics behind it, there are a few threads on the topic here).


  7. Ben on June 26th, 2009 at 14:44

    I’d support a Vote Informal campaign.

    It’d be easy to get people to vote informal. Think of all the ways you can deface a ballot! People who wouldn’t normally vote could easily be tempted to vote informal.

    In terms of your game theory I put it to you that the following is a win:

    (%Informal + %Yes > %No) and (%Informal > Typical%Informal)

    With this analysis and any kind of half-arsed Vote Informal campaign I think that the best game theoretic solution is to vote informal.

  8. Lew on June 26th, 2009 at 18:40


    The strong position which will be held by the winner of a plurality (essentially the ability to say “we won, you lost, eat that” on the grounds that nobody else got more votes) means this strategy isn’t as strong as a pure strategy of “vote informal” or “vote yes”. BK Drinkwater has the formal analysis here. Given that there is no “vote informally” campaign in existence, while there is a “vote yes” campaign and that electors tend to not spoil ballots out of respect for official process, voting informally is nothing more than a good way to spoil The Yes Vote’s campaign, which is already well and truly running and has the support of a number of high-profile celebrities and charities.


  9. Pascal's bookie on June 26th, 2009 at 19:37

    I don’t know much about this game theory business, but I’m voting yes based on the following:

    1) The whole point of the thing is for the petitioners to get a number to waive around. They are pretty sure the law isn’t going to be changed, and this is a way for them to reassure themselves that yes, they are being oppressed.

    2) They want as big a No vote as they can get, in terms of percentage of valid votes. That’s why the question is so leading.

    3) It would be nice for them if they got a big turnout, but they won’t mind a small one if it gives them a higher percentage of ‘no’. They know that their voters are most likely to turn out.

    4) Any talk about how that percentage is meaningless, or the number of informal votes, will be ignored. More so as time goes on. They will be using this stat for years.

    5) Turnout is going to be low.

    6) Especially given 5, every yes vote counts toward lowering that ‘no’ percentage.


    7) vote ‘yes’ if the aim is to lessen the utility of the result for the petitioners.

  10. […] Kiwipolitico provide an excellent discussion of game theory applied to the referendum. However, as with all arguments, it all hinges on the presuppositions —and in our case the relevant one is: Given that there are a hard core of people who are strongly motivated to vote “no” in this referendum, the adoption of this strategy {ballot spoiling / not voting} will send the (incorrect) message that the bulk of the electorate doesn’t care either way, ceding the field to the “no” voters […]

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