Alcohol and social choice

Here's a fun one. New Zealand's debating changes to the alcohol purchase age. The three options:

• Status Quo (Keep it 18)
• Split purchase age (18 in bars, 20 for buying alcohol off-licence)
• Raise it to 20

The New Zealand Herald tallies MPs' support for the different options. Of 121 MPs, 30 wanted to keep it 18, 27 wanted it raised to 20, and 22 wanted it split. Among the remaining 42, 10 "were considering" split and "several others have previously indicated they preferred the split option". 

Says The Herald:

The outcome could depend on the order the options are voted on, which has not yet been decided by Ms Collins. 

Unless something weird is going on in MPs preference orderings, or one group of MPs starts voting strategically, a split purchase age is the most likely outcome.

Suppose for now that everyone who wants to keep it 18 (Option A) prefers a split purchase age (Option B) to a blanket increase to 20 (Option C) and that all the prohibitionists who prefer raising the age to 20 prefer a split purchase age to keeping it 18. We'll split the undecideds proportionately across the options after putting 10 undecideds into the "split" category, and we'll split the splitters proportionately between second choices of A and C. We then have:

• 41: A > B > C
• 23: B > A > C
• 20: B > C > A
• 37: C > B > A

Let's start by assuming sincere voting. Here are the possible agendas and outcomes:

• (A vs B) vs C: B beats A 80:41, B beats C 84:37. Outcome: B
• (A vs C) vs B: A beats C 64:57, B beats A 80:41. Outcome: B
• (B vs C) vs A: B beats C 84:37, B beats A 81:41. Outcome: B

There isn't a sincere-voting agenda that leads to a non-B outcome. What happens with strategic voting? A supporters want A vs C in the second round, because they know they lose to B but they beat C. So A supporters vote for C against B in the first round. Everything beats C: it's a Condorcet loser. You can't manipulate a sequence of pairwise votes to get an outcome where a Condorcet loser comes out on top; B is the best C voters can hope for. In that case, unless C voters are dumb, they support B in the first round against their most-preferred option. But let's run it both ways:

• (A vs B) vs C: No potential for strategic manipulation as nobody can improve his position by lying about his preferences. If C voters lie, they get a second-round A vs C contest that they'll lose.
• (A vs C) vs B: No potential for strategic manipulation. If B voters lie in the first round, they still win in the second. If A voters lie in the first round, B still wins in the second. And C can't do anything.
• (B vs C) vs A: Here we have potential action. 
• A supporters act strategically. C beats B 78:43. Then A beats C in the second: 64:57.
• A AND C supporters act strategically. B beats C 80:41, then B > A 80:41.

It looks like the ordering of the vote doesn't matter unless the Keep it 18 supporters act strategically while the prohibitionists fail to do the same.

Outcomes in pairwise sequences of votes can be sensitive to the ordering of votes, but that usually requires that some reasonable proportion of voters have non-single-peaked preferences. 

So if there are a lot of "Keep It 18" people who prefer raising it to 20 than having a split age in hopes that that outcome later leads to a reversion to 18, or a lot of prohibitionists who prefer keeping it 18 to having a split purchase age in hopes that more drunk teenagers helps build later support for moving it to 20, then ballot ordering can matter.

Full disclosure: my current iPredict portfolio has me 300 short on Keeping it 18, 220 short on raising it to 20, and 20 short on a split purchase age. I'm short everything because novice traders keep pushing up the price of their preferred option and consequently the sum of all bids is often higher than $1.10. But my net position is long on a split purchase age. I expect Key to see it as a moderate compromise and to care more about that than about the utter lack of evidence of any crisis demanding changes to the youth purchase age. And I expect it to be a median voter outcome where MPs have single-peaked preferences over outcomes on this dimension.

Kudos to the Greens for registering their support for keeping it 18, and shame on "Once Were Liberals" ACT for not doing the same.

Update: If this policy winds up being part of a broader logroll on a multidimensional alcohol package, then all bets are off. We can imagine some movement to "Keep it 18" from the splitters or from the prohibitionists if there were big moves on price, availability, or other regulations. It's harder to imagine movement from "Keep it 18" to tougher age regs in exchange for a bundle with smaller-than-expected regulatory increases elsewhere; more of that support is on an age-rights dimension than on an overall "toughness of the regs" continuum.