Flag Cycles

I guess we'll never know whether the flag referendum has chosen the right flag. Why? Elections NZ cannot tell us.

Let's step back. Recall that the preferential ballot that will be used would provide us all the data we need to choose a Condorcet winner, if there is one. The Condorcet winner is the flag that would beat all other flags in a head-to-head match-up. So if my preferred flag, monkey-butt, would beat each of the fern designs and the red peak design in a head-to-head match, monkey-butt would be the Condorcet winner.

It's dead simple to check for a Condorcet winner in the preferential ballot. For each of the pairings, you pretend that all the other options don't exist and see how many voters say A beats B and how many say B beats A. If a majority of voters rank A higher than B in their preference ordering, regardless of how they rank them relative to all the other options, then A beats B. You do that across all the potential options. If some flag would beat each other option, that's the right flag.

Unfortunately, a preferential ballot with sequential elimination of options that receive the fewest first choices can sometimes choose the wrong option. Suppose some flag is everybody's strong second choice but the first choice of few voters. It could be quickly eliminated from the preferential ballot. It isn't necessary that a Condorcet winner exists, or that a preferential elimination would fail to choose an existing Condorcet winner, but it is definitely possible and it is definitely easily avoided. How? Before running the preference ballot, check to see if any option beats all the others and declare it the winner if so.

Even more unfortunately, we'll never know whether we've chosen the wrong flag. The Electoral Commission replied to my request as follows:

Dear Mr Crampton, Thank you for your e-mail of 24 September 2015 regarding the results of the first flag referendum and a request to provide the number of votes that conform to each of the potential preference orderings and publish the aggregates.

Section 38(1)(a) of the New Zealand Flag Referendums Act 2015 (‘the Act’), provides that in the case of the first flag referendum, once all the voting papers have been processed, the Returning Officer must:
(i)     calculate the number of first preference votes received for each option; and(ii)    count the votes in the manner described in Schedule 4; and
(iii)   declare the result of the referendum by giving public notice of the following:(A)     the absolute majority of votes determined at the first iteration; and(B)     the number of first preference votes received for each option; and(C)     the absolute majority of votes determined at each iteration at which an option was successful or excluded; and(D)     the number of votes recorded for each option and the number of transferable votes at each iteration at which an option was excluded; and(E)     the iteration number at which each option was excluded, where applicable; and(F)     the number of informal voting papers; and(G)     the outcome of the referendum; and 

The results will be published on the Electoral Commission's website: www.elections.govt.nz in accordance with these requirements.  The preliminary results will be released after 7pm on 11 December 2015 and the final result after midday on 15 December 2015.
 

Unfortunately, the Electoral Commission is unable to provide the additional result information that you would like because it is not permitted under the legislation.
 Yours sincerely

I wonder if it's too late to get an emergency change to the referendum legislation.

Update: A follow-up email confirms that the Electoral Commission would decline any OIA requests for those more detailed vote tally breakdowns as they view it as illegal for them to provide it.

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.

STV isn't subject to manipulation? Ahem.

Kiwiblog points to Graeme Edgeler, below, and advises sincere voting in the STV local body elections.

(Edgeler)
But is it a good idea to rank everyone?

Yes.

But if I give someone I don't like a rank, couldn't this hurt the chances of candidates I like more?

No.

Your lower preferences cannot ever harm the election prospects of anyone you rank higher than them.

But some of my vote could still go to someone I'm not a fan of?

Yes. But only if all the people you ranked higher than them have already been elected, or cannot possibly win.

By ranking a candidate lowly, you're not helping them beat people you like more than them, you're only helping them against people you hate more.

In the 2002 French Presidential election, there was a vote-off between the top two candidates, the right wing incumbent Jacques Chirac, and far right National Front leader Jean-Marie Le Pen. Many left-wing voters did something they never thought they would do, and voted for Chirac. They weren't using STV, but the principle is identical. In Australian Senate Elections, and some state elections – which do use STV – the Labor Party has advised its supporters to rank the right-wing Liberal Party above Pauline Hanson's One Nation Party. Voting this way doesn't hurt the Labor Party, but it makes it as unlikely as possible that One Nation gets anyone in.

Like the French voters who "voted for the crook, not the fascist", ranking all the candidates helps ensure that what you might consider "the greater of two evils" won't be elected.

Let's consider a contest for a single member district: one candidate will be elected.

There are five types of voters.

Group 1, 10 people, prefer candidate A over C over B over D: A>C>B>D
Group 2, 7 voters, prefer: B>C>A>D
Group 3, 5 voters, prefer: D>C>B>A
Group 4, 3 voters, prefer: C>B>D>A
Group 5, 4 voters, prefer: D>C>A>B

Everyone votes sincerely. In the first round, nobody meets the quota of 15 first choices. So the candidate who is the least preferred is dropped. Candidate C is the first choice of only 3 voters and so is dropped. Again, nobody meets the quota of 15 first choices: B and A now tie at 10 first choices, D has 9 and is dropped. In the third round, B reaches the quota of 15 first choices and is elected.

Suppose, though, that Group 5 votes strategically. B is that group's last choice and was the outcome of the STV election. If they had instead reported their preference ordering as having been C>D>A>B, the selection would have run as follows: D would have been dropped in the first round as the first choice of only 5 voters. In the second round, C would be the first choice of 12, A of 10 and B of 7 so B would have been dropped. In the third round, C makes quota with 19 votes; C is the winner.

So can your placing a candidate lower down the ordering ever hurt the chances of someone you've ranked higher? That's been proven above. Now, it may be very very difficult in the real world because nobody has access to the kind of information we've used in this example. But in a single-candidate district, a non-crazy rule of thumb might be that if your first choice is a candidate who is hated by lots of other folks (like D, above, who was the first choice of 9 but the last choice of 17), you may do better by listing as your first choice somebody a bit further down your preference ordering who's more likely to win (like C, above, who was the second choice of lots of folks) if your last choice otherwise has reasonable support.

I don't think that kind of a rule is computationally hard.

Let's look now to Graeme's precise scenario: he argues you can never hurt the chances of someone higher up by ranking lower order candidates rather than leaving them blank. I think he's right about that: your lower preferences are never checked unless your higher preferences have been eliminated. But you can sometimes do better by lying about your preference ordering than by reporting things sincerely. So Farrar's line at Kiwiblog is, I think, incorrect:

Don’t try and be strategic and working out who is most popular and hence I will rank them lower as they don’t need my vote etc. Just rank candidates in order of your true actual preference.

Farrar is right that you won't waste your vote in a multimember election by keeping a popular guy as your first choice if he is your first choice; any votes in excess of quota are allocated to your lower order preferences. But that doesn't mean you can't do better by being strategic if your first choice is a bit of an odd one.

Studying Oscar

I'm now rather curious whether the Academy of Motion Picture Arts and Sciences could ever be convinced to release ballot data from the period in the 1930s-early 1940s when they last ran the preferential ballot. I'd be pretty surprised if they'd be willing to release anything from the current period, but it's been now seventy years since these votes; it's hard to imagine that anybody would still be alive to pine over how far behind he really was in the 1941 Best Picture running.

A quick flip through the academic literature shows some work on the Oscars, but nothing using ballot paper data.

Iain Pardoe finds that data on nominations in other categories and wins in other awards predicts about three quarters of best picture picks.

William Gehrlein and Hemant Kher provide an excellent overview of the Oscar nomination and selection procedures ca 2004: a form of preferential ballot was used in the selection of nominees, followed by plurality vote among nominees. So there exists preference ordering data even in the plurality system! They work through the mechanics of the system with hypothetical preference orderings, and I'd guessed they'd have used real data if it were available.

Oscar: if the ballots still exist, releasing the data with a 70 year moving wall would be very very cool. I can't see it hurting anybody's feelings or causing problems in getting people to fill in ballots today. If anybody knows anybody at the Academy....

Some things I'm curious about:

• In how many years do Condorcet Winners exist?
• What fraction of Condorcet Winners are selected?
• What are the sizes of minor cycles within overall preference orderings?
• How big are problems of ballot drop-off (do all voters rank all films or only their favourites?
• Assuming truthful preference revelation, in how many cases would an alternative voting mechanism have yielded different results?
• Which voting mechanism would yield results viewed as "best" by retrospective evaluations of film quality?

Previously: all Oscar voting systems subject to manipulation; Social Choice and the Oscars.

But they're all subject to manipulation...*.

Justin Wolfers lauds the new Oscar voting system, also described here. He claims:

• The new system will see less manipulation
• The system picks Condorcet winners:
  

  “There cannot be a loser who would be preferred by more than 50% of the people to the winner. The winner will always be preferred by at least 50% of people to any other movie.”

Really?

Let's take Wolfers's example: 1997's win by Titanic over As Good As It Gets, The Full Monty, Good Will Hunting and LA Confidential. Wolfers says that someone expecting Titanic and As Good As It Gets to be the top picks would have an incentive to lie about his true preference for LA Confidential and to vote for his favourite among the two likely front runners. But mightn't folks have incentive to lie also under the elimination ballot?

Suppose we have 5800 Members of the Academy voting, with preferences as listed below.

The first set of voters, 2000-strong, prefers Titanic to anything else, followed by LA Confidential, followed by Good Will Hunting, followed by Full Monty, followed by As Good As It Gets.

The second set of voters, all 1400 of them, prefers Good Will Hunting followed by LA Confidential followed by The Full Monty, followed by Titanic, followed by As Good As It Gets.

The third set of 1000 voters prefers As Good As It Gets, followed by LA Confidential, followed by Good Will Hunting, Titanic, and The Full Monty.

The fourth set of 600 voters prefers LA Confidential, then Good Will Hunting, then Good As It Gets, then Full Monty, then Titanic.

The final set of 800 voters prefers As Good As It Gets followed by LA Confidential, Full Monty, Titanic, and Good Will Hunting.

On a straight plurality vote, Titanic wins with 2000 votes to As Good As It Gets's 1800.

Under a sincere elimination ballot, Full Monty is eliminated on the first round (nobody's first pick) followed by LA Confidential on the second (first pick of only 600), As Good As It Gets on the third (now the first choice of 1800), and Titanic on the fourth (now first choice of 2800), leaving Good Will Hunting as winner.

Is it then true that Good Will Hunting is preferred by a majority to any other film? Obviously not. LA Confidential is preferred over Good Will Hunting by all but the second group of voters: 4400 preferred LA Confidential, 1400 preferred Good Will Hunting. Indeed, LA Confidential is the Condorcet Winner in the preference ordering I've set up above. It's true that the winner on the elimination ballot is preferred by a majority to the film it beats out in the last round, but that's hardly the same thing as being majority preferred over all other nominees. I'm guessing that Wolfers here must have been misquoted.

As for manipulation, imagine that you're in the final group of voters and you've a decent idea of how things are going. You and the rest of your group will not be happy if Good Will Hunting wins: that's your last choice. How can you change the outcome? Lie about your preference between As Good As It Gets and LA Confidential! Doing so flips the outcome to LA Confidential, your group's second choice, from your group's last choice. The elimination sequence then runs Full Monty on the first round, Good As It Gets on the second (1000 votes), Good Will Hunting on the third (1400 votes), and LA Confidential beats Titanic in the final round, 3800 to 2000. Lying in this case helps in choosing a Condorcet Winner, so that's a decent result, but it doesn't have to be the case.

Now it's true that the informational requirements for productive preference misrepresentation under the elimination ballot may generally be higher than under plurality, but we can easily imagine rules of thumb that wouldn't be too bad. If your top-ranked option is likely to lose, push it down your preference ordering; if your last-ranked option is likely to win, claim to love anything that other folks are likely also to support. Since everybody else is likely to be doing the same thing, things will be messy. But that's also true under plurality. While Titanic won by plurality in our example above, it also was very low in everyone else's preference orderings. Titanic fans could easily imagine the fourth group supporting As Good As It Gets to stop Titanic, in which case they could flip to LA Confidential and encourage Group 2 to do the same; in that case, it's folks preferring one of the "big two" who do better by lying.

It's because social choice gets so messy that I went to the data to tell me which system gave better results. I can't see much difference between them in terms of retrospective critical evaluation of film quality. Don't get your hopes up too high....


*Except for dictatorship of course, unless reasonable homunculi disagree...

Social Choice and the Oscars

Colby Cosh reports that the Academy of Motion Picture Arts and Sciences is switching from a first past the post ballot for best picture to single transferable vote. I like this, mostly because I go over that system in my public choice class and sometimes get asked if anybody in the real world uses the system. Now I'll be able to say "Well, the Oscars". That's more fun than saying "Well, the Australians".

Voters will rank order the ten nominated films. If any film has a majority of voters picking it as top choice, it's elected. If not, the film with the fewest first place votes is eliminated and that film's supporters are counted as voting for their second choice. Repeat until some film has majority support. Writes Cosh:

Even in the old five-nominee Oscar races, a winner in the single round of voting could conceivably win even though 25 or 30 per cent of the voters loved it and everybody else hated it. (This may have enabled some Best Picture wins later considered controversial, like that of Crash in 2005 or Shakespeare in Love in 1998.) In a 10-nominee field, a mere 15 per cent might be more than enough. The board of governors, mindful that preferential voting was used in 10-nominee Best Picture races from 1936 to 1943, decided to re-adopt the old prophylactic measure against unpopular winners.

It's possible that the old system was more manipulable: if you could get about a fifth of voters to agree on a common first choice, you could potentially get it through despite a majority hating the film. That doesn't worry me too much: I liked both Crash and Shakespeare in Love. What worries me more in the old system is a plurality of uncoordinated voters with mediocre tastes coordinating around some unimaginative Schelling point (Avatar!). So I'll expect fewer oddball good picks like Crash but also fewer lukewarm picks.

I am rather curious about Colby noting the change in voting system at 1943. It would be really neat to compare current evaluations of Oscar winners for the period before and after the change as a measure of which system did better in picking the films later viewed as being very good. Let's give it a shot. Wikipedia lists all the winners and nominees; IMDB and Rotten Tomatoes score the films. A quick flip through doesn't show a clear winner across the two systems, mostly because both fare horribly. I apologize for the table formatting below.

Year	Winner	Bested by (IMDB)	Bested by (Rotten Tomatoes)
1936	The Great Ziegfeld	Dodsworth, Libeled Lady, Mr. Deeds Goes to Town, San Francisco, The Story of Louis Pasteur, A Tale of Two Cities (6 of 9 other nominees)	Dodsworth, Libeled Lady, Mr. Deeds Goes to Town, Romeo and Juliet, San Francisco, A Tale of Two Cities (all rated nominees)
1937	The Life of Emile Zola	The Awful Truth, Captains Courageous, Dead End, The Good Earth, Lost Horizon, Stage Door, A Star is Born (7/9 other nominees)	As IMDB, 7/7 rated nominees
1938	You Can't Take It With You	The Adventures of Robin Hood (1/9 other nominees)	The Adventures of Robin Hood, Boys Town, Four Daughters, Grand Illusion, Jezebel (5/6 rated nominees)
1939	Gone With The Wind	Mr. Smith goes to Washington, The Wizard of Oz (2/9)	Ninotchka, Of Mice and Men, Stagecoach, The Wizard of Oz, Wuthering Heights (5/9)
1940	Rebecca	none	none, though many tie
1941	How Green Was My Valley	Citizen Kane, The Little Foxes, The Maltese Falcon, Sergeant York (4/9)	Citizen Kane, Here Comes Mr. Jordan, The Little Foxes, The Maltese Falcon, Suspicion (5/6 rated)
1942	Mrs. Miniver	Kings Row, The Magnificent Ambersons, Random Harvest, The Talk of the Town, Yankee Doodle Dandy (5/9)	As IMDB, and also 49th Parallel, The Pied Piper, The Pride of the Yankees, Wake Island (9/9: Every other film rates higher on Rotten Tomatoes)
1943	Casablanca	none	The More the Merrier (1/6 rated)
1944	Going My Way	Double Indemnity, Gaslight, Since You Went Away (3/4)	Double Indemnity, Gaslight (2/3 rated)
1945	The Lost Weekend	none	none
1946	The Best Years Of Our Lives	It's a Wonderful Life (1/4)	Henry V, The Yearling (2/4)
1947	Gentleman's Agreement	The Bishop's Wife, Crossfire, Great Expectations, Miracle on 34th Street (4/4)	Great Expectations, Miracle on 34th Street (2/4)
1948	Hamlet	The Red Shoes, The Treasure of the Sierra Madre(2/4)	As IMDB, 2/3 rated
1949	All the King's Men	The Heiress, Twelve O'Clock High (2/4)	Battleground, The Heiress, A Letter to Three Wives, Twelve O'Clock High (4/4)
1950	All About Eve	Sunset Boulevard (1/4)	none
1951	An American in Paris	Decision Before Dawn, A Place in the Sun, A Streetcar Named Desire (3/4)	None, though Streetcar ties

In the era of single transferable vote, the Academy picked the later-ranked best film once or twice depending on whether you take IMDB or Rotten Tomatoes ranking; it picked the worst ranked film three times according to Rotten Tomatoes. In the plurality era, it picked the best film once or thrice depending on the ranking and picked the worst film once according to Rotten Tomatoes. Under STV (using IMDB), 35% of nominees score higher than the winning film; that rises to 50% under plurality but the number of nominees drops considerably, and presumably the best nominees are kept. If we use IMDB to place the winning film in the top five nominated films, the winning film's position averages half way between third and fourth place under STV and slightly worse than third place under plurality. Both systems pick a film ranked better than the median of the top four other nominees three times in eight.

So it looks like the Academy picked about as many winners and dogs under both systems last time they ran the experiment and tend towards middling-ranked films. I was kinda hoping that there'd be interesting differences in results to report. There could have been a paper in it had there been. File it under dead ends, and post it so that anybody else that takes an interest can save himself the couple hours. Perhaps there's something in just how bad the Academy's choices are in later retrospect... "The invariance of bad Oscar picks to choice of voting system"...