Occasional reflections on Life, the World, and Mathematics

Archive for November, 2018

Social choice Brexit, 2: The survey

Last week I suggested that it could very well be that a second Brexit referendum would stumble into Arrow’s paradox, with Remain preferred to soft Brexit, soft Brexit preferred to no deal, and No Deal preferred to Remain. I wasn’t expecting rapid confirmation, but here it is, from a poll of about 1000 British adults:

Frustrated billionaire seeks new tax haven

“…but it reduces the chance of taxes”.

Pareto’s revenge

Several months ago I suggested that no one could ultimately support soft Brexit, because the soft Brexit strategy — something like EFTA, formally outside of the EU, but still in a customs union and/or the single market, still recognising most rights of EU citizens in the UK — is, to use a bit of economics game-theory jargon, Pareto dominated by staying in the EU. Even if the damage wrought by a no-deal Brexit would be vastly better worse by a negotiated surrender, if you look at it category by category — rights of UK citizens, disruption to markets, business flight, reputation, civil peace, diplomatic influence, sovereignty over market regulations — staying in the EU would be even better. There’s nothing you can point to and say, this is what we got for our trouble (which is why Theresa May was at such pains to bash immigrants when announcing her deal). We’ll always have Parisians.

Apparently, some other leading Brexiters are noticing their Pareto trap. Earlier in the week Dominic Raab resigned in protest that the deal (that he was responsible for negotiating himself!) was worse than staying in the EU. Today it’s Shanker Singham, leading trade adviser to the Leave campaign, who says “From a trade policy perspective this is a worse situation than being in the EU.” (Much of the Guardian article explains how this leading intellectual light of the Leave campaign has a mostly fake CV.)

The effect will be zero. The Brexit dead-enders only need to keep Parliament in turmoil and run out the clock, until their glorious Thelma & Louise consummation. I’m sure Jacob Rees-Mogg has shorted the pound, and the FTSE, so he’ll be fine. Would that count as insider trading?

Medical hype and under-hype

New heart treatment is biggest breakthrough since statins, scientists say

I just came across this breathless headline published in the Guardian from last year. On the one hand, this is just one study, the effect was barely statistically significant, and experience suggests a fairly high likelihood that this will ultimately have no effect on general medical practice or on human health and mortality rates. I understand the exigencies of the daily newspaper publishing model, but it’s problematic that the “new research study” has been defined as the event on which to hang a headline. The only people who need that level of up-to-the-minute detail are those professionally involved in winnowing out the new ideas and turning them into clinical practice. We would all be better served if newspapers instead reported on what new treatments have actually had an effect over the last five years. That would be just as novel to the general readership, and far less erratic.

On the other hand, I want to comment on one point of what I see as exaggerated skepticism: The paragraph that summarises the study results says

For patients who received the canakinumab injections the team reported a 15% reduction in the risk of a cardiovascular event, including fatal and non-fatal heart attacks and strokes. Also, the need for expensive interventional procedures, such as bypass surgery and inserting stents, was cut by more than 30%. There was no overall difference in death rates between patients on canakinumab and those given placebo injections, and the drug did not change cholesterol levels.

There is then a quote:

Prof Martin Bennett, a cardiologist from Cambridge who was not involved in the study, said the trial results were an important advance in understanding why heart attacks happen. But, he said, he had concerns about the side effects, the high cost of the drug and the fact that death rates were not better in those given the drug.

In principle, I think this is a good thing. There are far too many studies that show a treatment scraping out a barely significant reduction in mortality due to one cause, which is highlighted, but a countervailing mortality increase due to other causes, netting out to essentially no improvement. Then you have to say, we really should be aiming to reduce mortality, not to reduce a cause of mortality. (I remember many years ago, a few years after the US started raising the age for purchasing alcohol to 21, reading of a study that was heralded as showing the success of this approach, having found that the number of traffic fatalities attributed to alcohol had decreased substantially. Unfortunately, the number of fatalities not attributed to alcohol had increased by a similar amount, suggesting that some amount of recategorisation was going on.) Sometimes researchers will try to distract attention from a null result for mortality by pointing to a secondary endpoint — improved results on a blood test linked to mortality, for instance — which needs to be viewed with some suspicion.

In this case, though, I think the skepticism is unwarranted. There is no doubt that before the study the researchers would have predicted reduction in mortality from cardiovascular causes, no reduction due to any other cause, and likely an increase due to infection. The worry would be that the increase due to infection — or to some unanticipated side effect — would outweigh the benefits.

The results confirmed the best-case predictions. Cardiovascular mortality was reduced — possibly a lot, possibly only slightly. Deaths due to infections increased significantly in percentage terms, but the numbers were small relative to the cardiovascular improvements. The one big surprise was a very substantial reduction in cancer mortality. The researchers are open about not having predicted this, and not having a clear explanation. In such a case, it would be wrong to put much weight on the statistical “significance”, because it is impossible to quantify the class of hypotheses that are implicitly being ignored. The proper thing is to highlight this observation for further research, as they have properly done.

When you deduct these three groups of causes — cardiovascular, infections, cancer — you are left with approximately equal mortality rates in the placebo and treatment groups, as expected. So there is no reason to be “concerned” that overall mortality was not improved in those receiving the drug. First of all, overall mortality was better in the treatment group. It’s just that the improvement in CV mortality — as predicted — while large enough to be clearly not random when compared with the overall number of CV deaths, it was not large compared with the much larger total number of deaths. This is no more “concerning” than it would be, when reviewing a programme for improving airline safety, to discover that it did not appreciably change the total number of transportation-related fatalities.

Fantasy queues

Reviving the spirit of the Blitz! Food queues in wartime London.

On moving to the UK almost a dozen years ago I quickly noticed that the one thing that unites the political establishment, left and right, is that they don’t like foreigners. Or rather, maybe better phrased, they may personally like and even admire some foreigners, but they recognise that such exotic tastes are not for everyone, and that disliking foreigners is a valuable national pastime, deserving of their official support.

And so, after claiming through the Brexit campaign that it was all about national sovereignty and repatriating billions of pounds for the NHS, and having spent the better part of two years diplomatically digging a grave for the national future, the Tories strike on bedrock: We have betrayed national sovereignty and destroyed the national economy, but it’s all worth it because we still get to kick out the foreigners. Or, in the prime minister’s words:

“Getting back full control of our borders is an issue of great importance to the British people,” she will say, adding that EU citizens will no longer be able to “jump the queue ahead of engineers from Sydney or software developers from Delhi”.

I’m willing to go out on a limb here and suggest that the subset of British — or, given their current fragile mental state, I should perhaps call them Brittle — voters who voted Leave with the thought uppermost in their minds of improving the prospects for Indians to migrate to the UK was… less than a majority. But even more striking, EU citizens who moved to the UK over the past 40 years, following the same agreements that allowed Brittle people to seek work and better lives anywhere on the Continent, are retrospectively branded as “queue jumpers”, the most rebarbative class in the English moral order. Theresa May is summoning her countrymen and -women to defend a fantasy queue.

In the 1990s the German media teemed with entreaties to tear down the Mauer im Kopf, the “mental wall” (a phrase of the author Peter Schneider that actually long preceded the fall of the physical wall in Berlin), as a necessary prelude to a stable national identity, and a democratic and prosperous future. Maybe the Brittles need to dissolve their fantasy queues, to break up the Schlange im Kopf, before they can start building a new nation on the rubble they are making of their past.

A missed opportunity in metrology

The international community has responded to the shrinking of le Grand K by deciding to redefine the kilogram without reference to a standard artifact. As I pointed out here, the decision to preserve the kilogram at exactly the same mass squanders a rare opportunity for the metrologists to contribute to public health:

Just a 10% increase in the size of the kilogram  — easily achievable with current technology, and barely even noticeable to the casual observer — would produce a 9% reduction in BMI, and thus reduce the number of obese Britons and the attendant costs by more than half. This approach is found to be vastly cheaper than the next most cost effective plan for reducing obesity, a complicated scheme which involves citizens exercising more and eating less junk.

As I further point out, the international metrologists could learn from the UK Department of Education, which has been much more proactive in providing low-cost improvements through creative control of measurement.

On the other hand, as I’ve pointed out here, the benefits of reducing BMI may be overstated…

Social choice Brexit

The discussion over a possible second Brexit referendum has foundered on the shoals of complexity: If the public were only offered May’s deal or no deal, that wouldn’t be any kind of meaningful choice (and it’s absurd to imagine that a Parliament that wouldn’t approve May’s deal on its own would be willing to vote for the fate of Brexit to be decided by the public on those terms. So you’re left with needing an unconventional referendum with at least three options: No deal, May’s deal, No Brexit (plus possible additional alternatives, like, request more time to negotiate the Better Deal™).

A three-choice (or more) referendum strikes many people as crazy. There are reasonable concerns. Some members of the public will inevitably find it confusing, however it is formulated and adjudicated. And the impossibility of aggregating opinions consistent with basic principles of fairness, not even to say in a canonical way, is a foundational theorem of social-choice theory (due to Kenneth Arrow).

Suppose we followed the popular transferable vote procedure: People rank the options, and we look only at the first choices. Whichever option gets the smallest number of first-choice votes is dropped, and we proceed with the remaining options, until one option has a first-choice majority. The classic paradoxical situation is all too likely in this setting. Suppose the population consists of

  1. 25% hardened brexiteers. They prefer a no-deal Brexit, but the last thing they want is to be blamed for May’s deal, which leaves the UK taking orders from Brussels with no say in them. If they can’t have their clean break from Brussels, they’d rather go back to the status quo ante and moan about how their beautiful Brexit was betrayed.
  2. 35% principled democrats. They’re nervous about the consequences of Brexit, so they’d prefer May’s soft deal, whatever it’s problems. But if they can’t have that, they think the original referendum needs to be respected, so their second choice is no deal Brexit.
  3. 40% squishy europhiles. They want no Brexit, barring that they’d prefer the May deal. No-deal Brexit for them is the worst.

The result will be that no deal drops out, and we’re left with 65% favouring no Brexit. But if the PDs anticipated this, they could have ranked no deal first, producing a result that they would have preferred.

So, that seems like a problem with a three-choice referendum. But here’s a proposal that would be even worse: We combine choices 2 and 3 into a single choice, which we simply call “Leave”. Then those who wants to abandon the European project entirely will be voting for the same option as those who are concerned about the EU being dominated by moneyed interests, and they’ll jointly win the referendum and then have to fight among themselves after the fact, leaving them with the outcome — no-deal Brexit — that the smallest minority preferred.

Unfortunately, that’s the referendum we actually had.

Schrödinger’s menu

I was just rereading Erwin Schrödinger’s pathbreaking 1944 lectures What is Life? which is often praised for its prescience — and influence — on the foundational principals of genetics in the second half of the twentieth century. At one point, in developing the crucial importance of his concept of negative entropy as the driver of life,  he remarked on the misunderstanding that “energy” is what organisms draw from their food. In an ironic aside he says

In some very advanced country (I don’t remember whether it was Germany or the U.S.A. or both) you could find menu cards in restaurants indicating, in addition to the price, the energy content of every dish.

Also prescient!

How odd that the only biological organisms that Schrödinger is today commonly associated with are cats…

FDA sample menu with energy content

Brexit deal still halfway concluded!

I cited this joke in the context of Brexit before:

A rabbi announces in synagogue, at the end of Yom Kippur, that he despairs at the burning need for wealth to be shared more equally. He will depart for the next year to travel through the world, speaking to all manner of people, ultimately to persuade the rich to share with the poor. On the following Yom Kippur he returns, takes his place at the head of the congregation without a word, and leads the service. At the end of the day congregants gather around him. “Rabbi, have you accomplished your goal? Will the rich now share with the poor?” And he says, “Halfway. The poor are willing to accept.”

And it’s returned, because we again have these headlines:

Except the backing of the “cabinet” means the backing of those who didn’t resign because they wouldn’t back the agreement. Including the Northern Ireland Secretary (!) and the Brexit Secretary (!!) who was tasked with negotiating the thing. So, except for all the members most relevant to the deal (oh, yes, the Foreign Secretary already resigned over Brexit a few months ago), Theresa May has managed to get her handpicked cabinet to accept the negotiated agreement. All that remains is the other half of the task, which is to get it through Parliament, which only requires that she corral votes from her coalition partner, who see the backstop on Northern Ireland as a fundamental betrayal, and sufficient members of the opposition parties, because why wouldn’t they sign up to take responsibility for an agreement that everyone will blame for everything that goes wrong, even if nothing goes wrong, rather than forcing new elections?

The Silver Standard 4: Reconsideration

After writing in praise of the honesty and accuracy of fivethirtyeight’s results, I felt uncomfortable about the asymmetry in the way I’d treated Democrats and Republicans in the evaluation. In the plots I made, low-probability Democratic predictions that went wrong pop out on the left-hand side, whereas low-probability Republican predictions  that went wrong would get buried in the smooth glide down to zero on the right-hand side. So I decided, what I’m really interested in are all low-probability predictions, and I should treat them symmetrically.

For each district there is a predicted loser (PL), with probability smaller than 1/2. In about one third of the districts the PL was assigned a probability of 0. The expected number of PLs (EPL) who would win is simply the sum of all the predicted win probabilities that are smaller than 1/2. (Where multiple candidates from the same party are in the race, I’ve combined them.) The 538 EPL was 21.85. The actual number of winning PLs was 13.

What I am testing is whether 538 made enough wrong predictions. This is the opposite of the usual evaluation, which gives points for getting predictions right. But when measured by their own predictions, the number of districts that went the opposite of the way they said was a lot lower than they said it would be. That is prima facie evidence that the PL win probabilities were being padded somewhat. To be more precise, under the 538 model the number of winning PLs should be approximately Poisson distributed with parameter 21.85, meaning that the probability of only 13 PLs winning is 0.030. Which is kind of low, but still pretty impressive, given all the complications of the prediction game.

Below I show plots of the errors for various scenarios, measuring the cumulative error for these symmetric low predictions. (I’ve added an “Extra Tarnished” scenario, with the transformation based on the even more extreme beta(.25,.25).) I show it first without adjusting for the total number of predicted winning PLs:

image

We see that tarnished predictions predict a lot more PL victories than we actually see. The actual predictions are just slightly more than you should expect, but suspiciously one-sided — that is, all in the direction of over predicting PL victories, consistent with padding the margins slightly, erring in the direction of claiming uncertainty.

And here is an image more like the ones I had before, where all the predictions are normalised to correspond to the same number of predicted wins:

TarnishedSymmetric

 

Tag Cloud