Derren Brown, the illusionist, is no stranger to the use of the idea of the wisdom of crowds as part of his entertainment package. A few years ago, for example, he selected a group of people and asked them to estimate how many sweets were in a jar.
All conventional ‘wisdom of crowds’ stuff, albeit wrapped as part of a magical mystery tour. His relatively more recent venture into this world of apparent wisdom went down a rather singular avenue, however, as he explained how a group of 24 people could predict the winning Lottery numbers with uncanny accuracy.
The idea in essence was that each of the 24 would make a guess about the number on each ball and the average of each of these guesses would converge on the next set of winning numbers. It appeared to work – but that is the thing about illusionists; they are good at producing illusions.
I will not go into how he did generate the effect of predicting the lottery draw, because there is no point if you already know, and because it would spoil the fun if you don’t. What is sure, however, is that the musings of the crowd had nothing to do with it.
But why not? After all, if the crowd can accurately guess the weight of an ox or the number of jelly beans in a jar, why not the numbers on the lottery balls? The simple answer, of course, is because the lottery balls are drawn randomly. And the thing about random events is that they are unpredictable. This is at the heart of what economists term ‘weak form market efficiency’, i.e. that future movements in market prices cannot be predicted from past movements. In this sense, the series has no memory.
So what is likely to happen if you do get a group of friends around and ask each to guess the number that will appear on each of the balls drawn next Saturday? If you take the average of the guesses about each in turn, my best estimate is that you are likely to end up with a prediction for each ball that is about 30 or less. Why so? Partly this is because people tend to pick birthdays but it’s also because the averaging of a large number of guesses is likely to produce a number somewhere nearer the mid-point of the set of numbers than the extremes.
But if you do use these numbers and just happen to win, you’re likely to be sharing your winnings with a lot of other people who’ve chosen the same numbers as you. The better strategy is to populate your ticket with bigger numbers, which are likely to be less popular.
This strategy won’t alter your chance of winning but it will increase how much you can expect to win if you do win. And that is no illusion!
When asked to list my all-time heroes, the name of William of Ockham (or Occam) is never far from my lips. Born in the late 13th century, in the Surrey village of Ockham, this Franciscan philosopher, theologian and political writer, is generally considered to be one of the major figures in medieval scholarship.
In this regard, he ranks alongside the likes of his fellow theologians Thomas Aquinas and John Duns Scotus in the pantheon of great pre-Renaissance thinkers. Despite the title he earned at Oxford University of Venerabilis Inceptor (‘Worthy Beginner’) it is therefore by his alternative title of Doctor Invincibilis (‘Unconquerable Doctor’) that he comes down to us. Of all his writings, and they are each worthy of separate study, it is for his principle of parsimony in explanation and theory-building that he is best known today. It is a principle that Fox Mulder refers to in an episode of the X-files and that Jodie Foster defers to in ‘Contact’. Indeed, in William Peter Blatty’s novel, Legion (on which ‘The Exorcist III’ is based), the lead character complains that he was not put on earth “to sell William of Occam door to door.” He needn’t have bothered. William of Ockham sells himself well enough without help, through the principle that is known as ‘Occam’s Razor.’
The Razor is perhaps most clearly defined in Encyclopedia Britannica’s Student edition, where it is taken as an admonishment to devise no more explanations than necessary for any given situation. Put another way, it advises that one should opt for explanations in terms of the fewest possible number of causes, factors or variables. The adults’ version of Encyclopedia Britannica puts it more elegantly, but perhaps less clearly, in these terms – ‘Pluritas non est ponenda sine necessitate’ (‘Plurality should not be posited without necessity’). As such, the principle can be interpreted as giving precedence to simplicity; of two competing theories, the simplest explanation of an entity is to be preferred. There are some higher truths, which may be known to us by experience or revelation, and which Ockham witnesses as necessary rather than contingent entities, to which we are not advised to apply the razor. This is a part of Ockham’s trenchant analysis which is often forgotten, but at least need not concern us when considering the theme of today’s article.
So how do modern-day analysts stand on the shoulders of this medieval giant? The best explanation is perhaps by way of example, and for this we need to travel to the Hong Kong racetrack and to the professional gamblers who devise sophisticated forecasting models of the outcomes of the races run at the Sha Tin and Happy Valley tracks. The basic methodology is to identify each individual factor that could possibly predict the outcome. And what do you do then? How do you decide what to include and what not? For the answer I asked a man who has conservatively made tens of millions of dollars at the track from this very approach. As we enjoyed the view from his Sydney penthouse, he summed it up in a sentence. “I apply Occam’s Razor”, he said, “it really is as simple as that!”
Now say that you have a missing aircraft, and the number of explanations are seeming to grow by the minute. What should we do? Apply Occam’s Razor, of course. And see what we get.
I was once told a story about the value of crowd wisdom in turning up buried treasure. The story was that by asking a host of people, each with a little knowledge of ships, sailing and the sea, where a vessel is likely to have sunk in years gone by, it is possible with astonishing accuracy to pinpoint the wreck and the bounty within. Individually, each of those contributing a guess as to the location is limited to their special knowledge, whether of winds or tides or surf or sailors, but the idea is that together their combined wisdom (arrived at by averaging their guesses) could pinpoint the treasure more accurately than a range of other predictive tools. At least that’s the way it was told to me by an economist who was in turn told the story by a physicist friend. To any advocate of the power of prediction markets, this certainly sounds plausible, so I decided to investigate further. Soon I was getting acquainted with the fascinating tale of the submarine USS Scorpion, as related by Mark Rubinstein, Professor of Applied Investment Analysis at the University of California at Berkeley. In a fascinating paper titled, ‘Rational Markets? Yes or No? The Affirmative Case’, he tells of a story related in a book called ‘Blind Man’s Bluff: The Untold Story of American Submarine Espionage’ by Sherry Sontag and Christopher Drew. The book tells how on the afternoon of May 27, 1968, the submarine USS Scorpion was declared missing with all 99 men aboard. It was known that she must be lost at some point below the surface of the Atlantic Ocean within a circle 20 miles wide. This information was of some help, of course, but not enough to determine even five months later where she could actually be found. The Navy had all but given up hope of finding the submarine when John Craven, who was their top deep-water scientist, came up with a plan which pre-dated the explosion of interest in prediction markets by decades. He simply turned to a group of submarine and salvage experts and asked them to bet on the probabilities of what could have happened. Taking an average of their responses, he was able to identify the location of the missing vessel to within a furlong (220 yards) of its actual location. The sub was found. Sontag and Drew also relate the story of how the Navy located a live hydrogen bomb lost by the Air Force. Now this story has got me thinking. Let’s just say we are looking for a missing aircraft. Could prediction markets possibly help? It’s a question I’m currently asking myself. Maybe others should be as well!
Arbitrage is the practice of making a risk-free profit by taking advantage of a price differential between two or more markets. For example, if it is possible to BUY the number of corners in a soccer match at 10 with one odds-maker (so that a profit is obtained for every corner in excess of ten) and to SELL the number of corners at 11 with another odds-maker, a profit will accrue whatever the actual number of corner kicks taken. Such examples of free money are in short supply, however, and a more realistic trading approach may be to employ what I first proposed and termed in 2000 as a ‘quasi-arbitrage’ or ‘Quarb’ strategy. The assumption underpinning this Quarb strategy is straightforward. It is that the average market opinion (where there is a range of opinions) is a better indicator of the truth than the outlier (or ‘maverick’) opinion. Take that number of corner kicks as an example. If there are four market-makers, say, three of which offer clients the chance to BUY at 10 and SELL at 11 and the fourth which allows you to BUY at 11 and SELL at 12, the average market price is the sum of the mid-points (10.5+10.5+10.5+11.5) divided by four, i.e. 10.75. If we take this to be the best estimate of the actual expected value of the outcome, a SELL at the ‘maverick’ price of 11 is a value bet. In other words, the ‘Quarb’ strategy advocates the aggregation and averaging of the range of forecasts, implied in the odds on offer from professional odds-makers, to identify the best possible forecast of the actual outcome.
PollyVote (www.pollyvote.com) is an election forecasting site which follows this principle of combining forecasts. By aggregating the vote-share snapshot contained in traditional opinion polls with a panel of American politics experts, a prediction market and a range of quantitative forecasting models, Polly provides a daily updated forecast of the share of the two-party vote that the Democratic and Republican Presidential candidates will obtain on polling day. For their polling input they use a variation of the RealClearPolitics average and for their prediction market they use the Iowa Electronic Markets, a research and teaching-oriented marketplace which allows small bets on a range of contracts including the Presidential vote-share. The panel is made up of respected political scientists and pundits and the quantitative models (based on an analysis of the likely impact of variables ranging from unemployment and inflation to incumbency and wars) draw on an array of different methodologies. Each of these forecasts is assigned an equal 25% weight and in 2004 generated an almost spot-on forecast of the actual respective vote shares.
Is the RealClearPolitics average the best baseline to use for aggregating the polls? Is the Iowa market the best choice of prediction market? Is the chosen panel and the way its views are aggregated the best way to assimilate the combined knowledge of the political intelligentsia? Is the range of forecasting models appropriate? Does the averaging of the four methodologies perform better than any one alternative forecasting methodology?
This debate will continue, and has been informed by how well Polly has performed over the elections from 2004 to 2012 in forecasting the vote shares of the candidates. The answer is very well indeed. In 2016 things went very wrong, but this was not the fault of the combining methodology but rather that all the separate methodologies failed. Having been fed the wrong food, the parrot suddenly got very sick. Time will tell whether it was a short illness or a harbinger of things to come.
The conventional wisdom for the last several days is that the betting markets are pointing to the re-election of the President while the polls apparently have it too close to call, or have Mitt Romney as the narrow favourite.
So what’s the evidence?
Certainly, a glance at the betting markets reveals a pretty strong consensus that President Obama has a strong edge with the bookmakers, the spread betting operators and the betting exchange, Betfair.com, each of these currently converging at a probability of re-election of about 75%. Intrade.com has it a bit lower, but still make President Obama the very clear favourite.
So what about the opinion polls? Here the idea that Mr. Romney is ahead is in great part derived from an inspection of the headline national poll findings published on the RealClearPolitics.com (RCP) web-site. RCP publish a selection of the latest polls and take an average of this selection to come up with their overall figure. This average had Romney leading by up to a point or so over the last few days, and currently has it about tied.
But is this what the opinion polls are actually showing? The answer depends on whether you look at all the published polls, as broadly available on Pollster, or whether you exclude the polls you don’t favour, a methodology favoured by RCP. Not only do they not include a number of these polls in their overall average, they do not recognize them at all!
Taking average of all the national polls still has it close, but close in the President’s favour.
More important than the national picture, as Al Gore found to his cost, are the state findings. An analysis of all the state polls shows that President Obama is rather more comfortably ahead, including in the key swing states of Ohio, Virginia, Wisconsin, Colorado, Iowa, Nevada and New Hampshire.
Combining the national and state polls, and awarding them a similar weighting, reveals Mr. Obama to be polling close to 2.5% ahead of Mr. Romney – more in the state polls and less in the national polls.
Depending on the statistical analysis used to convert polling advantage into probability of winning, current polling evidence would seem to give the President somewhere above an 8 in 10 chance of winning (based on national and state polls) to rather more than a 90% chance (based on the state polls alone). FiveThirtyEight.com and the Princeton Election Consortium (http://election.princeton.edu/) represent good examples of this sort of analysis.
So the betting markets, contrary to conventional wisdom, are in fact more conservative in their evaluation of Mr. Obama’s chances than are the polls.
Why so?
There are a number of possibilities, but I will highlight three of them.
First is the well-established favourite-longshot bias which occurs in most betting markets, whereby the markets tend to under-estimate the true likelihood of the favourite winning, and vice-versa.
Secondly, the markets may be allowing for the uncertainties a model can’t allow for them, such as some late surprise. The point is that volatility is the friend of the underdog, and the enemy of the favourite.
Thirdly, the markets may be wary that one of the outlier polling organisations might just possibly be right, and the overwhelming polling consensus might just possibly be wrong. This is what I call the ‘Rasmussen effect’, after the polling company that seems to have leaned Republican by a few points in its national and state polling for some time now (http://www.huffingtonpost.com/alan-abramowitz/the-rasmussen-difference_b_2030330.html?utm_hp_ref=@pollster.This) effect was particularly prominent in the 2010 elections (http://fivethirtyeight.blogs.nytimes.com/2010/11/04/rasmussen-polls-were-biased-and-inaccurate-quinnipiac-surveyusa-performed-strongly/), and this is the pollster that had Mr. Bush leading by nine per cent on election day, 2000, as evidenced by the National Council on Public Polling (http://www.ncpp.org/?q=node/20). That was about ten points out!
If Rasmussen is right, though, the race is very tight in the key states and Obama would be much less of a favourite than the polling consensus suggests.
So Rasmussen must be right and the other polls wrong, and Obama must lose Ohio, which Rasmussen is calling a pure toss-up, and he must not win elsewhere to compensate. All other routes are regarded as far more unlikely by the markets, though by no means impossible.
So what is the most likely outcome of this election? However you cut the data, the answer is the same. It’s a win for the President.
Polls don’t decide elections, however, and neither do the betting markets. People do, and that’s why anything can happen, and sometimes does!
When even a CNN poll, composed of a sample of debate watchers they freely admit to be eight per cent more Republican than the country as a whole, hands the debate to President Obama by seven percentage points, you know that Governor Romney has taken something of a beating. The win was also recorded by CNN’s focus group of uncommitted voters in Ohio, and was confirmed by the consensus of other instant polling, notably from Survey USA, CBS News, Battleground, Google Consumer Surveys and Public Policy Polling (PPP). The most interesting of these polls is perhaps the PPP survey of independents watching the debate in the swing state of Colorado. By 58% to 36%, these voters named Obama the winner.
Those who prefer to track the debate through the online betting markets, such as Betfair and Intrade, saw things no differently, as a flood of money came for the President through the course of the debate. Betfair traders piled their money into backing the re-election of the President, while Intrade ran a market exclusively on who would win the debate, deferring to the CNN instant poll as the final arbiter. The latter market started out marginally favouring Mr. Obama but soon attracted a growing tide of support for the incumbent, until by the end of the debate the odds implied a probability of an Obama win of more than 90%. Brave traders indeed, trusting to a CNN poll which had already heavily over-sampled Republicans in the Vice-Presidential debate. Either they were pretty sure that the President had won so handsomely that he could overcome a potential repeat skew, or they were unaware of it. Whatever the reasoning, the market got it right.
According to this evidence, Mitt Romney not only lost the second Presidential debate, he was bludgeoned out of it.
But will it make a difference to the election outcome?
For the answer to this we can turn to those all-important fluctuating price lines which represent the probability that one candidate or other will take the White House.
Interestingly, it was such a price line that signalled, during the first of the UK Prime Ministerial debates in 2010, the impending disappearance of the Conservative Party’s hopes of winning an overall majority in that year’s General Election. David Cameron’s performance in that debate mirrored perceptions of Barack Obama’s performance in the first of this year’s Presidential debates. Cameron’s performance in the second debate was substantially better, mirroring again Obama’s performance in his second debate.
Does this tell us something? The Conservative leader’s first debate flop almost certainly cost his party an overall majority in the House of Commons. His second debate performance helped him to Downing Street at the head of a coalition government. So are there any parallels we can draw for the US election?
In one sense, the parallels are limited because the US Presidential election is winner-takes-all. But there is another sense in which a parallel does exist. If we consider control of the Senate and House of Representatives as being in some degree linked to the performance and popularity of the President, what is sometimes called the ‘coattail’ effect, we might just have witnessed a performance outstanding enough in the context of the two debates to hand the White House and Senate to the Democrats, but perhaps not enough for a full sweep of Congress.
Is this the way it will eventually turn out?
We shall see!
A pretty good way of finding out where things stand during the course of any event on which money is traded is to track the state of the in-play markets, and in particular the betting exchanges like Betfair. This is a particularly useful guide when it is not always easy to gauge all the variables, such as in Formula 1 racing, where there are pit stops, tyre degradation, in-race penalties and so much more to factor in. So when I watch a race led on the track by Lewis Hamilton in the McLaren but led in the markets by Fernando Alonso, it is to the Spaniard in the Ferrari that I will look to take the chequered flag.
It’s pretty much the same in a Presidential or Vice-Presidential debate, when the analysis of all those who are willing to venture their money to support their judgement comes together in the shape of a market price or prices. These fluctuating price lines represent variables such as the probability that one or other party will take the White House.
It was such a price line that, during the first ever UK Prime Ministerial debate in 2010, alerted analysts to the end of the Conservatives’ hopes of winning an overall majority in that year’s General Election. Before that debate, the likelihood of an overall Tory majority was significant. After the unexpectedly good performance in that debate by Liberal Democrat leader, Nick Clegg, and the unexpectedly bad performance of Conservative David Cameron, it was not. So much for those who say that debates don’t matter!
So what can we learn from the in-running markets about the debate between Vice-President Joe Biden and Congressman Paul Ryan? It is in fact possible to visualize the shape a contest is taking by simply following the flows of money tracing their way through the relevant markets. Interpreting the patterns of price lines to paint a picture is more science than art, but in truth it is a bit of both.
So what picture did the markets paint? It was a picture of the sort you would expect in a boxing match, when one boxer broadly dominates a round, with a mixture of penetrating jabs and controlled hooks, while his opponent blocks and parries to good effect, preparing to regroup in the next round. In this picture, it is the Vice-President throwing the telling blows and the Congressman adopting the well-rehearsed defensive stance.
And then it came to the judges to score the round. One of the judges was CBS News, whose poll of undecided voters gave the round decisively to Vice-President Biden by 50 points to 31. The other was CNN, whose poll of debate watchers appeared to give the edge to Mr. Ryan by 48 points to 44. Only later did we learn that the CNN scorecard had been tampered with, courtesy of a sizeable over-sampling of Republicans. By then, though, the narrative had been re-defined. The referee called it a draw, and the markets settled down again to where they were before the bell had sounded for the round to begin.
Professor Leighton Vaughan Williams 