The British Prime Minister Benjamin Disraeli is famously reputed to have said that statistics were worse than 'lies' or even 'damned lies'. That said, most modern politicians and journalists know that opinion polls can prove remarkably accurate indicators of how an election will play out.
The problem with polls is how they can often be misrepresented. Take the example of a journalist who writes that the White House race is 'tightening' because Obama's lead over McCain is (say) 50-44, when last week it was (say) 52-44. In fact, such numbers are often what pollsters dub 'statistical noise' - normal variation in how well a sample will represent the population it is taken from.
Most polls have a 'sampling error' of around 3 points (plus or minus). This means that if a poll shows Obama on 50 percent and McCain on 44 percent, the Democrat likely has the support of between 47-53 percent of voters, and the Republican the support of around 41-47 percent.
An eager McCain supporter might point out then that, according to these figures, his candidate might have as much as 47% and Obama as little as 47% - making the race a virtual tie. Yes, but the 47-47 split is only one possible outcome, according to the above figures, among many others:
Obama 47 - McCain 47
Obama 47 - McCain 46
Obama 47 - McCain 45
Obama 47 - McCain 44
Obama 47 - McCain 43
Obama 47 - McCain 42
Obama 47 - McCain 41
We could reproduce the same table above with Obama on 48, compared to McCain's 47, 46, 45, 44, 43, 42, or 41 percent share. And again with Obama on 49, or 50, or 51, or 52 or 53 percent. Taken all together, of the 49 possible combinations McCain ties Obama in just 1 and is behind in the other 48. Worse for the McCain supporter, 21 of the 49 possible combinations have McCain's deficit at even greater than 6 percentage points. In 39 of the 49 combinations, Obama still leads by at least 4 points.
McCain really might be neck-and-neck with Obama (47%-47%), but he could also really be as much as twelve points behind (53%-41%). The fact that the real figure is probably somewhere between these two extremes is not going to be any comfort for Republicans.
Tuesday, October 28, 2008
Monday, October 27, 2008
Photos from Stockholm
Just returned from a flying visit to Sweden to help promote the Swedish edition of 'Born On A Blue Day' (Född en blå dag). Above is a photo from my interview for the morning programme 'Efter Tio Med Malou' (After Ten With Malou), which was a lot of fun. The other guest was from France, so we chatted afterwards in French.
The weather in Stockholm was predictably cold, so I had to wrap up warm for the photographers needing outside shots like the one above:
The city's library was wonderful to visit. Built in 1928 and constructed with round, red walls it looks rather like a lighthouse! If you look hard enough in the photo above, you'll see me walking among its shelves.
For any Swedes reading this: Du kan finna mer information om boken och köpa den på: http://www.nok.se/nok/allmanlitteratur/titlar-allmanlitt/f/Fodd-en-bla-dag-ISBN-9789127100053/
Friday, October 17, 2008
The Probability of an Obama Victory
An excellent statistical guide to the election's ongoing state-of-play is the website 'fivethirtyeight.com' - http://www.fivethirtyeight.com/ According to its latest calculation, the probability of an Obama victory is 94.7%, compared to just 5.3% for McCain.
There's an important qualification to make here, though: the percentages above are equivalent to predicting what would happen were there 1,000 elections held simultaneously on Election Day - Obama would win around 947 of them, and McCain just 53. But here's the thing: there aren't going to be a thousand elections on November 4th, just one. McCain's hope will be that one of those 53 possible combinations comes up for him on the day.
For Obama supporters then, the key will be voter turnout - ensuring that the swing states that are leaning his way at present go for him on election day, when the polls really count.
There's an important qualification to make here, though: the percentages above are equivalent to predicting what would happen were there 1,000 elections held simultaneously on Election Day - Obama would win around 947 of them, and McCain just 53. But here's the thing: there aren't going to be a thousand elections on November 4th, just one. McCain's hope will be that one of those 53 possible combinations comes up for him on the day.
For Obama supporters then, the key will be voter turnout - ensuring that the swing states that are leaning his way at present go for him on election day, when the polls really count.
Wednesday, October 15, 2008
Is John McCain Too Old To Be President?
Like many people outside the United States, I've been following this year's presidential race with considerable interest. The 2008 election is shaping up to be one of the most fascinating and important in history. I'll be sharing my perspective of some of the contest's key issues from a mathematical point of view in a series of pieces here up to Election Day on November 4th. Feel free to leave your own thoughts and comments!
One of the biggest points of debate so far in this election has been the issue of age - the Republican candidate John McCain is 72 years old; a victory in November would make him the oldest man ever elected to the office of President of the United States.
Some commentators argue that McCain is too old to be running for President. They point to actuarial tables which suggest that a 72-year American male has a 1 in 3 chance of dying in the next 8 years (the period that McCain would serve as President were he to be re-elected). The same tables suggest he has a 1 in 7 chance of dying before finishing a single term in office.
But the argument doesn't quite add up. For one thing, actuarial tables are used to estimate the average lifetime of large groups of people, but are lousy at foretelling how long any one person in particular might live.
For another, McCain is hardly an average 72 year old - after all, most septuagenarians don't have full-time, top-level political careers.
In fact, McCain's longevity prospects look pretty good. His mother, Roberta, is still active at 96, as is his aunt of the same age (Roberta's twin sister). His maternal grandfather, Archibald Wright, also lived well into his nineties.
A final note: Modern presidential candidates (from the 1930s on) appear on the whole to have above-average lifespans. Presidents Gerald Ford and Ronald Reagan both lived to 93, while Herbert Hoover also reached his 90th birthday and Harry Truman lived to 88. Presidents Jimmy Carter and George H. W. Bush are both still active at 84.
Presidential runners-up fare well too: the 1972 Democrat nominee George McGovern is 86, while the party's 1984 nominee Walter Mondale celebrated his 80th birthday this year. The 1996 Republican nominee Bob Dole is now 85, while the Republicans' 1964 candidate Barry Goldwater lived to 89. The longevity prize, however, goes to the Republican's 1936 candidate, Alf Landon, who died a month after his 100th birthday in 1987.
In conclusion: There may be all kinds of reasons to oppose a McCain victory in November, but age isn't one of them.
One of the biggest points of debate so far in this election has been the issue of age - the Republican candidate John McCain is 72 years old; a victory in November would make him the oldest man ever elected to the office of President of the United States.
Some commentators argue that McCain is too old to be running for President. They point to actuarial tables which suggest that a 72-year American male has a 1 in 3 chance of dying in the next 8 years (the period that McCain would serve as President were he to be re-elected). The same tables suggest he has a 1 in 7 chance of dying before finishing a single term in office.
But the argument doesn't quite add up. For one thing, actuarial tables are used to estimate the average lifetime of large groups of people, but are lousy at foretelling how long any one person in particular might live.
For another, McCain is hardly an average 72 year old - after all, most septuagenarians don't have full-time, top-level political careers.
In fact, McCain's longevity prospects look pretty good. His mother, Roberta, is still active at 96, as is his aunt of the same age (Roberta's twin sister). His maternal grandfather, Archibald Wright, also lived well into his nineties.
A final note: Modern presidential candidates (from the 1930s on) appear on the whole to have above-average lifespans. Presidents Gerald Ford and Ronald Reagan both lived to 93, while Herbert Hoover also reached his 90th birthday and Harry Truman lived to 88. Presidents Jimmy Carter and George H. W. Bush are both still active at 84.
Presidential runners-up fare well too: the 1972 Democrat nominee George McGovern is 86, while the party's 1984 nominee Walter Mondale celebrated his 80th birthday this year. The 1996 Republican nominee Bob Dole is now 85, while the Republicans' 1964 candidate Barry Goldwater lived to 89. The longevity prize, however, goes to the Republican's 1936 candidate, Alf Landon, who died a month after his 100th birthday in 1987.
In conclusion: There may be all kinds of reasons to oppose a McCain victory in November, but age isn't one of them.
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