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п»їWhat was the probability that Barack Obama would win the US election?
On the face of it this seems an odd question. After all, he won. But before the election it was uncertain whether Obama would win, and probability is the way that uncertainty is quantified, so maybe it is reasonable to ask what that probability was.
We know that there were betting odds – a betting exchange such as Intrade allows people both to accept or make bets and so converges, at any point in time, to a certain set of odds at which people are willing to be either the better or the bookmaker. This prediction market provides a ‘probability’ on Obama winning that kept changing for the year before the election – this is shown in Figure 1 with some of the main events of the year marked in.
'Probabilities' of Obama and McCain winning the 2008 US Presidential Election.
A ‘probability’ of 20% means that people were willing to take and make bets at ‘4 to 1 against’, which means that if someone put £1 on Obama winning, they would receive back £4 winnings plus their stake to make £5 in total. [I don’t usually gamble, but in January 2008 I did place an online bet of £1 on Obama at 4 to 1 odds , in the middle of a lecture to a post-graduate class in Cambridge in order to illustrate how odds transform to probabilities: this choice was treated with some derision at the time. Gambling during a lecture probably also broke some medieval statute of the University!].
But do these betting odds really represent the probability? How does this fit with how probability is taught in school? In fact what does probability mean? Does it even exist? These are reasonable questions to ask, and we quickly get into some tricky philosophical issues.
Assessing probability in a non-repeatable situation.
Let’s look at the different ways we might think about probability, and whether each way might tell us what the probability of Obama winning might have been.
The Classical idea of probability is based on equally likely outcomes: if there are $N$ possible outcomes the probability of each one is $1/N$. This is what is generally taught in schools, and works fine for coins, dice and other physical objects where it may be reasonable to assume some symmetry between the outcomes. In the election there were two main candidates, so would the probability of Obama winning be 50%? Just because there are two alternatives does not mean they are equally likely. And in fact there were up to 14 other candidates including names that could be written in, depending on the state, but a probability of 1/15 seems even more unreasonable. So the classical view does not work here. The frequency interpretation is based on what proportion of events happen in the long run: for example, we might say the probability of a dropped piece of toast landing butter-side down is 80% if that is the proportion of times it happens if we keep droping toast (in controlled conditions) for millions of times. But this interpretation is difficult to apply to specific events such as Obama becoming President since they are essentially unique. We would need to place the event in a class of repeatable opportunities that stretch into the future, such as ‘black men becoming president’. Looking into the past we note that there have been 43 Presidents of the USA of whom precisely 0 have been black, so the current observed proportion is 0/43. Does this mean the best estimate of the probability that Obama becoming President was 0%? Clearly this would be ridiculous. Even if we were misguided enough to place Obama within this class of events, there is a better way of working out a probability which will be explained below. Another possibility that has been suggested is that there is some true underlying ‘degree of belief’ in the statement ‘Obama will be the next President’ that, given the knowledge that we have, it would be logical to hold. This proposal leaves open the question of how to estimate this quantity and does not seem helpful in this situation. Rather more attractive is the idea that there is some true underlying propensity for an event to happen – this is an objective state of the world but needs to be estimated from what we know. One mental picture for this is to consider all the possible ways in which things might turn out, and then think of what proportion of these possible futures end up with Obama being President. This approach seems a bit shaky from a philosophical point of view (can we really think of the set of ‘possible futures’?), but means that we can think of probability as a frequency without having to think of some class into which to embed the event we are interested in. The final way of thinking of this probability comes back to the betting: the probability is essentially the odds you are willing to accept in a bet based on your own subjective judgement. The betting exchange probabilities plotted above provides a kind of group assessment. Such probabilities could be interpreted as your best current estimate of the ‘true’ probability (which is not directly measurable).
Alternatively, and a view that I prefer, we can say that the probability is not an estimate of any actual quantity in the outside world, but simply an assessment of the odds that You are willing to take. You don't have to actually place any bets: Your probability that Obama will be President is, say, 50% if you are indifferent between the following two options: either (a) obtaining a reward if Obama becomes President, and (b) obtaining the same reward if a flipped coin comes up heads.
The attractive thing about this interpretation of probability is that it does not matter whether the event is truly unpredictable, or whether it is pre-ordained and you just don’t happen to know how things will turn out. For example, before I flip a coin, you may say your odds are 50:50 on heads. If I flip the coin but cover up the result , your odds should not change, even though the uncertainty is now due to our ignorance rather than any essential unpredictability. If I then look at the coin but don't show you , then Your probability should still be 50%, even though mine is either 0 or 100%.
So this view says that probability does not exist , but is simply a numerical expression of Your personal uncertainty, given the current information. Rather strangely, it means that probabilities can be quantified but not measured, rather like the value of anything, whether a painting or a loaf of bread, does not objectively exist but depends on what people are willing to pay.
Assessing probabilities in repeatable situations.
Things are are made easier if we see the current event as part of a sequence stretching back into the past and forward into the future, and we have no reason to think that any member of the sequence is systematically different from any other. We call the events ‘exchangeable’, and if we are willing to assume this (which we would not for Obama), there is a neat way of assessing the probability of the next event.
An Italian actuary called de Finetti showed that if we are willing to assume exchangeability, then it is as if there is some true underlying chance for the event to happen, we just don’t know what it is. In the long run the proportion of events that occur will tend to this underlying chance.
Suppose we have observed $n$ possibilities for an event to occur, and it has actually occurred in $r$ of them? What is the chance it will occur at the next opportunity? This is a classic problem, dealt with by the clergymen Thomas Bayes in an article published in 1763 and also by Laplace in 1814. Laplace provided the simple rule:
But this number [the odds of the sun coming up tomorrow] is far greater for him who, seeing in the totality of phenomena the principle regulating the days and seasons, realizes that nothing at present moment can arrest the course of it.
showing that applying his formula in an unthinking manner can be absurd.
So suppose you are told that a bag contains a mixture of black and white balls, but you are not told the proportion of each. You draw out 10 balls, putting each back after you have drawn it, and 3 of them are black. What is the chance that the next is black? Well, assuming that the balls are well-mixed, and that you thought before you started that all proportions were equally likely, then the chance is 4/12 = 1/3.
Laplace’s law of succession can be obtained with some basic integral calculus: have a look at an explanation of Laplace's analysis.
So now you know how to use past evidence to assess the chances of future events, but only if you think that the future is going to carry on just like the past, and that can be a very dangerous assumption: if you want an example, think of the free-range turkey on Christmas Eve, happily looking forward to the next day of food and shelter, just as he has always known in the past.


Biden’s Election Odds Improve Following Obama Endorsement.
Democratic presidential candidate former US Vice President Joe Biden speaks during a town hall . [+] meeting in Newton, Iowa, on January 30, 2020. - Joe Biden went on the attack Thursday against Donald Trump, as the Democratic frontrunner campaigned in Iowa hours before the US president jets in to divert attention ahead of the state's first-in-the-nation vote. (Photo by JIM WATSON / AFP) (Photo by JIM WATSON/AFP via Getty Images)
AFP via Getty Images.
After receiving a strong endorsement from former President Barak Obama, Joe Biden has seen his 2020 election chances improve. While the endorsement comes as no surprise, it does highlight an interesting trend in that others talking about Joe Biden seem to be driving his success rather than the candidate actually speaking himself.
New York Governor Andrew Cuomo has emerged as a betting longshot, with his daily press appearances throughout New York’s battle against Covid-19 giving his popularity a boost with democratic voters.
Sportsbooks Offer Trump & Biden At Even Odds.
It was assumed that Obama had withheld his formal endorsement to avoid causing any disturbances in the Democratic nomination process, but the announcement couldn’t have come at a better time for Biden.
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A former Biden staffer has accused her former boss of sexual assault, an accusation that the candidate has publicly denied, and while only an accusation at this point, negative press can be detrimental to a candidate whose odds seem to improve when the spotlight focuses on someone else.
Where this news could have led to a dip from an odds perspective, the well timed Obama endorsement helped quickly remedy the situation by instantly becoming the focal point of all Biden campaign conversations.
This paired with the ongoing coronavirus situation and Trump’s ongoing quarrels with Dr. Anthony Fauci and the World Health Organization helped to create a “tale of two candidates”, with one being lauded with support and praise from peers while the other struggles to find balance under pressure.
Beauty is in the eye of the beholder, and the ongoing narratives on both sides of the fence will likely have little impact in changing the vote of most Americans, but the sheer.
With the odds now even at many sportsbooks, it looks like we could be in for a race much tighter than the one pundits and oddsmakers expected only a few short weeks ago.
Democratic VP Odds Per BetOnline.ag.
Kamala Harris 2/3 Gretchen Whitmer 9/2 Amy Klobuchar 5/1 Michelle Obama 12/1 Stacey Abrams 12/1 Elizabeth Warren 14/1 C.Cortez Masto 20/1 Hillary Clinton 33/1 Val Demings 40/1 Barack Obama 50/1 Tammy Baldwin 50/1 Tammy Duckworth 50/1.
Presidential Election Odds Per BetOnline.ag.
Donald Trump 10/11 Joe Biden 10/11 Andrew Cuomo 40/1 Hillary Clinton 40/1 Michelle Obama 66/1 Mike Pence 66/1 Nikki Haley 100/1 Mark Cuban 150/1.


Updated Vice Presidential Odds After Michelle Obama FEC Filing.
WASHINGTON – A new political action committee (PAC) has formed with the goal of encouraging Joe Biden, the presumptive Democratic presidential nominee, to choose former first lady Michelle Obama as his vice president.
The PAC filed with the Federal Election Commission (FEC) on April 26, although it is unaffiliated with both the Biden campaign and Obama herself.
According to Clyde Lederman, a spokesperson for the committee and a former staff member on Mike Gravel’s presidential campaign, the group’s goal is to “ build substantial grassroots support for a potential Michelle Obama candidacy and help garner Media attention [for her candidacy]. ”
The group has already begun releasing targeted digital and social media ads to raise awareness and support for Obama.
Joe Biden has indicated in the past that he would nominate Obama as his VP “in a heartbeat,” but expressed doubt that she has any wish to live in the White House again.
Lederman told reporters from ABC that although the PAC’s focus remains on Obama, it will pivot to support the eventual nominee no matter who it is.
Obama’s vice-presidential betting odds have noticeably shortened since the PAC filed with the FEC. While it is a very grassroots group, it could have a sizable impact on political betting odds for the 2020 election cycle.
Updated Vice President Betting Odds After FEC Filing.
Back in mid-March, right after Biden had taken comfortable control of the Democratic primary, Obama was only a blip on the VP radar.
Since then, it has come out that Barack Obama played a big role in helping Biden’s campaign mount a huge comeback against challenger Bernie Sanders on Super Tuesday.
This could indicate that the Obama family isn’t quite done with political life just yet .
Betting odds on the Democratic vice-presidential nominee can be very volatile, but Obama is one of the few candidates for the job to see her odds grow consistently shorter.
Those odds remain considerably longer than three other women who ran large campaigns for the 2020 Democratic presidential nomination, but Biden himself was a massive underdog in the primary at one point.
Other candidates have experienced momentary surges, but Obama seems to have steady momentum. Given her popularity and experience, Obama would be a strong bet to earn the VP bid , except that there’s no guarantee she wants to be considered for the job.
Would Michelle Obama Want To Return To The White House?
On paper, a Michelle Obama VP nomination would be a slam dunk, but before that can happen, she has to approve the idea herself, not just the legal sports betting sites.
Obama has not completely ruled out the possibility of running but in the past, she has expressed disinterest in returning her family to the intense public scrutiny of life in the White House.
Michelle Obama enjoys widespread popularity among Democratic voters, even among many progressive groups who didn’t approve of her husband’s time in office. With concerns mounting about the viability of Biden’s campaign, Democratic groups will likely do everything they can to court Obama’s candidacy.
Even then, there’s no guarantee she would accept. She wrote a bestselling book in 2018 and has maintained a heavy public presence since leaving the White House in 2016, but there is a big difference between life as a celebrity and life in the White House.




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