Any problem solvers about ?

RATM

Hiya,
Im just starting a research proposal for uni and have hit a wee maths problem. My topic is on the 2008 US Presidential Election. What I am looking to compare is the accuracy of opinion polls compared to that of the political futures markets run by http://www.biz.uiowa.edu/iem// and the prices that were available. My hypothesis is that markets are better indicators of who will be the next president than opinion polls are.

So the problem is this- Im going to graph the shifting positions of where opinion polls and markets lay for 11 months before polling day on who would be the next president. Now the problem arises as to the two different entities, namely that the polls are asking "Who will you vote for" and the political futures markets "Who do you think is going to win".
For eg on Nov 4th the opinion polls stood at McCain 47% Obama 53%. The Iowa Electronic Markets were selling contracts on Obama for $0.91 and McCain 9¢, ie the market was saying it thought Obama had a 91% chance of success and the polls were saying 53% of people intended voting for him.

What I need is a way of comparing the two figures like for like and I cant seem to figure it out, anyone got any ideas ?

corglass

Sounds good. Good luck with the project. I'm thinking.................

Thomas_S_Hunterson

Can see this one in my head I think, just trying to stick it down on paper.

Thomas_S_Hunterson

Ok this is what I came up with:
linky

It doesn't take account of psychological factors or anything, and the diagram is a bit rough and ready, but you should get the picture.

The key factor here is what the traders view of what the variance is, assuming they're all educated as to the result of the surveyed sample. You could estimate the variance by p(1-p)/n where p is the sample proportion voting for Obama and n is the sample size.

Maybe I'm off the mark here (perhaps i've oversimplified), it's a bit early, but it stands out to me as a way to link the two statistics.

The function in the bottom left is the CDF for a standard normal curve btw.

Tau

This is worth a look:

http://electoralmap.net/index.php

Especially this:

http://electoralmap.net/polling.php

TommyGunne

Yeah you gotta factor in the fact that the opinion polls are a little awkward for prediction by merit of the american election system. As the vote is broken down into individual states, you should be looking at %polls in each state, figure out variance etc by statistical methods (easy to do), and from that you can estimate the expected probability of each politician winning.

Markets are definitely better indicators simply than the 53%-47% stat, but if you wanted to work out the breakdown of %s by state and add in a couple more variables, then that is most definitely a better indicator than the markets, cos those markets were hugely illiquid for large periods of time, and there appeared to be a few very odd trends in there for a few week periods, which might suggest that McCain was a bit too expensive for a significant period of time.

There were also more than two politicians in the race for most of the time....

So basically you should adjust the 53%-47% stat to be more accurate by using per state stats (obv adjusted by the amount of nominations that each state has) and then do what Sean K suggested. Also this was not a two horse race, but that should be easily adjusted for.


Also, with a username like that you can't go wrong! Saw them in Am Ring and the festival which cannot be named on boards. Wow.

Pherekydes

Mebbe Obama supporters are bigger gamblers? Gamblers would not be a representative cross section of the population. Do the markets give a better/stronger prediction? If so, why?

Fremen

I'm pretty sure that even if the polls suggest 53/47 in favout of Obama, this does not mean the probability of an Obama win is 53%. To clarify: if the polls said 80/20 in Obama's favour, a landslide win for Obama would be almost inevitable, rather than four times out of five.

On the other hand, the market price of an Obama contract is a true indicator of the percieved probability of an Obama win.

I think that what you're looking for is a way to convert the 53/47 statistic into the probability of an Obama win. You might be able to do this by calculating the probability that the poll is wrong. This can be recast into a problem of the following type:
Given N independent samples of a bernoulli random variable with statistical mean M (with .5 <= M <= 1), calculate the probability that the true mean m is less than .5
So in this case M is .53, and N is whatever the sample size was.

RATM

Thanks very much for the help, Im just at the proposal stage at the moment and wanted to know could it be solved as a maths problem ( which usually tend to go over my head:p) I'll be collating the data in the next few weeks, maybe I could get back to some of you guys when it comes to working through the conversion problem ?

RATM

Pherekydes wrote: »

Mebbe Obama supporters are bigger gamblers? Gamblers would not be a representative cross section of the population. Do the markets give a better/stronger prediction? If so, why?

For sure, research here has shown that FF'ers are bigger gamblers than any other party members. However there is also research that says there tends to have big hitters playing predictive markets, often playing for big money with inside information ( ie political journalists, pundits, commentators, back room staff etc ) who can shape the market with their knowledge which is what give then an edge over polls. Its an aggregation of knowledge that makes the market more successful.

For instance Intrade.com correctly predicted the electoral college votes to within one vote of the true result this year. Pretty amazing stuff consider ing there were over 500 electoral college votes on offer.
As well as that in 2004 every network and poll was calling Florida for Kerry. Intrade's markets were saying it was going to Bush for over two weeks before the election. The markets picked up a late shift but the polls did not. Intrade were ultimately proved correct over the polls and Bush got another four years:mad:

amen

just on thing on those electoral maps they show the winner in each state but what they are not showing is the thightness of the vote
in some state (particulary after 2004 election) vote was 47/53 or less but the map displays Republican and if you break down into counties per state it can be worse

National geographic had some nice maps for the USA with a grey colour for counties where there was less than a 2.5 difference between Rep/Dem. A lot of the countrywas gray