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Author Topic: Find the fraudster! A polling simulation game  (Read 2524 times)
Nichlemn
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« on: April 30, 2014, 09:11:57 pm »
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I've noticed in polling threads, people love to cast aspersions on whether a polling company is biased or fraudulent. So here's a game to test how good you are at detection.

In this game, the country of Fictionland has two parties, the Leftists and the Rightists. They hold elections every four years. There are four pollsters in Fictionland, Aardvark Polling, Badger Opinion Strategies, Cheetah Marketing and Dolphin Reports. The companies poll every month, second month, third month and fourth month respectively, except the latter three also poll every month in the last four, three and two months prior to an election, respectively, as well as the eve of an election.

Three of the companies are legitimate pollsters, albeit with their own systematic biases. One of the companies is a complete fraud, consisting of numbers that I just made up as I went along. The fraudster may be trying to be accurate, or may have a partisan agenda. 

The game takes place over 20 years. (In real time, it'll probably be no more than a couple of weeks). The game starts with the first election result, then polling starts up in earnest. Your objectives are:

a) To predict the popular vote in each of the five polled elections as accurately as possible.
b) To determine who the fraudulent pollster is.
c) To determine what the biases of each pollster are, and how much the pollsters as a whole are biased.

No need to sign up. Just post your thoughts and predictions whenever you feel like it, or right before an election.
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Nichlemn
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« Reply #1 on: April 30, 2014, 09:12:21 pm »
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How it is simulated

You can skip this post if you don't care about the math, but it may help you make more accurate predictions.

I'm using Excel's random number function to simulate swings in support for the parties and for the legitimate polls.

Each month a "true" support level for the parties is generated. First, I multiply last month's true support level by 98% and add 50% * 2%. Basically, this creates some "regression to the mean" to make it nearly impossible for one party to get to unrealistically high levels of support. Then, to make the parties support level fluctuate, I add the inverse of the normal cumulative distribution for a random number between 0 and 1. What this means is there's an equal chance of a positive or negative swing, and the swing is most likely to be low but has a small probability of being quite large. So for example, if the random number generated is 0.05, there's a -1.64% swing. If it's 0.45, there's a -0.13% swing. If it's 0.95, there's a +1.64% swing. If it's 0.999, there's a +3.09% swing. This "true" level of support is not known to me or any of the pollsters, except for elections. The first election (and data point you get) comes from a point hundreds of "months" into my simulation.

The legitimate pollsters generate "polls" with an inverse binomial distribution. Every poll, the true level of support, with some added bias, is the probability of "success" on a trial. There are 1,000 "trials" to represent 1,000 people polled. I generate a random number, and that represents how big a sampling error they had. So for instance, a pollster that happened to have zero bias would take the true level of support for that month (say 55% for the Leftists), and if the random number was 0.05, it would get 524 "successes", or a poll representing 52.4% of the vote. This number, incidentally, is an error of 2.6% - hence where you might have heard "2.6% margin of error at 95% confidence" from in a poll of a similar sample size.

However none of the pollsters can perfectly sample the population. Each pollster has a consistent bias. A pollster with a 1% left-wing bias, for instance, in a month where the Leftists' true support was 55%, would conduct a "poll" where the probability of a success was 56% of the vote. With the same random number of 0.05, it would instead produce 534 "successes", or 53.4% for the Leftists.

The biases are generated in two ways. Firstly, there is a "common" polling bias generated again inputting a random number in the inverse cumulative normal distribution. Whatever this number is gets added to all of the legitimate firms' error. So if this number was +1, every legitimate poll would, on average, overestimate the Leftists by 1%. Then, each pollster gets its own bias, generated in the same way. So there might be a common leftist bias of +1%, but the three legitimate pollsters could have +2%, +0.2% and -1.1% of additional bias. The latter pollster is the most right-leaning of all the pollsters, but because of the overall left-wing bias, in this case it would end up most accurate.
All of these biases remain consistent the entire game.

Then there's the fraudulent pollster. Before I start, I use more random number generations to determine a) which one of the pollsters is the fraudulent one and then b) whether the pollster has a Leftist bias, a Rightist bias, or no partisan bias. All have equal probability. Once that's done, there are no more calculations, I just quickly come up with numbers off the top of my head every time a poll is due for a fraudulent firm. As I do this, I don't know what the true levels of support are, nor do I know the current months' results from other pollsters.
If the firm is biased, I try to make the numbers favour the party it is biased towards while still attempting to be believable. If the firm isn't biased, it takes a rough approximation of the recent polling average to try to come up with "accurate" results.

All polls have results to 1 decimal place. I understand that this is considered bad form in the real world of polling, but for the sake of the game I think it makes it more interesting, easier to be more accurate in your estimations and makes the fraudulent pollster easier to find.

There are also no undecided voters, third parties, "registered" and "likely" voters, or anything else tricky like that, for simplicity's sake.
« Last Edit: May 02, 2014, 10:36:52 pm by Nichlemn »Logged

Nichlemn
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« Reply #2 on: April 30, 2014, 09:18:24 pm »
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First Election

The first election takes place in December 2000.

The results are a strong victory for the Rightists, who win by a 56.5 to 43.5 margin.
« Last Edit: May 01, 2014, 09:42:03 pm by Nichlemn »Logged

Nichlemn
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« Reply #3 on: April 30, 2014, 09:57:43 pm »
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Polling for 2001

January 2001

Aardvark Polling:
Rightists 53.9%
Leftists 46.1%



February 2001

Aardvark Polling:
Rightists 57.1%
Leftists 42.9%


Badger Opinion Strategies:
Rightists 55.8%
Leftists 44.2%



March 2001

Aardvark Polling:
Rightists 55.8%
Leftists 44.2%

Cheetah Marketing:
Rightists 57.0%
Leftists 43.0%



April 2001

Aardvark Polling:
Rightists 53.1%
Leftists 46.9%

Badger Opinion Strategies:
Rightists 53.0%
Leftists 47.0%

Dolphin Reports:
Rightists 52.0%
Leftists 48.0%




May 2001

Aardvark Polling:
Rightists 52.0%
Leftists 48.0%



June 2001

Aardvark Polling:
Rightists 51.7%
Leftists 48.3%

Badger Opinion Strategies:
Rightists 54.2%
Leftists 45.8%

Cheetah Marketing:
Rightists 55.4%
Leftists 44.6%



July 2001

Aardvark Polling:
Rightists 52.9%
Leftists 47.1%



August 2001

Aardvark Polling:
Rightists 51.1%
Leftists 48.9%

Badger Opinion Strategies:
Rightists 52.5%
Leftists 47.5%

Dolphin Reports:
Rightists 54.5%
Leftists 45.5%




September 2001

Aardvark Polling:
Rightists 52.4%
Leftists 47.6%

Cheetah Marketing:
Rightists 55.1%
Leftists 44.9%



October 2001

Aardvark Polling:
Rightists 54.2%
Leftists 45.8%

Badger Opinion Strategies:
Rightists 52.3%
Leftists 47.7%



November 2001

Aardvark Polling:
Rightists 53.5%
Leftists 46.5%



December 2001

Aardvark Polling:
Rightists 54.3%
Leftists 45.7%

Badger Opinion Strategies:
Rightists 54.9%
Leftists 45.1%

Cheetah Marketing:
Rightists 53.8%
Leftists 46.2%

Dolphin Reports:
Rightists 55.8%
Leftists 44.2%


« Last Edit: May 01, 2014, 08:49:59 pm by Nichlemn »Logged

Never
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« Reply #4 on: May 01, 2014, 10:28:26 am »
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This sounds exciting. It appears that you have put plenty of work into this. Based on your explanation, I think I have an understanding of how this works. As someone who enjoys reading polls, I look forward to the progression of this game.

It seems like Badger Opinion Strategies is the likeliest fraudulent pollster, but I am not 100% sure about this, because it appears this polling company caught a genuine shift to the rightists in 2001 before it showed up in the other three polls. Dolphin Reports apparently has a leftist bias of 1-2%, while Aardvark Polling has a rightist bias of 0.4% and Cheetah Marketing could have a leftist bias of 0.1%. Aardvark and Cheetah might be the most reliable pollsters.
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Nichlemn
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« Reply #5 on: May 01, 2014, 08:22:24 pm »
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Dang it, I thought that I'd stopped Excel from recalculating, but I forgot to turn off "recalculate when saved", so I've lost the rest of that. Never mind, it's just a case of editing the numbers.
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Nichlemn
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« Reply #6 on: May 01, 2014, 08:51:26 pm »
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Changed data to reflect new random number generation. Never Convinced's post refers to the old data.
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« Reply #7 on: May 01, 2014, 09:21:44 pm »
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Changed data to reflect new random number generation. Never Convinced's post refers to the old data.
Darn! I guess I'll have to go back over the data again.
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Nichlemn
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« Reply #8 on: May 02, 2014, 12:02:08 am »
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Should I post graphs of each year's polling? It could make it easier to detect patterns, but I'm concerned that too much information might be "doing the work for you" and make the exercise more dissimilar to the existing exercise of critiquing polls as they get posted.
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Nichlemn
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« Reply #9 on: May 05, 2014, 05:55:37 am »
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Dang, it reset again! I'd need to retrieve all of it at once if this is going to work.
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ilikeverin
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« Reply #10 on: May 06, 2014, 05:51:41 pm »
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"Paste Values" Smiley
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Nichlemn
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« Reply #11 on: October 10, 2014, 11:05:09 pm »
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I'm getting sufficiently annoyed of bad polling analysis that it's made me consider trying this again. Any interest?
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« Reply #12 on: June 16, 2016, 12:16:36 pm »
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Just found out about this thing. I know Nichlemn barely posts any more, but if anyone would make another of these it'd be great!
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