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The Influence of One Vote

Sieben
Posts: 2,736
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3/31/2011 8:02:19 PM
Posted: 5 years ago
Let's just get this question settled.

A popular, general election. No electoral college. For any population size. No vote trading.

Can we use the binomial distribution? The assumptions are that each voter is an independent random variable with a certain chance to vote a certain way.

http://en.wikipedia.org...

The chance that an INDIVIDUAL vote will influence the election are if the whole population is split right down the middle. So in the equation, k=n/2. The BEST chance that the election will come down an even split is if the gross population is actually split down the middle, so p=0.5

Can we at least agree on this? Its the chance that ONE vote will make a difference.
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Ore_Ele
Posts: 25,980
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3/31/2011 8:15:38 PM
Posted: 5 years ago
At 3/31/2011 8:02:19 PM, Sieben wrote:
Let's just get this question settled.

A popular, general election. No electoral college. For any population size. No vote trading.

Can we use the binomial distribution? The assumptions are that each voter is an independent random variable with a certain chance to vote a certain way.

http://en.wikipedia.org...

The chance that an INDIVIDUAL vote will influence the election are if the whole population is split right down the middle. So in the equation, k=n/2. The BEST chance that the election will come down an even split is if the gross population is actually split down the middle, so p=0.5

Can we at least agree on this? Its the chance that ONE vote will make a difference.

Sure, the odds that 1 single vote will swing a national election is so miniscule that it would have to be measured in scientific notation.
"Wanting Red Rhino Pill to have gender"
Sieben
Posts: 2,736
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3/31/2011 9:14:57 PM
Posted: 5 years ago
At 3/31/2011 8:15:38 PM, OreEle wrote:
At 3/31/2011 8:02:19 PM, Sieben wrote:
Let's just get this question settled.

A popular, general election. No electoral college. For any population size. No vote trading.

Can we use the binomial distribution? The assumptions are that each voter is an independent random variable with a certain chance to vote a certain way.

http://en.wikipedia.org...

The chance that an INDIVIDUAL vote will influence the election are if the whole population is split right down the middle. So in the equation, k=n/2. The BEST chance that the election will come down an even split is if the gross population is actually split down the middle, so p=0.5

Can we at least agree on this? Its the chance that ONE vote will make a difference.

Sure, the odds that 1 single vote will swing a national election is so miniscule that it would have to be measured in scientific notation.

Its hard to do 0.5^(10^6). I'm trying to find some way to bound it it and just use another (generous) well defined function.
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FREEDO
Posts: 21,057
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3/31/2011 9:15:41 PM
Posted: 5 years ago
The chance of a single vote swaying an election in an actual one we have now, with electoral college and all, is not even a fraction, it is zero.
GRAND POOBAH OF DDO

fnord
PervRat
Posts: 963
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3/31/2011 10:00:43 PM
Posted: 5 years ago
At 3/31/2011 9:15:41 PM, FREEDO wrote:
The chance of a single vote swaying an election in an actual one we have now, with electoral college and all, is not even a fraction, it is zero.

The electoral college system we have now makes single votes count more when an election is 'close.' The last several presidential elections had a number of states within a tiny fraction of going one way or another, but the electoral college votes for the states made them decisive. The electoral college is meant to balance out, to a degree, the concentrated political force of our large cities so they won't drown out the voices of farmers and those who live in lower-population areas.
Ore_Ele
Posts: 25,980
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4/1/2011 10:08:00 AM
Posted: 5 years ago
At 3/31/2011 9:14:57 PM, Sieben wrote:
At 3/31/2011 8:15:38 PM, OreEle wrote:
At 3/31/2011 8:02:19 PM, Sieben wrote:
Let's just get this question settled.

A popular, general election. No electoral college. For any population size. No vote trading.

Can we use the binomial distribution? The assumptions are that each voter is an independent random variable with a certain chance to vote a certain way.

http://en.wikipedia.org...

The chance that an INDIVIDUAL vote will influence the election are if the whole population is split right down the middle. So in the equation, k=n/2. The BEST chance that the election will come down an even split is if the gross population is actually split down the middle, so p=0.5

Can we at least agree on this? Its the chance that ONE vote will make a difference.

Sure, the odds that 1 single vote will swing a national election is so miniscule that it would have to be measured in scientific notation.

Its hard to do 0.5^(10^6). I'm trying to find some way to bound it it and just use another (generous) well defined function.

you convert 2^(10^6) into 10^x via logrhythm. Then you represent it as 10^(-x).
"Wanting Red Rhino Pill to have gender"
Rob1_Billion
Posts: 1,300
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4/1/2011 11:49:04 AM
Posted: 5 years ago
The margin for error in the voting process is greater than one order of magnitude. I don't know what rules the idiots in power have in place for elections that are smaller than the margin for error, but I do know two things:

1) Politics, as well as economics, may employ scientific principles (within their erroneus paradigms) but are not based themselves on science.

2) George W. Bush was able to not only win with <50% of the popular vote, but with a vote total < the margin for error:

http://www.msnbc.msn.com...

We're not just talking about counting errors here, after all. Candidates in national elections with a population on the order of 3 x 10^9 shouldn't be decided by 1 x 10^1 votes. That's like a baseball umpire deciding if the winning run in the World Series was safe or out based on a difference of 1 x 10^- 8 seconds, while he is drunk and there is a glare.

The interesting thing about this analogy is that sports people know there is a margin of error, and are smart enough to build in a fail-safe to avoid making the poor umpire have to strain: "tie goes to the runner." IOWs, when it is too close to call (i.e., the margin for human error is much greater than the actual measurement needed), then it is declared a tie, and framework is built to deal with a tieing result in the most equitable and efficient way.

Unfortunately we put much more effort and finesse into our sports rules than we do our political ones.

Some relevant facts:
Reagan won in 1980 by 7 orders of magnitude
Reagan... " " 1984 " 8 " " "
Bush 41... " " 1988 " 7 " " "
Clinton.... " " 1992 " 7 " " "
Clinton.... " " 1984 " 7 " " "
Gore....... " " 2000 " 6 " " " <-----------------------------@@@
Bush 43... " " 2004 " 7 " " "
Obama.... " " 2008 " 8 " " " *(wasn't quite ten million votes, but was greater than 9.5 million.

From this perspective, we can see abouts where we are comfortable: at least 7 orders of magnitude. Once this falls to 6, our system cannot even effectively 'count' who won. When it comes down to it, though, we vote in districts and states so we're not even actually trying to represent the voting accurately.
kfc
innomen
Posts: 10,052
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4/1/2011 12:03:23 PM
Posted: 5 years ago
At 3/31/2011 8:02:19 PM, Sieben wrote:
Let's just get this question settled.

A popular, general election. No electoral college. For any population size. No vote trading.

Can we use the binomial distribution? The assumptions are that each voter is an independent random variable with a certain chance to vote a certain way.

http://en.wikipedia.org...

The chance that an INDIVIDUAL vote will influence the election are if the whole population is split right down the middle. So in the equation, k=n/2. The BEST chance that the election will come down an even split is if the gross population is actually split down the middle, so p=0.5

Can we at least agree on this? Its the chance that ONE vote will make a difference.

Here's how it works: You have a ton of people on each side that cancel out each other. You have all the hard core democrats canceling out all the hard core republicans and you are left with the middle who are swing voters. The swing voters are really the ones who determine an election. Generally speaking this can be a margin of about 3-8% of those who vote have the real power.

If you look at the Bush Gore election that % of the middle was tiny, and yeah each vote was counted over and over in Florida (sorry electoral college talk, but still).

The value of each vote is somewhat irrelevant as a part of the process. It is simply the way it works, and the process is somewhat dependent on a minimal value on each vote. I really don't understand why you have such objection to this.
darkkermit
Posts: 11,204
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4/1/2011 12:09:18 PM
Posted: 5 years ago
I don't think anyone contends that an individual vote doesn't make a difference, on an economic scale.
However, there are social and personal benefits to voting.
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innomen
Posts: 10,052
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4/1/2011 12:28:00 PM
Posted: 5 years ago
At 4/1/2011 12:03:23 PM, innomen wrote:
At 3/31/2011 8:02:19 PM, Sieben wrote:
Let's just get this question settled.

A popular, general election. No electoral college. For any population size. No vote trading.

Can we use the binomial distribution? The assumptions are that each voter is an independent random variable with a certain chance to vote a certain way.

http://en.wikipedia.org...

The chance that an INDIVIDUAL vote will influence the election are if the whole population is split right down the middle. So in the equation, k=n/2. The BEST chance that the election will come down an even split is if the gross population is actually split down the middle, so p=0.5

Can we at least agree on this? Its the chance that ONE vote will make a difference.

Here's how it works: You have a ton of people on each side that cancel out each other. You have all the hard core democrats canceling out all the hard core republicans and you are left with the middle who are swing voters. The swing voters are really the ones who determine an election. Generally speaking this can be a margin of about 3-8% of those who vote have the real power.

If you look at the Bush Gore election that % of the middle was tiny, and yeah each vote was counted over and over in Florida (sorry electoral college talk, but still).

The value of each vote is somewhat irrelevant as a part of the process. It is simply the way it works, and the process is somewhat dependent on a minimal value on each vote. I really don't understand why you have such objection to this.

Add to this a third party element and those with a percent of 4% can draw votes one way or another to have a massive influence on a national election. It isn't the vote as a generic thing, it's the nature of the vote that actually matters. Each vote serves a function in it's own minuscule way.
Ore_Ele
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4/1/2011 12:36:46 PM
Posted: 5 years ago
I'd like to ask, maybe it is just that Oregon does it differently, but when you guys vote (or have the option of voting for those that choose to not bother), do you only vote for president at that time? Or do you vote for everything? Pres, house member, senate (if up that year), local offices, local laws, and local levies and taxes?
"Wanting Red Rhino Pill to have gender"
Sieben
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4/1/2011 11:45:47 PM
Posted: 5 years ago
The Code:

n=230000;

term1=0;
term2=0;
term3=0;
p=.51;

for i = 1:n
term1=term1+log(i);
end

for i =1:n/2
term2=term2+log(i);
end

term3=(n/2)*log(p)+(n/2)*log(1-p);

logprob=term1-2*term2+term3;

prob=exp(logprob)

The Explanation

Chose 230k voters because that's how many turned out in 2008.
Chose 51% as my p because that's what the first source on the wiki article has for Obama winning (actually this is really generous because its Obama 51, McCain 43). http://en.wikipedia.org...

Took the log of everything so I could actually calculate 230,000! (factorial).

Results:

prob=1.7359e-023

So to make a vote worth one dollar, the net benefit would have to be $57 sextillion dollars PER PERSON. Literally a 57 Billion Trillion dollars.

On a NATIONAL scale, this would amount to 17 nonillion dollars. I.e. 17 quadrillion quadrillion dollars. I.e. 17 thousand million billion trillion dollars.

But yeah you care about legalizing marijuana so much you're going to vote anyway.
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Grape
Posts: 989
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4/2/2011 1:00:48 AM
Posted: 5 years ago
At 4/1/2011 12:03:23 PM, innomen wrote:
The value of each vote is somewhat irrelevant as a part of the process. It is simply the way it works, and the process is somewhat dependent on a minimal value on each vote. I really don't understand why you have such objection to this.

He might be able to get to explaining that if it weren't for the constant debate about the math. He's presenting evidence to show that in principle there is a very low probability of a vote mattering and calculating the required payoff to make it worth it. You and OreEle (actually, mainly OreEle) are challenging the numbers, which forces him to use increasingly abstract models. The end conclusion is that in principle there is insufficient motivation to vote intelligently for people to be responsible about their decisions in a democracy.

I don't understand why Sieben continues to put so much effort into arguing this on this forum. The problems with democracy are obvious. I can vote for Santa Claus in the next election and lose virtually nothing. There is absolutely no disadvantage. The only way I can influence the election would be by convincing other people to vote en masse, and every one of them would have no individual incentive to vote either.

If you are committed to defending the current system, consider the following: I live in New York. It is certain that Barack Obama will carry the state in 2012. You can talk about political activism all you want, give me one good reason why it matters what name I put down in the booth. Barack Obama, Ron Paul, or Easter Bunny, it doesn't matter. Won't influence a thing. If you argue for getting rid of the Electoral College then you forfeit all the swing-state arguments. Or perhaps you think it's just that the President is elected solely by the citizens of Florida?
Sieben
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4/2/2011 3:25:46 PM
Posted: 5 years ago
If 300,000,000 people voted in the election, the chances of your vote making a difference are e^(-6.0022e4), which just shows up as zero on computers.

e^(-6.0022e2) is 2.13e-261.

But yeah, the war in iraq is just that important to americans. Go go vote!
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mongoose
Posts: 3,500
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4/2/2011 11:05:26 PM
Posted: 5 years ago
You can't assume a binomial distribution. You know that each side is going to get votes from:
Themselves
Their families
Their campaign staffers
Their campaign supporters
Their donors
Enough people to make the run worth it.

Overall, it has to be much more complicated.
It is odd when one's capacity for compassion is measured not in what he is willing to do by his own time, effort, and property, but what he will force others to do with their own property instead.
Sieben
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4/2/2011 11:28:27 PM
Posted: 5 years ago
The binomial distribution is just a *model*. Of course some people always vote one way. The binomial distribution will capture this though. There's a 99.9999% chance that every trial run under these assumptions will have at least 48% voting one way.
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mongoose
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4/3/2011 12:31:36 AM
Posted: 5 years ago
At 4/2/2011 11:28:27 PM, Sieben wrote:
The binomial distribution is just a *model*. Of course some people always vote one way. The binomial distribution will capture this though. There's a 99.9999% chance that every trial run under these assumptions will have at least 48% voting one way.

It has a great impact on the magnitude of the vote's importance.
It is odd when one's capacity for compassion is measured not in what he is willing to do by his own time, effort, and property, but what he will force others to do with their own property instead.
innomen
Posts: 10,052
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4/3/2011 5:09:03 AM
Posted: 5 years ago
At 4/2/2011 1:00:48 AM, Grape wrote:
At 4/1/2011 12:03:23 PM, innomen wrote:
The value of each vote is somewhat irrelevant as a part of the process. It is simply the way it works, and the process is somewhat dependent on a minimal value on each vote. I really don't understand why you have such objection to this.

He might be able to get to explaining that if it weren't for the constant debate about the math. He's presenting evidence to show that in principle there is a very low probability of a vote mattering and calculating the required payoff to make it worth it. You and OreEle (actually, mainly OreEle) are challenging the numbers, which forces him to use increasingly abstract models. The end conclusion is that in principle there is insufficient motivation to vote intelligently for people to be responsible about their decisions in a democracy.

I don't understand why Sieben continues to put so much effort into arguing this on this forum. The problems with democracy are obvious. I can vote for Santa Claus in the next election and lose virtually nothing. There is absolutely no disadvantage. The only way I can influence the election would be by convincing other people to vote en masse, and every one of them would have no individual incentive to vote either.

If you are committed to defending the current system, consider the following: I live in New York. It is certain that Barack Obama will carry the state in 2012. You can talk about political activism all you want, give me one good reason why it matters what name I put down in the booth. Barack Obama, Ron Paul, or Easter Bunny, it doesn't matter. Won't influence a thing. If you argue for getting rid of the Electoral College then you forfeit all the swing-state arguments. Or perhaps you think it's just that the President is elected solely by the citizens of Florida?

I don't argue for getting rid of the electoral college, i think that it's a part of a states rights value, so that one state or a couple states don't have a dominant effect on the entire country. I live in Massachusetts so i feel your pain.

I do believe that it is in the middle that the presidents are elected, middle being those voters who are inclined to go one way or the other. Oddly enough we are dependent on those with wishy washy convictions, but that's the way it is. There is no perfect process, and a quest for such will lead to disappointment or disaster.
Sieben
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4/3/2011 8:33:35 AM
Posted: 5 years ago
At 4/3/2011 12:31:36 AM, mongoose wrote:
At 4/2/2011 11:28:27 PM, Sieben wrote:
The binomial distribution is just a *model*. Of course some people always vote one way. The binomial distribution will capture this though. There's a 99.9999% chance that every trial run under these assumptions will have at least 48% voting one way.

It has a great impact on the magnitude of the vote's importance.
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