IOWA!

@maxdancona,

I guess we'll be referring to one another as Hillary haters and Hillary lovers.

...unless the people who are trying to write the narrative agree that Hillary Clinton has earned her reputation.

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@maxdancona,

maxdancona wrote: " Puzzled person. There is fairly basic math, there is no discretion of the observer analyst. There is one answer that is mathematically correct. Any other answer is wrong. The odds of the situation you describe happening is 1 in 2^12."

No. If engineer and I flip a coin twelve times, and each of us wins half of the time, that is even odds, not the highly improbable odds you stated.

You don't seem to understand that in dividing twelve coin flips into two distinct sets, based on the temporal separation of those two sets of six flips, you have created two collections of "improbable" sets, each with a probability of 1/64 and with a combined (series) probability of (1/64)^2 = 1 in 2^12.

But that division is entirely at the arbitrary discretion of the observer. Each flip is supposedly independent of each other flip, so the choice to group six flips or twelve flips together in a "set" for probability analysis is subjective. Not only does the observer separate twelve flips conducted by the two participants according to arbitrary temporal parameters, but the observer also arbitrarily excludes all other flips made with the same coin, whether by the same or other participants; also all other coin flips in general; and for that matter, all other nominally random binary-valued events (the latter being undefined and indefinable).

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@Blickers,

"How does that 34% undecided and 25% leaning toward some candidate compare with the usual breakdown for polls a week before a Republican primary?"

Good question, but I don't have an answer.

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@puzzledperson,

Quote:

50 for it to be 50/50 (25 for each)."

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@puzzledperson,

Quote puzzledperson:

Quote:

You don't seem to understand that in dividing twelve coin flips into two distinct sets, based on the temporal separation of those two sets of six flips, you have created two collections of "improbable" sets, each with a probability of 1/64 and with a combined (series) probability of (1/64)^2 = 1 in 2^12.

But that division is entirely at the arbitrary discretion of the observer.

Dunno. If you lump them all together to one session of 12 coin flips, wouldn't the question then be: "What are the chances of one side winning all of the first six, and the other side winning all of the second six?" I'm sure the answer, whatever it is, is considerably less than 50%.

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@puzzledperson,

Quote:

Let's say that engineer and I conduct a set of six coin flips. I win all of them. The odds of this are (1/2)^6 = 64 to 1 against.

A week later, we do the same thing, only this time, engineer wins all six tosses; again at odds of 64 to 1 against.

Read what you are saying puzzled person.

1) The chance that You flip 6 coins and they all come up heads is 64 to 1.
2) The chance that Engineer flips 6 coins and they come up tails is 64 to 1.

You really think that the chance of both of these events taking place is 50-50?

Or did you really mean to claim something else.

1 Reply

@maxdancona,

For the record, the probability of flipping 12 coins, and having exactly 6 (i.e. any 6 of them) of them come up heads is 22.6%. (This is calculated using the method explained here... https://en.wikipedia.org/wiki/Binomial_distribution)

The chance that the first 6 will be heads and the second six will be tails is 1 in 2^12.

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@maxdancona,

Thanks. I took statistics in college, but forgot how to set up the formula.

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@Lash,

Lash wrote:

He didn't win. It's a lie. Read Snopes.

I did, but the question still remains. You say if Clinton wins 6 of 7 that she must have cheated. (The probability of one person winning six of seven coin tosses is over five percent, very reasonable, but this is your issue.) If it turns out that Sanders won six of seven, do you conclude that he cheated?

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@engineer,

The question remains, and a key fact remains to be noted:

The probability that in seven flips of a coin, one contestant or the other will win at least 6 flips, is 1 in 8.

The probability of Hillary winning at least 6 times was 1/16.
(7 choose 6)*(1/128)+(7 choose 7)*(1/128)= 1/16

The probability of Bernie winning at least 6 times was 1/16.

Since these are mutually exclusive events the probability of one of those two things happening is 1 in 8. If they conducted such a contest every day one or the other event would happen almost every week. We're not exactly talking about an August snowstorm in Georgia here.

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@ehBeth,

This is a perfect example of how unreliable and/or how untrustworthy the modern media is. I heard reporters and/or commentators on both FOX and CNN tell the story as HRC winning the coin tosses. I'm sure of it because in each case the person made a point of "wondering" what Sanders was going to do about it.

Has it come to the point that viewers have to fact check what news sources are telling us? This has to have something to do with the mad rush to be the first to break a story, and I wouldn't be surprised if they were hoping Sanders would get ugly with Clinton. More than one of them has been badgering him about going after on the e-mail. It must drive them nuts that so far he's refused to go for her jugular on it.

Having seen the Republican candidates only too happy to give them what they want they want the Democrats to get on the train.

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@maxdancona,

Well, with two coins there are just four possibilities, two of which involve results of half heads and half tails (one of each), in which case the odds of getting an equal number of heads and tails are 1/2. But if you increase the number of coins to four, then of the sixteen possibilities, six involve equal numbers of heads and tails; so the odds are 6/16, which are less than even odds. (The easy way to prove this is to print out the numbers from 0 to 15 in binary, then count how many of the sixteen possibilities have equal numbers of heads and tails.) Inferentially, the more coins you add (doubling each time), the lower the odds of getting an equal number of heads and tails.

I'll accept your probability of 22.5% in the case of 12 coins as a stipulation, without calculating it.

That said, I still say that probability is a quantity associated with a set of events, and that where events are causally independent of each other, the selection of a particular grouping of events, constituting a "set" for purposes of statistical analysis, is a subjective, observer dependent act, which in turn determines the probability associated with the event set.

Consider a set of 12 coin flipping machines. Each machine has a single coin; and each machine makes a single flip. Each flip constitutes an "event". Neither the spatial nor the temporal proximity of these events is specified. All twelve machines could be in the same room, executing their flips simultaneously. They could be in the same room, with their flips separated by minutes, days, or years. They could be scattered across the world, conducting their flips simultaneously. They could be scattered across the world, conducting their flips at different times.

There may be a number of other such coin flip machines. The number of other machines is not specified, and may not be known or knowable. The spatio-temporal relations of the coin flips of these additional machines, whether to each other or to the original dozen under consideration, is not specified. These additional machines do not enter into this hypothetical, except to flesh out the boundary conditions a bit.

The coin flip of each machine is causally independent of the coin flips of the others.

First, note that the selection of 12 particular machines, out of a possible myriad such machines, is a subjective, observer dependent act.

As it so happens, among our 12 machines, half toss "heads" and half toss "tails". You specified the probability of this result as 22.5%, which is between 1/4 and 1/5.

However, if we define as a "set" only the six that flipped heads, and ask what the probability is of flipping six heads with them, the answer is 1/64.

If we define as a set the six machines that tossed tails, the probability of six tails is also 1/64.

If we ask what is the probability of one set of six machines tossing six heads, with another set of six machines tossing six tails, you've said that the probability is 1/4096, which is the product of the two individual probabilities, (1/64) * (1/64).

Yet, we've already stipulated that the probability of getting half heads and half tails from the same 12 machines is much greater, between 1/4 and 1/5, or specifically 22.5%.

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@Kolyo,

Kolyo wrote: "Since these are mutually exclusive events the probability of one of those two things happening is 1 in 8. If they conducted such a contest every day one or the other event would happen almost every week..."

I know that there is nothing controversial in your statement, but I just don't believe that the concept of probability is consistent with an open-ended series of casually independent events, even in theory.

Under such circumstances, no matter what the result of a series leading up to a new event, and no matter how long the initial part of the series leading up to it, the result of the new, independent event is not affected by what went before.

This means that a series of (say) "heads" of arbitrarily long length -- in fact indefinitely long length -- is possible even with a "fair" coin and a "fair" flip.

The way that probability theory deals with the possibility of (say) 100 heads flipped in a row, is to define "standard deviations". So we might say that if we consider ten-thousand series of 100 flips per series, we would only expect X number of series to have 100 heads in a row. But because each flip is causally independent, there is no reason why, even in theory, we couldn't get all heads in every flip of every series; and there is no way to define the probability of that happening without an infinite regress in which the probability assigned to every deviation has itself a probability defined in terms of ever larger numbers of events.

For me, this represents a fundamental logical inconsistency between two premises: the first being that every event is causally independent of every other event and of any collection of other events; the second, that collections of casually independent events must obey collective probability distributions.

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@puzzledperson,

P.S. Sorry, maxdancona said 22.6% not 22.5% as I erroneously attributed. That doesn't materially change my arguments, however.

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@puzzledperson,

Look at it this way... and you brought of binary, which is a convenient way to do this.

XXXXXXXXXXXX (this is 12 coins of unknown sides up)

The first question is: How many possible combinations of coins are there? I state there are 4096 possible ways that these coins can be set. I think you agree with me.

Now lets look at one possible state

(example 1) HHHHHHHHHHHH

Do you agree that the odds of getting this state is 1 in 4096?

Now what about this possible state

(example 2) HHHHHHHHHHHT

or this state

(example 3) HHHHHHHHHHTH

I claim that that all three of these examples have exactly 1 in 4096 chance of happening assuming you randomly flip each coin in order.

Do you agree?

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@Lash,

Lash wrote:

Did YOU read that what you emphasized from the Snopes cannot be proven?

Sure... and did you read it?
Care to back track on your claim of Hillary using fake coins to cheat? Or is what can't be proven only applied to the other side?

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@maxdancona,

Hillary hater might be one that accuse Hillary of fraud in coin tosses with no evidence to support that claim. Or do you think that would be a rational look at the evidence, or lack thereof?

1 Reply

No, Hillary Clinton did not win Iowa because of a coin flip

Quote:

CNN)—Hillary Clinton claimed victory in the Iowa caucuses Tuesday after topping Democratic rival Bernie Sanders by the skin-of-her-teeth margin of 49.9% to 49.6%. There's been some confusion about how much of a role -- if any -- coin flips played in determining who won delegates.

Coin flips -- specifically "games of chance" -- are used in rare circumstances at precinct caucuses to adjudicate ties or resolve issues created by rounding errors. At stake at these precinct-level coin flips is the one remaining slot in that precinct for a campaign to send a delegate to attend that precinct's county convention. Coin flips are not used to decide which candidate wins a state convention delegate or national convention delegate.

How many coin flips were there on Monday night?

The Iowa Democratic Party does not have comprehensive records on how many coin flips/games of chance were held Monday evening. However, they do have partial records.

More than half of the 1,681 Democratic caucuses held Monday night used a new Microsoft reporting app. Of those, there were exactly seven county delegates determined by coin flip. The remaining precincts did not use the Microsoft app, and instead used traditional phone-line reporting to transmit results. In these precincts, there no are records of how many coin flips occurred. There's only anecdotal information on these precincts.

Who won these coin flips?

Of the seven coin flips/games of chance that were held in precincts using the Microsoft app, six of those were flips to determine whether a county delegate slot went to Clinton or Sanders. Of those six Clinton-vs.-Sanders coin flips, Sanders won five and Clinton one. The seventh coin flip was used to determine whether a county delegate slot went to Sanders or Martin O'Malley. Sanders won that coin flip as well. So in the seven coin flips that the Iowa Democratic Party has a record of, Sanders won six of them.

So it's incorrect to say that Clinton won every coin flip.

As for the less-than-half of the precincts that didn't use the Microsoft app, it's unclear how many coin flips took place. Only anecdotal information is available on these flips, such as web videos that circulated Monday night.

Hillary Clinton's tough night

Did Clinton win the Iowa caucuses thanks to coin flips?

Clinton won the Iowa caucuses by the equivalent of about four state delegates. If the anecdotal evidence of Clinton winning six coin flips is correct, she would have won six county delegates through coin flips (setting aside the fact that party records show Sanders also won six county delegates as a result of coin flips). There is not a one-to-one correlation between county delegates and state delegates, or to national convention delegates.

Based on the party's delegate selection rules, a single county delegate represents a tiny fraction of a state convention delegate (the exact ratio is difficult to calculate because it varies from county to county).

Norm Sterzenbach, the former executive director of the Iowa Democratic Party who oversaw the party's 2008 and 2012 Iowa caucuses, told CNN:

"I can say with almost absolutely certainty this election would not have been changed because of the coin flips. It would take a very large number of these to make that kind of impact, and one candidate would have to win them all. Our empirical evidence and anecdotal information shows that one candidate didn't win them all, and that coin flips are not that frequent."

Sterzenbach has worked with the Iowa caucuses since 2000. He is not aligned with any 2016 campaign, has not endorsed a candidate, and did not caucus for any 2016 candidate.

He says that four state delegate equivalents may seem like a small amount, but that it would take "a lot" of county delegates to amount to four state delegates. Sterzenbach said based on his recollection, there seemed to have been more instances of coin flips being held in 2008 than in 2016

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@parados,

That's your definition of "Hillary Hater"? Actually something like this happens in almost every contested election... sometimes on both sides. I don't think it is rational, I do think it is human nature in the middle of an intense election.

Personally, I think the coin toss debacle, and the fact that they don't even record the fact a coin toss is used, is a sign of how screwed up the Iowa caucus is.

Maybe that makes me an "Iowa Hater".

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@revelette2,

Bernie said it yesterday in the debate. Quibbling over a couple of delegates is not worth the time.

As Engineer pointed out, in a perfectly random set of 7 coin flips, the odds that Hillary would win 6 of them is about 5.5%. That means that this will happen more than 1 out of 20 times. This single occurrence is hardly evidence of fraud. Add to this the fact that these coin flips were cobbled together by a reporter off of social media... no one truly knows how many coin flips actually occurred that night (which shows how screwed up the Iowa system is).

This has been over-analyzed already.

1 Reply

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