Reminder: betting markets have Bernie as the *most* electable candidate.

[DanTex]

Right now on PredictIt Bernie is at 58% for the nomination and 34% for the presidency. Simple arithmetic shows that the market odds of him beating Trump are 34/58 = 58.6%. This is the highest of all of the leaders, and it's been that way consistently since before Iowa. Biden at 6/11=54.5% isn't so far behind, but at the very least, this shows people betting actual money don't believe the "Bernie will get destroyed" talking point.

I know, I know, some people don't believe in betting markets (at least not when it's inconvenient). And I guess some people don't believe in the polls showing Bernie beating Trump either.

But there comes a point where you gotta ask, when all the data points in one direction, why do so people seem so unflappably convinced that Bernie can't win?

[TheCowsCameHome]

1. ...34% for the presidency...

That's a lousy bet.

Much too risky in these turbulent times.

[ChubbyStar]

23. Surely you remember mine that bird and Calvin Borel?

https://www.nbcsports.com/video/mine-bird-calvin-borel-unlikely-2009-kentucky-derby-winners


The insiders called him Calvin BoRail because that is what he did, ride the rail to victory.

[Green Line]

35. Remember it well

[mdelaguna]

25. I know. I wish someone would just rise to the top and unite us.

Not that I know who that is anymore.

[InAbLuEsTaTe]

2. DOHHhHH!!

Bernie/Elizabeth or Elizabeth/Bernie 2020!!
Either way, they're stronger together & can't be bought!!
Jump on the Bernie Bandwagon & join The Revolution!!

[LexVegas]

3. That's some interesting math.

[DanTex]

4. It's division. I divided 34 by 58.

[brooklynite]

57. A meaningless calculation

[njhoneybadger]

62. That's just fucking ridiculous

[msongs]

5. wow using betting markets as viable data only works in a loser paradise like las vegas IMO nt

[TexasTowelie]

6. Betting markets are based upon the amount of money people wager

rather than the number of voters that support that candidate. If one person wagers $500 while a second person wagers $20, the odds will be adjusted to cover the higher wager.

That's why betting markets are useless to predict voter behavior.

BTW, I have debunked the math that you are using in your OP at one point, but I'm not willing to repeat that futile exercise again. It's obvious from your example that you don't know anything about statistics.

[DanTex]

8. Actually, they are based on the odds that would get equal money to bet for and against.

The amount people wager is depends on the odds. If Bernie were at 10-to-1 there would be a lot more money bet on him than if he were at 2-to-1. What betting markets do is find the level of odds where there is the same volume of bets on one side as the other.

And the nice thing about it is that people who think the market odds are wrong can actually go in and try to make profit by placing bets of their own.

[TexasTowelie]

14. .

Get back to me when you have taken some statistics courses.

[Garrett78]

7. Uh oh, this will prove inconvenient for some folks.

[DanTex]

9. It's also kind of ironic that the socialist candidate is ahead in the markets, and the

people supporting more free-market candidates are the ones saying betting markets are useless.

[Garrett78]

12. The following also run counter to popular narratives:

https://fivethirtyeight.com/features/the-moderate-middle-is-a-myth/

https://www.thenation.com/article/archive/what-everyone-gets-wrong-about-independent-voters/

https://www.vox.com/2016/1/22/10814522/independents-voters-facts-myths

https://www.vox.com/policy-and-politics/2018/11/10/18076872/trump-46-percent-solition

[Loki Liesmith]

15. Markets require a large number of actors to leverage information

Political betting markets aren’t big enough and therefore can be easily biased by enthusiastic participants.

[Awsi Dooger]

20. Comical...try again

The vastly superior way to look at it is that late last fall when Biden was the frontrunner, Democrats were favored to win the White House and Trump was trading below 50%.

Now that Sanders is the frontrunner that has completely reversed. Republicans are favored to win the White House, currently trading at 57%. Trump is above water at 55%.

Bottom line: Trump has been underdog for 2020 throughout his presidency, until we stupidly shifted toward Bernie Sanders.

Go down below these charts and click on the 90 day graphs and you'll see what I mean. There is a direct relationship between Sanders becoming the frontrunner in January and the shifted favoritism toward the GOP. As soon as it reaches late January with Sanders pulling away from Biden, the same gap occurs with Republican favoritism widening. Democratic was trading at 51% on January 15. Now that Sanders is the established frontrunner, Democratic is trading at 43%:

https://www.predictit.org/markets/detail/3698/Who-will-win-the-2020-US-presidential-election

https://www.predictit.org/markets/detail/3633/Who-will-win-the-2020-Democratic-presidential-nomination

I love it when this wagering stuff shows up and people with 15 minutes of background think they know what they are looking at.

[JudyM]

32. Causal fallacy. What's comical is that you pin the change on Sanders' rise rather than impeachment

proceedings!

[tinrobot]

10. 34% is not very inspiring.

[DanTex]

11. It's 58.6%. 34% are the odds of both winning the nom and also going on to win the presidency.

And inspiring or not, it's higher than anyone else in the field.

[TexasTowelie]

16. You are taking the odds for two completely independent events

and calculating new odds by making them dependent. That clearly shows me that you don't know anything about statistics. The odds of Bernie winning are 34%, not the 58.6% that you are using "new math" to generate because you think that it will make Bernie appear more electable.

[TheCowsCameHome]

17. Odds are you're 100% correct.

[DanTex]

21. Huh? Winning the presidency and winning the nomination are not independent events.

Quite the opposite, they are highly dependent. Winning the nomination is a precondition to winning the presidency.

[TexasTowelie]

24. And that illustrates why you don't know what you are talking about.

I'm a trained statistician with courses in descriptive statistics, inferential statistics, and probability. The odds of Bernie winning the presidency are 34%--period. The calculation that does not involve taking the probability of the second independent event and dividing it by the probability of the first independent event.

Get back to me after you take some statistics classes.

[DanTex]

26. OK, so you know about conditional probabilities, and how they are calculated.

We have two events, (A) Bernie wins the nomination, and (B) Bernie wins the presidency. These are (obviously) not independent. Since Bernie can't win the presidency without first winning the nomination, that means event (B) is a sub-event of event (A), which means that

A⋂B = B

Using the formula for conditional probability, we can then calculate that the probability of winning the presidency, conditional on winning the primary, by:

P[ B | A ] = P[ A⋂B ]/P[ A ] = P[ B ]/P[ A ] = 0.34/0.58 = 0.586...

Which is to say, if Bernie wins the nomination, he has a 58.6% chance of going on to beat Trump.

Now, I suppose it's theoretically possible that Bernie somehow wins the presidency without winning the nomination, but the chances of that are infinitesmal, so the approximation P[ A⋂B ] ≃ P[ B ] will not affect the final estimate to any significant degree.

[TexasTowelie]

28. .

The thing is that the odds being calculated on the betting markets are not using conditional probability theory. The odds are set for independent events occurring.

I wish that people who don't know anything about statistics would stop arguing like they do.

[DanTex]

30. If you think that Bernie getting the nomination and Bernie becoming president are independent

events, then I'm sorry but you are mistaken. Independence has a specific meaning in probability theory, which is that

P[ A⋂B ] = P[ A ]P[ B ]

In this case we have

A = Bernie wins the nomination
B = Bernie wins the presidency
A⋂B = Bernie wins both the nomination and the presidency

Since it is virtually impossible that Bernie wins the presidency without winning the nomination, then we get P[ A⋂B ] ≃ P[ B ]. In effect, winning the presidency implies also having won the nomination. Therefore these events are far from independent, the independence condition doesn't come anywhere near equality.

[ehrnst]

49. That makes you look very smart - putting in probability theory and all those equations and letters.

I mean who could possibly doubt the expertise, or disagree in any way when math and equations are brought into a topic that is totally dependent on human behavior, which we all know is ruled by mathematical principles - particularly those that DanTex feels make the most sense?

No one, that's who!

This obviously puts an end to any dissent, and we can all go home, save the trouble of voting, and simply wait for Bernie to be bestowed the nomination that he's clearly entitled to.

[Awsi Dooger]

22. Correct

It's as if he somehow believes that Sanders will surge to 58% likely in those markets if Sanders is official as the nominee.

Hilarious

As I've mentioned, there is ongoing chatter on the wagering sites that Trump will become larger favorite if Sanders is indeed nominated. It is all but a certainty. Some guys began to speculate early along those lines once Sanders became the frontrunner in January. Right now obviously there is some play in the market due to uncertainty.

To be fair to the OP, Bernie is at 34% to gain the presidency right now because he still has to get through the primaries. It would be considerably higher than 34% right now if Bernie were a certainty to receive the nomination. It's like Super Bowl odds on a football team before playing the NFC Championship Game, during that brief window after the AFC Championship Game has already been decided. One is a guarantee and the other has 2 requirements instead of 1.

However, as I mentioned, the faulty thinking is that Sanders will jump to 58% after becoming the nominee. It won't be anything close to that.

People wagering on Sanders to win the presidency right now at 33 or 34% are making an asinine investment. Beyond asinine. The 57% toward the nomination is far superior value. Then if Sanders wins you take that profit and roll it over onto the presidential market, using any timeline you wish.

As I've mentioned, the 60 level is phenomenal for political wagering. I can't count how many wagers I have made in that territory. That 3-2 is a fantastic return given wagering options elsewhere. Often that 60 feels like outright theft, especially when I'm taking the GOP candidate in a state with 42+% self-identified conservatives. It's amazing how many of those races get shoved down toward 60 range when they should be 80-90 or above.

[DanTex]

27. It's an extremely straightforward calculation of conditional probability.

34/58 = 0.568...

This is basic. You might think that the prediction markets are wrong, fine. You can even go place some bets if you are confident. But the conditional probability of Bernie beating Trump if he wins the nomination, according to the current market odds, is 0.586, there's no ambiguity about that.

[TexasTowelie]

29. You moved the goalpost!

But the conditional probability of Bernie beating Trump if he wins the nomination, according to the current market odds, is 0.586.

You changed from Bernie has a 58.6% chance of winning the presidency to if he wins the nomination. That is moving the goalposts!

And by the way, the odds of Bernie winning the presidency are 34%, not 58.6%.

[DanTex]

31. That's not moving anything. It's a conditional probability calculation.

Yes, Bernie has a 58.6% chance of winning the presidency if he wins the nomination. That's exactly the point.

If Bernie wins the nomination, he has a 58.6% of going on to beat Trump. And that is higher than for any other candidate.

Which means that, according to betting markets, Bernie is the most electable candidate.

[TexasTowelie]

33. .

Get back to me when you take a statistics class because it is apparent that you are clueless.

Bernie does not have a 58.6% chance of beating Trump if he wins the nomination. Even in the most favorable polls Bernie is barely crossing 50% and with only a few points margin in a head-to-head challenge with Trump. There is no way that the odds are 58.6% - 41.4%.

[DanTex]

34. Anyone can follow the math. It's quite simple.

Your ad hominems about me and my knowledge of math and statistics don’t change the numbers.

The head to head polls have Bernie consistently ahead of Trump. So that’s another indication that Bernie isn’t “unelectable”.

[TexasTowelie]

37. There is more to statistics than just plugging numbers into a formula.

The odds that are set by the betting markets are based upon the probability of each independent event occurring, not on conditional probability. If you fail to recognize and understand that difference, then this discussion isn't going anywhere.

The probability of Bernie winning the presidency as determined by the betting markets is 34%. The probability of some other candidate (including all remaining Democratic candidates. all remaining GOP candidates including Trump, and all third-party candidates) is 66%.

Think of it this way, if Trump has a 94% probability of winning the GOP nomination and a 55% chance of winning the election (both numbers from PredictIt), then Trump's odds of winning the election do not become 55/94 = 58.5%. If you use the conditional probability formula, then both Bernie and Trump would have probabilities over 58% of winning the general election if they win their respective party nominations. It is not possible for both candidates to have over a 50% of winning since the total of the two percentages cannot exceed 100%. This demonstrates that the use of the conditional probability formula is wrong.

[DanTex]

38. True, but in this case, it really is that simple.

The events are not independent, obviously, and Bernie's probability of winning, conditional on Bernie winning the Dem nomination, is 58.6%.

You are correct that Trumps chances of winning, conditional on Trump winning the GOP nomination, are 58.5%.

There is no contradiction there, because these probabilities are conditional on different events (Bernie winning the D nom in the first case, Trump winning the R nom in the second case). So there's no reason they can't add up to more than 100.

[TexasTowelie]

39. LOL.

Thanks for demonstrating your mastery of statistics to someone that has a degree in mathematics and worked as a statistician for 25 years.

[DanTex]

40. Again, ad hominem attacks don't change the math, which is pretty straightforward here.

[TexasTowelie]

41. LOL.

Applying the wrong formula for a situation has very little to do with math. However, please continue believing that both Bernie and Trump have over a 58% chance of winning the general election. Perhaps they can be elected co-presidents in November?

[DanTex]

42. Right now Bernie has a 34% chance and Trump a 55% chance.

If Bernie wins the Dem nomination, his chances go up to 58.6%. But since he hasn't won the nomination yet, he's still at 34%. 58.6% is a conditional probability. I seriously don't understand why this is controversial at all.

[TexasTowelie]

43. I give up.

You are going to apply whatever statistical formula you believe will represent Bernie having an increased chance of winning no matter how wrong you are. I suggest that you find a statistics professor to discuss this with so you will see your error.

[DanTex]

44. Not "whatever statistical formula." The formula for conditional probability.

No need for a statistics professor, conditional probability is covered in the first few months of an intro course.

[ehrnst]

45. The ever moving goalposts...

See also: Gish Gallop...

[ehrnst]

46. Yes, that's always the best indicator. Why ever gave us the idea of voting in a primary

to determine our candidate?

[ehrnst]

47. But when you follow math that simply looks good to you, but isn't really accurate

you wind up with conclusions like "a chunk," right?

[ehrnst]

48. Bernie has a 58.6% chance of winning the presidency

Tell Nate Silver!!! He's doing it all wrong!!!

These predictions are completely accurate!!!

DanTex says so!!!!

[Deero]

13. betting markets are

awful at probability.

[uponit7771]

18. The 3 month swing state polling says they're wrong

[Sympthsical]

19. They don't want him to win,

It’s a form of wishcasting (rather than forecasting). I want it to be so, so it must be so.

At some point, and it’s drawing near, people need to have hatred of Trump outweigh their disdain for Bernie. Because this gross antipathy towards Sanders is far off the deep end now in some quarters. We’re not going to win with this volatility towards the man if he’s our nominee.

It’s becoming a bad, abusive, gaslighting relationship. “Bernie’s so divisive!” Like watching a spouse hit their partner and then declare, “Why do you keep making me be violent!”

I’m so, so over it. I was over it three years ago, to be honest.

[Desert grandma]

36. Maybe what you do not understand

is that we absolutely HATE Trump, THAT IS WHY we hope Bernie is not the nominee. Speaking for myself, and many of our Democratic friends, we have decades of life experience and have been through many election cycles...some we have won, as well as those we have lost. We do not "disdain Bernie"...we just do not want 4 more years of Trump. What I don't understand is why people can't see that the Republicans and Putin are attempting to help Sanders get the nomination. Why?? Because they know Trump wins then. We were successful in 2018 because for the most part we ran moderate/centrist candidates. We are patriotic Americans that believe we know what is coming if BS is the nominee.

[Grasswire2]

52. what you forget...

....is that your life experience is not the same as the life experiences of most of Bernie's coalition. You see him as something terribly negative because you lived through the Cold War? Like Chris Matthews equates him with Fidel Castro and says his rise is akin to the fall of France to Hitler? While most of Bernie's base see honesty in him, and compassion for those who are struggling, and the promise of a life that is better than the oligarchy squeezing the life out of too many people, and consistency in his advocacy throughout his entire career.

They hate Trump just as you do. And they believe (as polling shows) that Trump would lose to Bernie.

Now. Democrats can either dither and fight each other over purity, or Democrats can put their energy toward election security issues. Because THAT is the real danger here. States are still buying hackable systems, and Trump has a plan to get the election to SCOTUS for resolution.

Skip the hysteria and get to work.

[Desert grandma]

65. Sorry Grasswire 2

It is not hysteria, and I am not hysterical. I am sharing my opinion. Why do you think Russia is helping the Sanders campaign and no other campaign except Trump's? I will reluctantly vote for Sanders if he is the nominee, but I will not work for a candidate I do not wholeheartedly endorse. He will have my vote, but not my heart. And whether you can understand it or not, I am not the only Democrat to feel this way.

[andym]

50. Your use of stats is quite wrong

First let me show you Trump's chance of winning the election using your formulas:
Trump's chance of winning his nomination is currently 93%. His chance of winning the election is 56% at the moment.
Using your formula for Trump 56/93= 60.2%.

According to these calculations Bernie's chances of winning the election are 58.6% but Trump's are 60.2%-- greater than Bernie's.
That's interesting because together these chances add up to 118.8%-- much better than 100%!!! That can't be correct.

Now if Bernie had a lower chance of winning the primary using your calculations, but kept his chances of winning the election the same (might not happen) his chances of winning the election would go up-- as would any candidate. At this very moment Bernie's chances of winning the nomination are now 65% on PredictIt and his chances of winning the election against Trump are 38%. So by your calculation Bernie's chances of winning the election have stayed the same, even though both numbers have risen 38>34 and 65>58)!! 38/65=58% thanks to winning Nevada which still doesn't jive with Trump's greater 60.2% chances.

So what's wrong with your calculation?-- it technically means that there will be a direct increase in percent chance to win the election with every increase in percent chance of winning the nomination. But why assume that given that winning the nomination only includes a set of Democrats and some Independents for Bernie, and basically Republicans for Trump, and not everyone together, many of whom won't even vote in the primaries (many independents and some Democrats and Republicans). So the probabilities are built on different populations. There is some overlap of dependence in the numbers, but you can't use them the way you are using them.

[DanTex]

51. You are conditioning on two different events, which is why it sums to more than 100.

https://www.democraticunderground.com/1287553543#post38

[andym]

53. That is so - you have indentified the flaw in your own approach

I just applied your own reasoning.

How are we to interpret your prediction then?
Are Bernie's chances of winning the election 58% or are Trump's 60%? According to you.

[DanTex]

54. There is no flaw, these are conditional probabilities.

Bernie's chances are 37%, Trump's are 56%.

If Bernie wins the Dem primary, then he has a 58% chance of winning. If Bernie loses the primary, then he has a 0% chance. Those are conditional probabilities.

[andym]

58. And Trump? If he wins the primary, his conditional probability is 60% of winning?

How could one rationally place a bet using your calculations? How do you ultimately reconcile these numbers is the question.

How would you calculate the final numbers: Bernie 37%, Trump 56% as you wrote? Or is that only at the moment. I don't really understand.

We know if Bernie wins the nomination his chances to win the election would go up, the question is how much-- you are saying his would go up to 58%. But why wouldn't Trump's number's follow the same formula and go up modestly to 60%? So how would we place our bets now based on your calculations? Ultimately we have to create a statistic where the total probability of either of two people winning is 100% discounting third parties.

[DanTex]

60. That's correct.

If Bernie wins the D nomination, his (Bernie's) number goes up to 58.
If Trump wins the R nomination, his (Trump's) number goes up to 60.

What you seem to be asking is what happens if both Bernie wins the D nomination and Trump wins the R nomination. Unfortunately, there's not enough information to calculate that just from the individual probabilities.

Another thing is, these numbers don't always add up to 100 because of imperfections in the market. The notable thing about Bernie's 58% is that it is higher than the comparable number for any other Democratic candidate, which means that the betting markets do not consider Bernie "unelectable", in fact, it's the opposite.

[andym]

63. So your numbers don't really mean that Bernie's chances are 58% of winning after the nomination

Last edited Sun Feb 23, 2020, 06:09 PM - Edit history (1)

Just that his chances of winning are greater than the current 34% -- that is correct.

Let me show you with a concrete example.
The problem of getting an accurate ultimate calculation is the differing sizes of pools of voters used in your calculations.

Let’s try some hypothetical numbers on for size (I think Bernie would actually do much better, but these illustrate the problem):

48 Democratic voters for Bernie ultimately (after no more Democrats running)
52 voters for Trump ultimately (after no more Republicans running)

[I've edited this OP to correct the misassumption that the percentage of votes is equivalent to the probabiity of success. Actually
the probability of success is equal to the probability of getting a majority (greaterthan 50%) given a random sampling of some size N. It is correctly determined by using a hypergeometric distribution (picking randomly without replacment) in which the one sums the number of all successes greater than 50%.
Here is a calculator https://stattrek.com/online-calculator/hypergeometric.aspx ]


Lets assume we are sampling half of the 48 Democratic voters (24) and then in the general election half the entire voting population of 100 (50) that I mentioned.

In this case using the calculator, Bernie would need only 26 voters out of the 48 Democrats (54%) to have a 61% chance of winning the nomination: population size 48, number of successes in population 26 (his total voters if everyone voted), sample size 24 (half of 48 Democratic the voters vote/are sampled for the nomination). Probability of getting 13 or more voters (13/24>50%) is 0.61= 61% (better than the Predictit 58%). So in the scenario Bernie needed to have 26/48 potential Democratic voters to have a 61% chance to win the nomination.

What about the general election? Let's again assume 50% of voters (this time all 100 voters vote)=50. Now we could choose the numbers so that Bernie wins the general election. But to show how one can't just assume winning the Democratic (or Republican) nomination proportionately increases the amounts in the general election, instead let's assume there are more voters who want Trump. Say 52 out of 100. Though Trump has a 93% chance according to Predict-it (the other 7% are assuming something happens to him presumably) these numbers would give him a 99% chance of winning his nomination.

So in this general election scenario, Bernie's chances of winning would be going down (not up): population size 100, number of successes in population = potential Bernie Voters 48, sample size of 50 (50% of everyone votes), number of successes in sample (majority of vote)= 26 (out of 50). The probability for Bernie to get 26 or more votes is 27% according to the calculator.

But according to your original post he could actually get 58 voters (58%), and that could eventually be true in reality. But there is no reason to believe that even if Bernie captured all of the votes of the other Democrats that his general electorate percentage would increase proportionately. It would likely increase, but limited by the number of people in the pool of potential Democratic voters.

The problem is the very different pools of voters over which your probabilities are calculated. That’s why you are receiving so much feedback.

[DanTex]

64. Correct.

If Bernie wins the nomination then his chances go up to 58%. But he hasn't won the nomination, so his chances are still at 34%. Actually the numbers have moved up since Nevada, but that's the idea.

[muriel_volestrangler]

67. That doesn't make any sense

40 voters for Bernie ultimately (after no more Democrats running)
60 voters for Trump ultimately (after no more Republicans running)

In this population to get 58% of the Democratic votes, Bernie would currently have 23 of the democratic voters 23/40=58%.

Trump would have 56 out of 60 (93%) of the potential Trump votes now.

No. We aren't counting votes; we're reckoning the possibility of a win. If I say "there's a 90% chance X will win the election", that does not mean "I think X will get 90% of the votes".

[andym]

68. I corrected/updated that post using the appropriate statistics: the hypergeometric series

Thanks, the post as I wrote was it not correct statistically. Now the post is statistically correct, but the original point stands about not being able to proportionately increase the probability of winning based on dividing the general election chances by the chances of getting the nomination.

[muriel_volestrangler]

66. You are not taking into account the chance of another Democrat winning the nomination

If they did, the PredictIt market is saying Trump's chance goes up.

What you have identified is that DanTex didn't take into account the possibility of Trump not getting the Republican nomination.

But that seems pretty damn unlikely to me, and it certainly affects DanTex's figures less than your omission of other Democrats.

What is more, the effect of Trump not running would affect the odds of other Democrats winning the general as well. DanTex has compared Sanders' chances with other Democrats' chances, and correctly found that Sanders' are reckoned the best.

And he is not trying to get a precise figure for it; only to say that Sanders' is reckoned, by this market, to have more electability than other Democrats. Which is correct.

[andym]

69. That is not the essence of my criticism

DanTex made 3 points (2 explicitly):
1) Bernie has the best chance of all candidates
He was correct given that Bernie had a 34% chance of beating Trump while the others were far less in that data. No need to do more.

2) He implied that when Bernie was the sole candidate his chances would increase.
I agreed with that as Bernie would capture some more of the other Democrats vote (in the other post however, I show that his chances could actually go down depending on the nature of the pools of voters-- but that is unlikely).

3) He incorrectly stated that the increased chances would be directly proportional to Bernie's chances of winning the nomination and that now Bernie would be favored to beat Trump.
Basically, 34/58=x/100 and solving for x. That assumes that every percentage of Democrats he gains would increase his general election chances proportionately which is not correct and certainly not to the point of being favored to win against Trump. That is the point that I and several others tried to make to Dantex.

[muriel_volestrangler]

70. No, this is not about the "percentage of Democrats he gains"

It's about what the market currently thinks about (a) Democratic candidates' chances of winning the nomination (b) the chances of that winner then becoming president. Not a "percentage of Democrats" (and it's not about a sample, so your revised hypergeometric calculation in #63 does not apply).

For Sanders, the figures (when the OP was written) were 0.58 for the nomination, and 0.34 for the presidency - which is an event which depends on the first happening (unless you think there is a chance of him winning it as an independent), so it is indeed 0.34/0.58=0.586 that the market reckoned for the second stage of "winning the general election after having won the nomination".

Using current figures, the chances for the major candidates are (though rounding with all apart from Sanders cause some problems):
Sanders = 0.37/0.65 = 56.9%
Bloomberg = 0.07/0.15 = 46.7%
Biden = 0.06/0.13 = 46.2%
Warren = 0.03/0.04 = 75%
Buttigieg = 0.03/0.05 = 60%
https://www.predictit.org/markets/detail/3633/Who-will-win-the-2020-Democratic-presidential-nomination
https://www.predictit.org/markets/detail/3698/Who-will-win-the-2020-US-presidential-election

Strictly, as you've pointed out, this is about each of them beating "whoever the Republicans nominate" (and whoever any 3rd party candidates are), rather than "Trump".

[andym]

71. It's true that it's gambling--but your post is incorrect

It doesn't matter whether its voters themselves or opinions held by bettors of how people will vote--in the end they are predicting how the population of voters will behave. The hypergeometric series (a very stripped down version of what pollsters do) does apply because the bettors should be trying to predict these very numbers (a rational bettor should look at the polls etc like 538 does and then place bets accordingly) and that should inform their bets.

The basic problem is that conditional probability that you and Dantex are promoting doesn't hold because you neglect to account for the possibility that bettors in the general election pool may not choose to believe that Bernie would win the general election even when his nomination odds are at 100%. That proportionality is based on the false assumption that all the bettors placing their bets on Bernie to win the nomination would naturally think he would win the election too-- no justification for that.

[muriel_volestrangler]

72. That's just wrong.

"The basic problem is that conditional probability that you and Dantex are promoting doesn't hold because you neglect to account for the possibility that bettors in the general election pool may not choose to believe that Bernie would win the general election even when his nomination odds are at 100%."

Wrong. And, frankly, that's gobbledegook. The bettors, as a group, say there is 65% chance Sanders will win the nomination. They say there's 37% chance he'll become president - which is, basically, dependent on him winning the nomination. That 37% figure is neither "0%" nor "65%", so it clearly does mean that some of them think he would win the general election "when his nomination odds are at 100%", ie if he's nominated, and some of them don't.

" That proportionality is based on the false assumption that all the bettors placing their bets on Bernie to win the nomination would naturally think he would win the election too"

No. If that were the case, then the figures would be equal.

[andym]

73. NO

Some of the bettors placing bets on Bernie winning the nomination may think that Trump will win the general election. Why not?
Clearly your assumption is wrong. There is a dependency problem with your conditional probability.

[muriel_volestrangler]

74. You do not make any sense.

You just now said "Some of the bettors placing bets on Bernie winning the nomination may think that Trump will win the general election."
Yes, that is what I said. I pointed out the chance for Bernie becoming president was given as somewhere in between zero and the chance of him winning the nomination.

"Why not?"
Why are you asking me that?

"Clearly your assumption is wrong."
What assumption?

"There is a dependency problem with your conditional probability."
Point it out.

[OliverQ]

55. Why only a 34% odd for the General election?

[DanTex]

56. Because to win the GE, Bernie first has to win the primaries.

Basically, 34% is the chance that he both wins the primaries and also goes on to win the GE. He needs to win two races to do that, which is why it's so low.

[Squinch]

59. All that sweet, sweet Russian help sure does help.

[musette_sf]

61. + 1