In the name of not putting a thumb on the scale in favor of top tier candidates

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Last edited Fri Jun 14, 2019, 07:33 AM - Edit history (1)

we actually handicapped them. Eight candidates polled above 2% and are in group 1 (Biden, Sanders, Warren, Buttigieg, Harris, O'Rourke, Booker, and Klobuchar) and twelve who are under 2% in group 2. So on each night 4 people from group 1 and 6 people from group 2 will be on stage. Now, at this point, Biden is the clear leader and the person who candidates want to be on stage with. If you are in group 1 and not Biden, then you have a 3/7 chance of being on stage with him and a 4/7 chance of not being on stage with him. On the other hand, if you are in group 2, you have a 50/50 chance of being on stage with him. That seems to punish success.

On edit it gets worse

As discussed above, the probability of any particular candidate, say Sanders, being on stage with Biden is 3/7. So say that happens. Now what is Warren's probability of being on stage with them? It is 2/6 which reduces to 1/3. The other 2/3 she would be in the debate that had neither of them. So Warren has a 1/7 chance of being on stage with both Biden and Sanders, a 2/7 chance of being on stage with neither one, and a 4/7 chance of being on stage with one of them. For those in the lower group the probabilities are 3/14 for both, 3/14 for neither, and 4/7 for one. So the lower group has a significantly better chance of being on stage with both than Warren (or any other top tier candidate for that matter) and no worse chance of being on with one of them.

[HerbChestnut]

1. Yup.

The Republicans, for all their faults, seemed to have a better system four years ago in a similar situation. Not sure if there's a perfect solution to this problem other than just hoping 20+ people don't run for office at the same time.

[JI7]

2. i don't think it's that important to be on the same stage as him

it's more about getting a positive soundbyte that could be replayed and probably more imporant at this point is to avoid a negative one that could be replayed.

[customerserviceguy]

4. I can see where it would be a plus to debate Biden

for a low polling candidate. I would imagine that at this point, Gillibrand would consider selling her soul for the chance to make a big splash coming at Biden in the same style she's used on Franken.

[customerserviceguy]

3. Too bad it couldn't be divided ten and ten

but, the under two percenters are so numerous this time around. That's not the DNC's fault.

[dsc]

11. a different split would only make this slightly less problematic

Instead of 3/7 and 4/7 it would be 4/9 and 5/9. In terms of percents it would make the 43 57 split and 44 56 split

[customerserviceguy]

13. Exactly

The coin flip goes the way the coin flip goes, and everybody who made the cut needs to deal with that.

Sen. Warren got a pass in my opinion, there's no way she's not going to make the cut for the next debate, all she really needs to do in the first one is swat flies. The only "serious" competition she's got is from O'Rourke and Booker, and they won't dare to attack her. It would be counterproductive in the future with female voters, and besides, it's just not their style.

[LibFarmer]

5. But -- for a given candidate

the odds are still 50:50. (Average of 3/7 and 4/7 is 1/2 or 50:50)

[dsc]

6. um no that isn't how it works

All probability distributions sum to 1 thus if we have two options the average will always be 1/2.

[dsc]

7. It actually gets worse

As discussed above, the probability of any particular candidate, say Sanders, being on stage with Biden is 3/7. So say that happens. Now what is Warren's probability of being on stage with them? It is 2/6 which reduces to 1/3. The other 2/3 she would be in the debate that had neither of them. So Warren has a 1/7 chance of being on stage with both Biden and Sanders, a 2/7 chance of being on stage with neither one, and a 4/7 chance of being on stage with one of them. For those in the lower group the probabilities are 3/14 for both, 3/14 for neither, and 4/7 for one. So the lower group has a significantly better chance of being on stage with both than Warren (or any other top tier candidate for that matter).

[LibFarmer]

8. You are making a classic coin-toss error

of aggregating the probabilities for each successive event.

Let's say you're tossing a coin and get heads on 20 successive tosses. The odds of that happening are 9.54E-07.

What are the odds for the 21st coin toss? They still remain 50:50 or 0.5

Aggregating a series of 21, you'd get the odds of 4.77E-07

[dsc]

9. No I am not when I get home from work I will show my work that got me those numbers

[dsc]

10. Here is the work behind the numbers

First the idea that Sanders (or any other top tier candidate who isn't Biden) is 3/7 with Biden and 4/7 not with Biden. Biden takes one slot out of 4 on his night. Sanders is one of seven remaining people who will take one of the 7 remaining slots (3 on Biden's night and 4 on the other night). He thus has a 3/7 chance of being on Biden's night and a 4/7 chance of not being on Biden's night. Conversely for those in the other group there are 6 slots on each night so they have an immutable 1/2 chance on being on either night. Thus they have a 1/2 chance of being with Biden and a 1/2 chance of not being with Biden.

Now as to the Warren probability. From above we know that 3/7 of the time Biden and Sanders will be on the same night and 4/7 of the time they won't. If they are on the same night, that leave two slots on their night and 4 slots on the other night. Warren(or any other top tier candidate who isn't Biden or Sanders) thus has a 2/6 reduces to 1/3 chance of being on the night with Biden and Sanders and a 4/6 or 2/3 chance of being on the other night. By multiplication of the probabilities we get (3/7) (1/3) reduces to 1/7 chance she is on their night and a (3/7)(2/3) reduces to 2/7 chance she is on the other night. Finally 4/7 of the time Biden is on one night and Sanders on the other so she has a probability of 1 that she would be on a night with one of them. By mulitiplication (4/7) (1) reduces to 4/7. Therefore she has a 1/7 chance of appearing with both candidates, a 2/7 chance of appearing with neither, and a 4/7 chance of appearing with one. Conversely, for the other group there is an immutable 1/2 chance on being on either night so if Biden and Sanders are on the same night they would have (3/7) (1/2) or 3/14 chance of appearing with them, and the same (3/7) (1/2) or 3/14 of being on the other night. Like Warren, if there is one candidate on each night then the probability if 1 that they appear with a candidate so (4/7) (1) = 4/7 thus they have 3/14 to appear with both, 3/14 to appear with neither, and 4/7 to appear with one.

[dsc]

12. Well Warren got screwed

Not only is she not on the stage with the candidates who are ahead of (Biden, maybe Sanders) or tied with (maybe Sanders) she also is not on stage with the two candidates below her who are the closest to her. She also is on the first night so she doesn't even get to respond to those candidates. So Andrew Yang and Marianne Williamson get prime slots and she gets outer Siberia.