Trump may very well get away with his crimes, but the idea this will have no political backlash is a fantasy. Trump's public support stems almost entirely from the Republicans.

The Russia Investigation

Trump did not collude with the Russian government to influence the 2016 presidential election, American voters say 48 - 39 percent. But voters are divided on whether the Trump campaign colluded with the Russians, as 46 percent say it did and 44 percent say it did not.

Special Counsel Robert Mueller is conducting a fair investigation into possible collusion, voters say 55 - 31 percent.

This investigation is "legitimate," 54 percent of voters say, while 40 percent say it is a "witch hunt."

A total of 63 percent of voters are "very concerned" or "somewhat concerned" that the Russian government may try to interfere in the 2018 elections, as 36 percent are "not so concerned" or "not concerned at all."

From July 18 - 23, Quinnipiac University surveyed 1,177 voters nationwide, with a margin of error of +/- 3.5 percentage points, including design effect. Live interviewers call landlines and cell phones.

The Quinnipiac University Poll, directed by Douglas Schwartz, Ph.D., conducts nationwide public opinion surveys, and statewide polls in Pennsylvania, New York, New Jersey, Connecticut, Florida, Ohio, Virginia, Iowa, Colorado and Texas as a public service and for research.

https://poll.qu.edu/national/release-detail?ReleaseID=2557

Let me know when it happens. In the meantime, feel free to continue and throw your votes in the trash.

Even if a "3rd party" became popular it would be at the cost of one of the current parties and we'd still be in a two party system. People would simply shift to the current dominate two parties. The only thing that would really happen is musical chairs with party labels.

Sure, people can definitely choose to throw their votes in the trash.

And your example is a false equivalence.

Leap frog.

Political belief.

Socialism.

I met a political sciencist who suggested no one is an Independent; instead they are just poorly informed people. He said when informed everyone leans more to one side than the other.

You modeled a different scenario than the OP, then argued that it was impossible for you to be wrong, as you claimed there is no such thing as being correct. However, this is not art class, and it is possible to be incorrect.

It would be a completely subjective and made up number.

The truth is, the OP never mentioned you'll get to open 100 envelopes. In fact in the OP there are only two envelopes and you only get to pick one of them. These "switching strategies" are not applicable, as you don't have a chance to learn the distribution though repeatedly opening envelopes.

A Bayesian inference is subject to the same fault, it will need several occurrences to correct the errors of baseless assumptions, before becoming accurate.

It should be noted the a so called "switching strategy" can only work if it has the time to learn the distribution. It only works because in the long run it can gather enough information to approximate the distribution, but at the start its predictions will be very unreliable.


Consider @Michael's simulation he posted: Here

Now he ran it for 10,000 times, that means it was able to gather a lot of information on the distribution but what if we try it with 5 times, what is our expected gain then? I will use his code but change the number of times to run it.

Let's give go at 5 iterations :

[1] "Gain: -0.112966601178782"

At 10 iterations:

[1] "Gain: 0.190537084398977"

At 20 iterations:

[1] "Gain: 0.468846391116595"

At 30 iterations:

[1] "Gain: 0.331561140647656"

At 50 iterations:

[1] "Gain: 0.146130465279402"

At 100 iterations:

[1] "Gain: 0.246130667031913"

Finally at 100 iterations do we get Micheal's predicted expected returns. A "switching strategy" depends on repeat occurrences to work, as it has to gather that information. So just how many envelopes do you think you'll get to open?

You did not read my replies. Like this one, where I said "you have no information that would let you calculate [the expected gain or loss]" and you replied with "you can't really calculate the expected value" as if I hadn't just said the same thing. — JeffJo

That was me quoting myself from earlier in the thread. I posted that before you even joined the conversation.

How's the weather in Russia these days?

With all the evidence we now have about how wide spread the practice of homosexuality is in the animal kingdom, only the ignorant could possibly concluded that homosexuality is somehow "counter" to evolution. Clearly homosexuality is neither culled by evolution nor does homosexuality impede evolution.

That is a horrible understanding of both homosexuality and evolution; however, what is even more outlandish is the notion that "the church" has a significant role in this. Your church as you know it, has not been around long enough to be a relevant factor. Especially since "the church" in relation to the history of homo sapien evolution has not been a wide spread influence. The hominid lineage diverged from apes about 5 to 8 million years ago and humans have been around for about 100,00 years. Furthermore homosexual behavior has been observed in about 1,500 animal species, with some species having as much as 80% of the population with homosexual preferences. A realm completely outside "the church".

The data are clear, homosexuality is wide spread, has likely been around forever, and is here to stay. The conclusion that somehow it is counter to evolution could only come from a mind that has no clue what that even means.

The more unnecessary assumptions you add to your model the more it will inflate your uncertainty; however, this uncertainty will not show up in your calculations. This is the price you pay for those assumptions.

Some probabilistic models are more reliable and accurate than others.

@JeffJo this is why I am stonewalling you, as you keep trying to argue points with me that I agree with and have already commented on. It is a clear indication to me that either you did not read the thread or you skimmed through it. Whatever the case, you have no clue what my actual position is, even though I have posted extensively on it.

If you do look, THERE IS PROBABLY AN EXPECTED GAIN OR LOSS, but you have no information that would let you calculate it. This is different from knowing it is 0. — JeffJo

So since you don't know which case you are in after seeing Y and they are not equal you can't really calculate the expected value. Now if you never opened A and never saw Y, that is a different story. — Jeremiah

You did not read the thread.

Did you read that? — JeffJo

I stopped there.

What you think I have issue with is not what I have issue with. I literally mean you are misinterpreting me. Furthermore what you are harping on is something I already commented on towards the start of the thread.

You are misinterpreting what I said, what your link says and your source is Wikipedia.

People who might be reading this thread, who have no exposure to random sampling or Bayesian inference, should not walk away with the idea that using random sampling is a random decision or that Bayesian inference is about guessing.

I already made several comments on the justification behind random samples. Read much?

You don't "guess" a prior. Even if you use an uninformative prior you have to justify that approach.

I already know where you stand, Michael.

Still not interested. I don't even read your post, I just kind of skim over them. You know, like you were doing to me.

You don't "guess" a prior. Priors have to be justified. If you don't know you use an uninformative prior.

The simple truth of this is, if I walked up to you on the street and handed you one envelope and said one of these has twice as much as the other, you'd have no clue as to range, distributions or anything of that sort, even after seeing Y. You could make speculations, but that is all they would be and they would carry a high degree of uncertainty you could never account for in your calculations, as they would just be wild guesses.

You could spin all types of models, but you're still just shooting in the dark. The truth of it is, in that moment, switching or don't, you stand to gain x and you stand to lose x. That is the one thing we know is constant.

without saying which it is that you think is correct — JeffJo

I have been very clear on my position, and this is why I stonewalled you. It was clear to me that you were not reading my posts. You kept "disagreeing" with me on points I agreed with you on.

Random selection, which means equal probability, mitigates observational bias by treating each n in a population the same. This helps maximize the influence of an unknown population distribution on your sample.

This is also the reason it is used as an uninformed prior in Bayesian statistics, by setting the unknowns equal the prior will have less pull on the posterior, allowing your sample to have more influence on the outcome.

If you don't know the distribution you try to give the population distribution as much room as you can to revel itself. You do this by trying to limit the influence of your personal bias both conscious and unconscious.

Not really something I should have to explain, but it seems it needed clarification.

[ I suggest that readers and contributors] check the definition of a random sample. It has a very interesting definition in this context, which I actually already posted in this thread.

Ask yourself why they generally are using equiprobability as a prior when they are uninformed. There is a reason why, [and] why random samples use equiprobability.

[Consider] the philosophy in Bayesian statistics of using an uninformative prior.

I'll tell you what next time I do a class project I won't use a random sampling method and we'll see if I get an F or an A. Good thing I am learning how to do statistics on these forums and not in the classroom.

Over the long run an equiprobability as a prior has the least amount of drag. Unless you can justify using a weighted selection method it is the best approach.

I should note a credit to the philosophers, I have found, after crossing over to science, that the science types do seem to have problems with the whys of their doings.