How high would presidential nominees' unfavorability ratings have to be to mathematically guarantee that the majority of the country does not support either candidate?

I think that you’re assuming a level of some kind of “actual knowledge” of the chosen candidate’s positions and ideas in order to make some type of informed choice – and which has not been very well demonstrated.

It’s been pretty well demonstrated that a lot of Hillary’s supporters have no idea of her actual stance on many issues here’s a proxy video to represent many such.

Bernie Sanders has no apparent idea of how a modern economy actually works.

And who knows what Trump supporters feel about his stand on many issues, since he himself doesn’t seem to know, changes his statements from day to day and doesn’t seem to be particularly coherent – unless he’s speaking about himself.

So how will these kinds of voters even be able to perceive that their candidates have negative ratings?

I am often voting against, rather than voting for.
This election will be easy. There aren’t many people who sicken me as much as Trump.

The question assumes that candidates always win with a majority. This is false. Many win with a plurality.

Guys, you are making this problem much too difficult. I am not making any assumptions. This is simple arithmetic. If a sufficient number of people dislike both candidates and, assuming, as I said, that they actually vote, there will be a majority who vote for someone they dislike. Trump is actually fairly close to this number. I will give the answer tomorrow.

@LostInParadise So this isn’t a real question, it’s a math test? Maybe you should have said so. I wouldn’t have wasted my time.

Damn, I was never any good at math. I will be following this question with the hope of finding out what the answer is.

Here is the answer and how it relates to the actual favorability rating. Suppose each candidate had a 75% unfavorability rating. What then is the percentage that dislikes at least one of the two candidates? We start by adding 75% + 75% = 150% From this we subtract the number of people who dislike both candidates, which has been double counted. Since we can’t have more than 100%, we can say that at least 50% dislike both candidates, meaning that no matter who they vote for, this 50% would be voting for someone they dislike.

Is 75% an absurdly high number. Trump comes pretty close. Take his net 41% unfavorability and divide in half to get 20.5%. His favorable rating is 50% – 20.5% = 29.5% and his unfavorability rating is 50% + 20.5% = 70.5%, which is pretty close to 75%. Doing the same with Clinton’s net 23% unfavorability gives her 38.5% favorable and 61.5% unfavorability. Applying the same analysis as above we get 70.5% + 61.5% = 132%, so at least 32% of the electorate dislike both Trump and Clinton. Something seems odd if about ⅓ of the electorate does not like either candidate.

You’re still making assumptions. There are more than two candidates.

@Irukandji that is true but in the end “There will be only two” that sounds oddly familiar for some reason

Not sure if just assuming anything over a hundred is the percentage of people who dislike both. It seems like you have to factor in the percentage of people who are favorable to a particular candidate somehow but not sure how.

@rojo In the end, there will be only one—the person who gets elected. The idea that there will be only two is a self-fulfilling prophecy in which third party candidates can’t win because no one will vote for them and no one will vote for them because they can’t win.

Well, the question assumes there will be two (__either candidate__).

I think you have to accept as a given that everyone hates the third party candidate otherwise they would be one of the two main rivals.

I think the number of contestants doesn’t really matter if their unfavorability rating was also dismal you would be dealing with x, y and z instead of just x and y.

Besides, even if the third party candidate was Jesus Christ and you have to assume that the majority of the population would not admit to not liking him he would not be elected with our system so you would still get a president where the majority of the citizenry did not support them.

@rojo I know the question assumes that there will be two candidates. But it also tries to ground the question in the real world, where there are more than two candidates. That’s why I think the assumption is problematic (although the whole question is problematic because it’s a math question masquerading as something else).

Also, there’s a big difference between “the majority doesn’t like the candidate” and “the majority voted for someone they dislike,” and having more than two candidates brings this difference to the foreground. Suppose there are three candidates. Candidate A is liked and supported by 40% of the population, Candidate B is liked and supported by 35% of the population, and Candidate C is liked and supported by 25% of the population. Suppose also that everyone totally hates the two candidates that they don’t like and support. In such a situation, it is possible for everyone to vote for someone they like while at the same time having a winner that the majority dislikes (in this case, A will win despite a 60% disapproval rating).

The other thing to notice is that nobody wins with a majority in the scenario I just described. Candidate A wins, but only with a plurality of the vote. Before @LostInParadise edited the question, there was more of an explicit assumption that all candidates win with majorities rather than pluralities.

You would be assuming that those who do not vote, did so because they hated all the choices. I’ve met plenty of people in the past who simply could care less because they think it doesn’t matter who you put in the white house because they believe that Presidents are little more than just a face for the nation. Like the Queen of England. Just a PR man.
And many won’t vote because they can’t be bothered. They have their own concerns and the nation doesn’t seem to concern them.