Mandatory funding of government.
Why do you think so? Based on their answers, lmd and dface don’t seem to agree. (I don’t agree either.)
In programming: if a function called max took a list of pairs of integers and the documentation said “returns the maximum pair of the list” I would assume the sums of the pairs were used to compare.
Also x and y are of the same type. If the values were in dollars you would say 2.) gives the most total dollars and is therefore the maximum pair. The question didn’t ask to compare pairs like:
- 5x,5y
- 4x,10y
- 11x,y
In this case I would want to know what x and y were worth.
I meant this in the context of general maximization, not in every situation where you need to convert a pair of numbers into a single value, which this sentence states.
No I dont think so.
Here I think was the intuition behind my choice: Option 1 seemed to get the highest values of both x and y. Option 2. seemed to represent maximizing y but with a decrease in x, and 3. seemed to be maximising x but with a decrease in y.
Yeah sure, seems like there could be. But it also seems like there could be problems maximising multiple things. I’ll try looking it up and see what I find. I’m going to be afk for a couple of days.
Let’s say we add option 4.: x=10,y=11. By your reasoning wouldn’t 4. be maximizing y but with a decrease in x (compared to 3.), and therefore not maximizing both?
I don’t think you can conclude 2.) is worse by only considering the x value and disregarding the y value.
Sorry, I meant decreased relative to option 1.
In your example of an option 4 I would consider that the best in terms of maximising x and y.
I think my intuition here resembles the reasoning @Dface gave.
Is this a trick question or am I missing something? I read some of the further discussion below the two posts quoted above and I’m confused: how do we know how much x or y can be increased too? Maximizing is increasing it as much as possible, right? Did Elliot give enough information here to know whats the maximum value of x and y?
I dont want to disregard the y value on 2.) cuz it is biggest out of the 3 options. However, I think the “and” in the question means we gotta take x and y as working like a team. Like, both x and y have to be maximized. Since x on option 2.) is not bigger than the other two options’s xs, option 2.) doesnt pass the maximize both values check list.
I still dont know why 1.) maximizes both values btw. I think im just using process of elimination
One way to think about it is you start with 0 of x and 0 of y. Then you have 3 ways to get more. You predict the first plan will get you 5 of x and 5 of y. The second plan will get you 4 of x and 10 of y. The third plan will get you 11 of x and 1 of y. Your goal is to maximize both x and y (which could be all kinds of things, including e.g. profit and customer satisfaction). Which plan should you choose?
1 Like
I dont think any of the three options maximize x and y cuz y in option 2 is the highest y could be and x in option 3 is the highest x could be. None of the options have both x and y maximized.
2 Likes
I guess where I’m a bit confused is that these are our only options, correct? How do we maximize x and y given that we can only do these three plans. I tried looking up maximizing stuff for math and either the material was covering stuff that was too advanced for me or stuff that I wouldn’t know to apply here.
What option should we choose? I don’t know how to word it but I would choose the option that gives us the largest of both values compared to other ones. So I would pick option 1. Assuming we can only do these three plans, if we choose option 2 we aren’t maximizing x as much as we can, if we choose option 3 we aren’t maximizing y as much as we can. Picking either 2 or 3 maximizes one value, but only 1 maximizes both.
Not @ActiveMind but I remember this from Atlas Shrugged:
“In his lifetime, every one of my ancestors raised the production of d’Anconia Copper by about ten per cent. I intend to raise it by one hundred.”
“What for?” Jim asked, in sarcastic imitation of Francisco’s voice.
“When I die, I hope to go to heaven—whatever the hell that is—and I want to be able to afford the price of admission.”
“Virtue is the price of admission,” Jim said haughtily.
“That’s what I mean, James. So I want to be prepared to claim the greatest virtue of all—that I was a man who made money.”
“Any grafter can make money.”
“James, you ought to discover some day that words have an exact meaning.”
I don’t think Francisco’s primary goal in the story was to ever maximize profit and I don’t think he maximized profit in the normal way, but he seems the closest to one of Miss Rands heroes I can think of that wanted to maximize profits.
First Francisco says he wants to raise production, not profit. Then he suggests that he only values certain types of making money that grafters can’t do.
1 Like
If you want to analyze this more (you don’t have to), here are two options:
- Go through the discussion history, look at all of LMD’s claims and premises, and see if you agree with them.
- Think about what you think maximizing is and how it works yourself, in general, to try to get an understanding of it that you’re comfortable with. Then, afterwards, you could try applying that to this question.
I tried looking up things like:
- how to maximise two parameters
- how to maximise two things
- optimising two variables
Everything I found used multivariable calculus, which I don’t understand.
I suspect that that kind of advanced math isn’t necessary to reach an answer on this, is that right?
So you had a pre-existing opinion that
- One can maximize 2+ different things.
- You know what that means and how to do it some.
If it required multivariable calculus, then (2) would be incorrect.
From this conversation, if it doesn’t require multivariable calculus, it’s also looking like (2) is incorrect. You thought you could explain how to do it, but when I asked for details and numbers, you didn’t have a clear answer.
If (2) is incorrect, then your belief in (1) should be questioned.
Does that make sense? Thoughts?
Yes that makes sense.
I knew doubting (1) was an option. But I couldn’t think of a reason why it might not be possible and my intuition said it was.
So what do I know. I have been unable to explain how (1) is done, and unable to explain how (1) is not possible. And the calculus lead on (1) I don’t understand.
I think maximising one thing is possible, and I think I understand how to do it. It means increasing the thing as much as possible. Selecting between values of x for which one maximises it means selecting the highest given value of x. So given what I know, it seems my position should be to doubt maximising more than one thing is possible.
Let’s say x and y are two different people. If they were going to purchase something together with the money then this makes sense. However, if they’re going to use their money for themselves then it doesn’t make sense. With my previous logic x=1$,y=100$ would maximize over x=50$,y=50$, which doesn’t make sense if the two people were going use their money independently and we’re claiming to maximize both x and y. I think the standard for “maximize x and y” should treat x and y as independent things. So (2) would be the wrong choice.
(3) is ruled out (it ignores y and maximizes only x). So I need a way to make (1) the maximum.
I thought of an algorithm that makes (1) the maximum:
Algorithm
Find an option where both x and y are larger than the smallest variable of the current option. If there are multiple options with the same smallest variable, pick the one with the largest value for the other variable.
For more than two variables you substitute “x and y” with “all variables”. When there are many options with the same smallest variable: take these options, remove the smallest variable, and run the algorithm on these modified options (which now have n - 1 variables with n being the previous amount of variables for each option).
This algorithm doesn’t ignore any variables, because when one variable is increased above the other, then it’s time for the other to get increased. I think that makes sense if you’re trying to maximize both.
A walkthrough of the algorithm on the given example:
Algorithm walkthrough
Starting with the lowest variable: y of (3) which is 1, since the x value is more than 1 we’ll look for an option with more than 1 for x and y (or 1 at one of the variables and the other variable being higher than (3)'s x, but I’ll ignore such cases in my explanation). (2) fulfills the criteria because both of its values are above 1. (2) has 4 at x and more than 4 at y, so we’ll look for an option that increases x without going below 4 + 1 at y. (3) fulfills this criteria, and there are no options with more x and y than (3).
(Notice how the y of (2) is treated as just “more than 4” since it doesn’t matter how large it is given it is more than 4.)