The CubeCast 2.0 - Montage Released!

[Stefan]

Thank you

Now you have a mistake in the 6 people case, where you overlooked the option to offer 2 to both A and B, and 0 to C.

 

[sneaklyfox]

Thank you

Now you have a mistake in the 6 people case, where you overlooked the option to offer 2 to both A and B, and 0 to C.

Oh yes, I did do that when I worked it out on paper but when I typed it up I forgot what I was thinking and left that out.

 

[Stefan]

Sorry, I should have made clear that that's the first error. Your answers for 7 and 8 people are wrong as well.

And I just saw your edits:

Edit2: And I still think it's more reasonable to assume that your vote is yes if you are offered everything. No unnecessary loss of life, you know.

That would be a bias for others, which the puzzler explicitly says they don't have.

And again, the same is true if their options are for example:
yes => 1 cent
no => 1 cent
Here, 1 cent is everything they can get. And if they did have something against unnecessary loss of life, you wouldn't need to offer 2 cents! But you do offer that.

 

[sneaklyfox]

Sorry, I should have made clear that that's the first error. Your answers for 7 and 8 people are wrong as well.

And I just saw your edits:



That would be a bias for others, which the puzzler explicitly says they don't have.

And again, the same is true if their options are for example:
yes => 1 cent
no => 1 cent
Here, 1 cent is everything they can get. And if they did have something against unnecessary loss of life, you wouldn't need to offer 2 cents! But you do offer that.

Yes, I know. It follows through to 7 and 8. I did that originally in my paper. Didn't have time to write out that that was so before dinnertime. But generally I still stick with my original solution. No, it's not a bias for others. It's just stupid. Imagine if you were offered all $8M. That's not a bias for other people. It's just logical since you cannot possibly get more than that. It just means you are happy with how much you're getting. Anything that's more than expected is of course something you would vote yes to, but they can't expect to get more than the maximum amount.

 

[Stefan]

Yes, I know. It follows through to 7 and 8. I did that originally in my paper. Didn't have time to write out that that was so before dinnertime.

So did you, on paper, finally arrive at my solution then? (The one I presented first but dismissed because there were several optimal splits)

No, it's not a bias for others.

Yes it is.

It's just logical since you cannot possibly get more than that.

In a 1 cent vs 1 cent situation, you also cannot possibly get more than that. And yet you agree that a "yes" costs 2 cents. You're inconsistent.

 

[sneaklyfox]

So did you, on paper, finally arrive at my solution then? (The one I presented first but dismissed because there were several optimal splits)

If it's the one that's still there on page 7 then no, I think I had some other answer because 1 cent is not enough.

Yes it is.

No it isn't.

In a 1 cent vs 1 cent situation, you also cannot possibly get more than that. And yet you agree that a "yes" costs 2 cents. You're inconsistent.

Yes, you can get more because the maximum amount is actually $8M so technically you could get more if someone offered you more. Perhaps you would be happier if I said you cannot possibly be offered more though actually no one would offer you more.

 

[Stefan]

If it's the one that's still there on page 7 then no, I think I had some other answer because 1 cent is not enough.

Yes, that one. Though I'll quote it here because I think you misread:

John gives 1¢ to the third-youngest and 2¢ to each of three of the five oldest and keeps the rest

So is that what you got?

No it isn't.

Yes it is. Particularly since your justification was "No unnecessary loss of life, you know". How is that not a bias for others? Their own life is not at stake here, so it must be someone else's.

If it was me and I'd get $8 million whether I say yes or no and I have no bias for or against the other guy, I'd flip a coin or something like that. My life is not affected, the money I get is not affected, and whether or not I get "the maximum possible" is not affected. The two options are worth exactly the same to me. I'm *not* guaranteed to say yes.

 

[Deleted member 19792]

By looking at a somewhat random argument in a thread, whether it is relative or not, it is appropriate to ask a question that might tickle everyone's minds.

Could someone tell me why pigs like to roll in mud?


Also, this was an entertaining show Nice job. Brings a lot back.

 

[sneaklyfox]

Yes, that one. Though I'll quote it here because I think you misread:

So is that what you got?

Ok, when I looked back at p.7 to check what you had written again I just read your final solution which was "John gives 1¢ each to the third-youngest, the fifth-youngest, and the two oldest, and keeps the rest." which was your answer because you believed there to be only one correct solution. But yes, I see where you're getting the 2 cents to each of three of the five oldest.

Yes it is. Particularly since your justification was "No unnecessary loss of life, you know". How is that not a bias for others? Their own life is not at stake here, so it must be someone else's.

Ah, I was saying that partly in jest. I didn't seriously mean that A would vote no because of the loss of life. If I started to consider ethics and more, I (if I were oldest, for example) would not vote yes for anything less than what I think is a decent amount and 1 or 2 cents is negligible. But all the money is all the money there is. That has nothing to do with other people.

If we truly believe there to be one correct answer then probably we should just go with this assumption: Anyone votes yes if they think they will not be offered more. This means that in the 2-person case, A votes yes. You can keep offering 0 to everyone because everyone thinks, "I'm not going to get any money anyway" except the next youngest person. Then Johnny gets all the money to himself with 7 yes votes and 1 no vote.

Edit: Now that my kids are in bed (finally), I can give a bit more time to look at your solution. Why do you give the 1 cents to 5th youngest(4th oldest) and two oldest if it can be any three of the oldest 5? What about the 3rd or 5th oldest?

 

[Stefan]

If we truly believe there to be one correct answer then probably we should just go with this assumption: Anyone votes yes if they think they will not be offered more. This means that in the 2-person case, A votes yes. You can keep offering 0 to everyone because everyone thinks, "I'm not going to get any money anyway" except the next youngest person. Then Johnny gets all the money to himself with 7 yes votes and 1 no vote.

Hmm, at first I didn't find such an affinity for "yes" rational, but it would help end the procedure earlier. And since time is money... ok

Edit: Now that my kids are in bed (finally), I can give a bit more time to look at your solution. Why do you give the 1 cents to 5th youngest(4th oldest) and two oldest if it can be any three of the oldest 5? What about the 3rd or 5th oldest?

That's because those are two separate answers stemming from two separate simulations. One for each of the two possibilities I mentioned:

If someone knows they'll get either 0¢ or 2¢ if they vote against me, clearly I can buy their vote by offering them 2¢ (they can't get more and it beats the expected value), but 1¢ might be enough (matches the expected value and beats the minimum).

That 1 1 0 1 0 1 0 X solution is for the latter case, where they can be bought with 1¢. If it's unclear why 1¢ might be enough, i.e., why 1¢ can be considered better than "0¢ or 2¢", imagine you're given this choice:

Option 1) You get 1 billion dollars.
Option 2) You either get 2 billion dollars or nothing (50/50 chance).

I think pretty much everybody would take option 1 (unless they have a particular need for more than 1 billion dollars, like they'll die tonight unless they pay 1.5 billion for a new heart, or you want to feed the poor people all around the entire world so you actually need even more). The expected value is the same, and one billion should be more than you'll ever need. A second billion isn't that valuable. This is an extreme example to make it intuitive, but it's true in general: The first $x are more valuable than the next $x because a fixed amount of money gets less important the more money you already have.

 

[sneaklyfox]

Hmm, at first I didn't find such an affinity for "yes" rational, but it would help end the procedure earlier. And since time is money... ok

Yes, to end the procedure earlier.

That's because those are two separate answers stemming from two separate simulations. One for each of the two possibilities I mentioned:

That 1 1 0 1 0 1 0 X solution is for the latter case, where they can be bought with 1¢. If it's unclear why 1¢ might be enough, i.e., why 1¢ can be considered better than "0¢ or 2¢", imagine you're given this choice:

Option 1) You get 1 billion dollars.
Option 2) You either get 2 billion dollars or nothing (50/50 chance).

Clearly option 1 is far better (unless you have a particular need for more than 1 billion dollars). The expected value is the same, and one billion should be more than you'll ever need. This is an extreme example to make it intuitive, but it's true in general: The first $x are more valuable than the next $x because a fixed amount of money gets less important the more money you already have.

Oh, I perfectly understood why 1 cent might be enough. I forgot I had to go through the simulation again to change the split proposals starting from the 6-person case. Now I get your second answer as well. You could have explained it better the first time (p.7). But I'm not positive that a sure 1 cent is better than 0 or 2 with 50/50 chance. If it was me, I'd toss a coin to see whether I should vote yes or no and risk double or nothing. Imagine that instead of it being a billion dollars which makes you feel like it's important, it's a pebble. Take away the fear of risk. It's the same as offering someone who's going to get nothing nothing which isn't enough for a yes vote.

All this to find out that Waffo, Ranzha, and Mitch don't already know the supposed answer?

I should be cubing instead of this...

Or better yet, sleeping to save up energy for taking care of 5 sick little kids...

Edit: Remember, these guys have just been involved in bank heists. They're probably risk takers.

 

[JemFish]

Hey, this looks pretty cool. I just finished listening to the Collin Burns episode and was surprised that he's only a year older than me (no, I'm not 8). Will listen to the Noah Arthurs episode tomorrow.

 

[Ranzha]

Sorry about the delay but hey, it's the CubeCast.

anyway, we're proud to announce probably our latest episode with Kit Clement! Please check it out in the episodes page!

Also under Season 3 is a montage compiled by the ever lovely montage master herself, Sarah Strong. Many thanks to her!

As for reminder, please send in all feedback, questions, taglines etc to our email. We also have a puzzler so send in all submissions us as well for a chance to win $5 to theCubicle.us.

Our next guest is Jayden McNeill, holder of both Skewb WRs, CRs for 2x2, Pyraminx, and Square-1 averages and one of the fastest solvers in Australia overall! Please stay tuned for that!

Watch Episode 3 here:

Spoiler

Episode 3 show notes.

Check out Sarah's Season 3 montage here.

Thanks for listening,

Ranzha, Waffo, and Mitch

 

[Stefan]

So who of you is 20 years old and why are you already thinking about retirement?

(not even going to try, btw, not interested in learning how it works)

 

[Ranzha]

So who of you is 20 years old and why are you already thinking about retirement?

(not even going to try, btw, not interested in learning how it works)

I'll be opening an IRA pretty darn soon. The more years to compound, the better off I'll be =)

 

[charmrence]

Do you just mention random NRs on the podcast? Because you missed a few.

 

[Kit Clement]

Do you just mention random NRs on the podcast? Because you missed a few.

This was recorded on February 28th, so NRs in the past two weeks will probably be mentioned in the next episode.

 

[Ranzha]

Do you just mention random NRs on the podcast? Because you missed a few.

These should have been accurate between the 13th and 27th of February. If results for competitions in that time period were posted after we recorded, there's no way we could have reported on them.

 

[CAL]

You have forgot a hole bunch of NR's at Hessen Open on 21th and 22th

 

[charmrence]

These should have been accurate between the 13th and 27th of February. If results for competitions in that time period were posted after we recorded, there's no way we could have reported on them.

I realise that, but there were a few at the comp where the clock WR happened, so that's why I was wondering.