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35224 No.36062   [Delete]   [Edit

Let's see if Aurorachan knows how to logic.

In Ancient Rome, there are five senior Senators in the Roman Senate who are all very intelligent but also politically cunning and greedy. A recent military campaign successfully conquered 10,000 square kilometers of land, and the Roman Emperor expects these Senators to distribute the lands fairly amongst themselves for governing.

The most senior Senator, known as the Consul, is expected to make a proposal on how to divide the lands. All of the five Senators shall vote on how the lands shall be distributed according to the proposal. If more than half of the Senators vote "Yes", then the 10,000 square miles of land shall be distributed as according to the proposal.

To emphasize efficiency in the voting process, the Emperor passes a law in which a Consul who makes an ill proposal during land distribution shall be stripped of power and his Senatorship.

Thus, if the Consul fails to acquire more than half of the votes (himself included), then he will lose support in the Senate, and shall be removed from his voting rights and his Senate seat. The remaining Senators shall vote again, with the next most senior Senator as the new Consul to make the proposal, bound to the same law of the Emperor.

What is the maximum number of square kilometers that the original Consul can distribute to himself without risking loss of his seat in the Senate? Explain your logic.

To keep things simple, let's round to the nearest hundred.

Also, since it wasn't pointed out noticeably in the original pasta, I'll go and add to the OP: You do need MORE than half of the votes to win. Even 50/50 (if you were a consul unfortunate enough to face an even number of voters) is not enough.

Last edited by moderator 13/05/18(Sat)18:27.

>> No.36063   [Delete]   [Edit]
File: 1368917355915.jpg -(73.4 KiB, 476x484) Thumbnail displayed, click image for full size.

According to my calculations, at a glance the safest way to divide up the land would be to assign 2000 square kilometers of it to each senior senator, including the Consul.
HOWEVER, this is assuming that they are all fair and reasonable people, which according to your first paragraph is not the case. As such, it might be safer for the Consul to give up 800 square kilometers of his land from that calculation, and give 200 of it to each of the other senior senators.
This results in him acquiring less land than his peers, but on the other hand he is likely to keep his office.

Last edited 13/05/18(Sat)18:49.

>> No.36064   [Delete]   [Edit]

That would end up with a distribution like this.

#1 - 1,200
#2 - 2,200
#3 - 2,200
#4 - 2,200
#5 - 2,200

However, here is where the dilemma gets really tricky: if the first Consul is removed from the Senate, the potential "equal" shares of the remaining four will become larger. Would it not still be more advantageous of them to say "no"?

>> No.36066   [Delete]   [Edit]
File: 1368920864390.jpg -(14.4 KiB, 150x222) Thumbnail displayed, click image for full size.

If the Consul really wants to be a douche, all he has to do is offer two of them more than the others and buy out their votes, thus ensuring a 3 out of 5 vote. Office secured and he gets a nice hefty piece as well.

By making them fight amongst themselves who get to be the 2 special senators with larger portions, he then keeps both animosity off of himself and ensure any rivalries will be directed at eachother rather than him. The two who he picks will then also ensure he remains in his position and rightfully so by controlling all the rest. This could lead to unforseen problems in the future but this is the best way to maximize his own profits and keep his position secure for the time being.

Just an example but you can't make the losing completely unfair unless you want them after all your heads.

Choice Senator:2500
Choice Senator:2500
Other Senator: 1000
Other Senator: 1000

Last edited 13/05/18(Sat)19:47.

>> No.36067   [Delete]   [Edit]
File: 1368921211683.jpg -(26.4 KiB, 497x222) Thumbnail displayed, click image for full size.

You got a point there, guess I was thinking TOO logically.

And Koon has the right idea here. Have the Consul play off of the greed of his peers to have them fight against each other instead of him directly.

>> No.36068   [Delete]   [Edit]

Actually, certain Senators might still gain more of an advantage by voting no even if your offer to them is higher than the others.

Remember that if you don't get at least 3/5, there will be a progression of the next most senior guy taking your place and having to make a proposal of his own to the remaining members. If he doesn't, he will be kicked out and replaced by the next and so on.

Thus, it really does change things depending on which senators you pick. Do you go for the next two guys in line? The last two? Some other combination?

Also, since it wasn't pointed out noticeably in the original pasta, I'll go and add to the OP: You do need MORE than half of the votes to win. Even 50/50 (if you were a consul unfortunate enough to face an even number of voters) is not enough.

Last edited 13/05/18(Sat)19:54.

>> No.36069   [Delete]   [Edit]
File: 1368921381779.jpg -(17.5 KiB, 352x318) Thumbnail displayed, click image for full size.


The amount of land isn't the only variable here either so you could also look at in an angle on the quality of land. Say you give them a smaller piece but it's nice fertile land and not 1000 sq km of swamps. No one wants to keep building their castles only for them to sink in the swamp over and over.

>> No.36070   [Delete]   [Edit]
File: 1368921701505.jpg -(50.2 KiB, 600x600) Thumbnail displayed, click image for full size.


The next most senior guy will be considered of course but if he can't be bought then by turning the others against him you ensure his hands will be tied. he could offer them more in order to depose the consul but by doing so he kills off his own chance at the land and i doubt very much he would do that.

In any case, I would make it so that in order for them to receive their land they have to sign a contract of written agreement for their votes. If a senator goes back on his word that is written in his own ink and exposed publicly. He will likely lose credit to everything himself and no one would want that.

>> No.36213   [Delete]   [Edit]

Since this has been off the first page for a while now, I'm gonna bump it and give people one last chance to weigh in before I reveal the super cool solution I came up with!

I didn't make up the puzzle, I got it from a thread on 4chan. I found the answer that the OP claimed was the real answer to be unsatisfactory. I'll reveal what that was too, even though mine is better.

>> No.39874   [Delete]   [Edit]

What i've deduced is that if Consul fails to get majority, the senator who gives winning proposal is certain. he is no.3.

>> No.39875   [Delete]   [Edit]

pay fourth senator more than 1/3 and second man more than 25%
that will make maximum availability for Consul =
less than 1-(.25+(1/3))= less than .416667 of total= 4166.66666666666666666666666 Square miles

Thank you

>> No.39876   [Delete]   [Edit]

actuall, for the second man, anything more than 20% should do.
So now our Consul gets anything less than 1-((1/3)+0.2)*10000= anything less than 4666.66666666666 square miles

>> No.40429   [Delete]   [Edit]

the consul will retain all 10,000 as they vote during session as the greatest fear is disobedience to the empire. if it were not divided evenly as ordered, they would all be stripped of power and protection. as no single body can be equal to the emperor's, the senators agree that each will build a house the one plot.

>> No.40430   [Delete]   [Edit]

as each senator votes, they must vote no either way for any proposal every time. each time, another consul is made and the old one retires with a house to be built later.

>> No.41144   [Delete]   [Edit]

Senator 1: 0
Senator 2: 300
Senator 3: 100
Senator 4: 0
Senator 5(Consul): 9600

And unless this ever gets revisited, I'm not explaining squat :U

>> No.43874   [Delete]   [Edit]
File: 1452455920000.png -(316.5 KiB, 600x637) Thumbnail displayed, click image for full size.

Ah, good, you got something similar to me~

The senators are rational and scheming, intelligent men who can think ahead to how this situation will go if they allow the first few consuls to be retired. If they're made an offer that's better than the next consul in line will give them, they will take it. They won't just sit by like morons and let it get all the way to the 5th consul who would just take everything. Keep in mind as well, that if you don't get a majority vote, you lose both your senate seat and any chances of getting land. You're basically voted out of the system. Also, 50/50 is not enough to win. There must be an odd number of senators to have any chance at all.

Even the third consul is too far, because he's in a position to be super greedy and probably still win.

What we're asking here is what the very first senator to be made consul can propose that will assure him a victory. What's the maximum amount of land he can propose for himself and not be voted down? My logic is as follows:

Let's say you lose. Here's what will happen if each successive Senator becomes the Consul:

if 2nd consul is appointed, here is how he would have to distribute the land in order to get a majority vote:

2-Consul, will vote yes to own proposal
3-Would need a huge payoff to be convinced to vote yes, and I mean huge
4-Pressured to say yes to any fair deal because 3 will give an unfair deal next time and there is no victory for a 4th Consul
5-Can win no matter what happens, his biggest advantage is to say "no" every time and get all 10,000.


if 3rd consul is appointed:
Last chance of anyone except #5 winning.
3- 9,900
4- 100 (it's either 100 or nothing and no senate seat.)
5 - 0 (fuck you #5)

If 4th consul:
Automatic loss unless he gives away all the land, 50/50 vote is not good enough.

5th Consul:
Last guy, last vote. All 10,000.

  • ----------------------------MY CONFIGURATIONS------------------------

The prices of the senators' votes:
1- This is you.
2-100 (he can't win as Consul unless he gives all the land away)
3-9,900 (can't be bought for any less than 9,900 because he stands to gain that much when he becomes Consul which will certainly happen if #1 fails)
4-200 (best he's going to get from ANYBODY)
5-10,000 (fuck this guy, seriously)

  • ----------------------------------------------------------------------

So in order to win as the first consul, you can propose this and get away with it:


Last edited 16/01/10(Sun)14:58.

>> No.43892   [Delete]   [Edit]


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