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 Emily Haney-Caron
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#43302
Hi Mike,

Thanks for posting! Are you referencing the inference Dave outlined early on in this thread? If so, the inference is just that at least one L must vote for it; that is, not all three Ls can be against. If I misunderstood your question, though, please let me know and I can try again. :-D
 hope
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#80768
Dave Killoran wrote:Hi Marie,

Thanks for the question. This is a very famous game, and one that we can really use as a tool to understand how games work. I'll give you two tips to help your setup:

First, let's start at the foundation of the game: what base did you choose for the game? Many people use the 7 judges, but instead, try the two groups of For votes and Against votes. That creates a two-value system in the game (which is immensely powerful) and also helps capture part of the numerical limitations.

Second, now that you have the two-value system, very carefully consider some of the contrapositives that are created by the rules, and also if any judges have to vote a particular way.

Ok, start there if you could, and let me know if that helps. If it still gives you trouble, we'll go into it a bit more deeply.

Thanks and good luck!
 hope
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#80769
DAVE WHERE IS IT WRITTEN IN THE SCENARIO THAT EACH GROUP HAS TWO VOTES?
 Adam Tyson
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#81197
Hey Hope, be sure to read the rules carefully! The third rule of this game tells us that "At least two of the judges voted for Datalog, and at least two voted against Datalog." So we know for sure that each group (the For group and the Against group) has AT LEAST two votes (and at least one group must have more than that because there are 7 total votes).
 hope
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#81320
Yes Adam I did see that. But what I am confused about is two things: How does the numerical distributions of 5-2 and 4-3 figure into that diagram where L is FOR and C is AGAINST? That diagram doesn't depict either numerical distribution. Second, are the other rules determined to be for and against?

How does CCL get the subscript A and how does MM get the subscript A and how does LL get the subscript F and so on and so on.

I don't see anywhere in the rules that assign those subscripts to those judges. Thank you.
 Adam Tyson
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#81325
Those aren't in the rules, but are inferences based on the interaction of the rules. From the top post in this thread:
The key inference to this game is that at least one L must vote for Datalog because all three cannot vote against Datalog. If all three L’s attempted to vote against Datalog, then both C’s would have to vote for Datalog, which is impossible according to the given rules.
This comes from the last rule of the game, that at least one conservative voted against Datalog. Our two groups should be the For group and the Against group, and so in your base you must have those two groups, each with a minimum of two slots, and there has to be a C in the Against group. From there, you can infer that there must be at least one L in the For group, per the inference described above.

The diagram showing CCL with an A subscript is just conditional. IF the two conservatives voted the same way as each other, that has to be in the Against group. If a liberal joins them, then both the moderates must also join them, giving you CCLMM in the Against group. That leaves only two liberals left, and since the For group needs a minimum of two member, LL has to go in the For group. This doesn't mean that there is always a CCL in the Against group, but only shows what would have to happen if that were to occur.

Also, the two numerical distributions are flexible. They only mean that there is either a group of 5 and a group of 2, or else there is a group of 4 and a group of 3. It's not absolutely predetermined which group must be the larger of the two. For example, while the grouping described above has a 2-5 distribution, with 2 in the For group and 5 in the Against group, there is a possible 5-2 distribution, with the For group consisting of LLCMM and the Against group having CL. The main diagram shows only the thing that must occur in every solution - at least one L in the For group and at least one C in the Against group, with a minimum of two slots per group.

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