>From nomic-discussion-owner@teleport.com Fri Nov 10 05:13:37 1995 Received: from desiree.teleport.com (desiree.teleport.com [192.108.254.21]) by Shamino.quincy.edu (8.6.12/8.6.9) with ESMTP id FAA07965 for ; Fri, 10 Nov 1995 05:13:31 -0600 Received: (from daemon@localhost) by desiree.teleport.com (8.6.12/8.6.9) id DAA13600 for nomic-discussion-outgoing; Fri, 10 Nov 1995 03:09:23 -0800 Received: from aurora.cc.monash.edu.au (gardner@aurora.cc.monash.edu.au [130.194.1.91]) by desiree.teleport.com (8.6.12/8.6.9) with ESMTP id DAA13594 for ; Fri, 10 Nov 1995 03:09:17 -0800 Received: (gardner@localhost) by aurora.cc.monash.edu.au (8.6.12/8.6.4) id WAA11981 for nomic-discussion@teleport.com; Fri, 10 Nov 1995 22:09:12 +1100 >From: Steve Gardner Message-Id: <199511101109.WAA11981@aurora.cc.monash.edu.au> Subject: The Cereal Box CFJ (790) To: nomic-discussion@teleport.com (Nomic Mailing List) Date: Fri, 10 Nov 1995 22:09:09 +1100 (EST) X-Mailer: ELM [version 2.4 PL21] MIME-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Content-Length: 17005 Sender: owner-nomic-discussion@teleport.com Precedence: bulk Reply-To: nomic-discussion@teleport.com Status: RO Never mind, Vanyel, I've dug it up myself: =============================================================== Judgement of CFJ 790 Steve receives 3 points for Judgement. =============================================================== CFJ 790 Caller: Chuck Statement: The Registrar's report of July 12 is incorrect in that it lists Swann as Notary, when in fact the Office is vacant. Barred: Kelly, elJefe, Vanyel Requested Injunction: None Judge: Steve Judgement: UNKNOWN Injunction: none Effects reported by COTC (* indicates new to this report): Brian gains 3 Blots for defaulting *Steve receives 3 points for Judgement ============================================================== ============================================================== History: Called by Chuck, July 17 1995, 14:12 CST Assigned to Brian, July 18 1995, 12:48 UTC Defaulted by Brian, July 25 1995, 12:48 UTC Assigned to Steve Tue, 25 Jul 95 12:41:55 CDT Judged UNKNOWN by Steve Mon, 31 Jul 1995 17:39:51 +1000 (EST) Judgement published {as of this message} ============================================================== Arguments of Caller (Chuck): On June 30, Registrar KoJen announced that the Office of Notary was vacant, and asked for volunteers. On July 7, KoJen wrote: >Volunteers for the Vacant Office of Notary were Chuck and Swann. > >I will now randomly choose the Notary. > >I have a cereal box in my lunch bag. It is "Raisin Squares". I will now count >the number of separate ingredients listed in the ingredients list. If it is >even, Chuck is the new Notary. If it is odd, Swann is. > >The number is 13. > > >The new Notary is Swann. Rule 790 states, in part: [...] the Electioneer shall randomly choose one player from those who indicated a willingness to hold the Office, and that Player shall become that Officer. Thus, if there is no random selection, then the office is not filled. (Random is defined in Rule 1079.) I maintain that KoJen's selection is non-random. Rule 1079 demands that the probabilities be equal for a random selection. No one expects the probabilities of a random selection to be perfectly equal (despite the fact that some Players have claimed that I do); this is unreasonable for any method of random selection. How large a tolerance is then reasonable? IMO, for a choice between two random alternatives, 51-49 is just on the border of being reasonable, and 52-48 is clearly too large a bias. Now, is it likely that the ingredients on KoJen's cereal boxes give an equal distribution between even and odd ingredients? Possible: yes. Likely: no. Let's assume, for a moment, that the cereal boxes in a grocery store are equally distributed between even and odd numbers of ingredients. (Even this is probably invalid, but lets assume it for a moment.) Does that mean that KoJen's cereals are evenly distributed between even and odd? No. KoJen, in all likelihood, does not buy every type of cereal in the store with equal frequency. I can't speak for KoJen, but it seems likely that he buys, oh, 10 or so kinds of cereals regularly (with any others making a negligibly small amount). Are these split 5 odd, 5 even? It's possible. But it's also likely that they're split 6-4 or 7-3. In order to be reasonably certain that the cereals were biased no worse than 51-49, KoJen would have to buy on the order of 10,000 cereals! Objection 1. "But it's equally likely that they're split 4 odd, 6 even or 4 even, 6 odd, so overall the probability is 50-50." This would be true if KoJen bought a different 10 cereals every month. But for the most part, he probably buys the same cereals. Thus, the split is fixed at one value or the other. Objection 2. "But we don't know which way the split goes, so it's still 50-50." The fact that we don't know the probability of KoJen picking an odd or even cereal does not magically make that probability 50-50. Take, for example, the cereals in my apartment at the time I wrote this. 3 of them have an odd number of ingredients, and 1 has an even number of ingredients. Thus there is a 75-25 bias towards odd. Now what would the case be if I had not gone and counted the ingredients on my cereals beforehand? The probability would still be 75 odd, 25 even. The fact that I didn't know what the probability was does not change the probability. Likewise, it is likely that KoJen's selection is biased. The fact that we do not know the bias does not change the fact that it *is* biased. Objection 3. "The assignment of Swann to odd and Chuck to even was random." No, this was an arbitrary assignment by KoJen. He did not use any method of chance, but assigned them arbitrarily. Is this random? It may not be possible to predict in advance of KoJen's decision which will end up with which, but I maintain that the selection is not random. It is impossible for the human brain, in and of itself, to make a truly random selection. Digits that you pick out of thin air are not random. If humans could pick randomly, we would not need to bother with any other random devices at all--how many people would be willing to accept that? Objection 4. "But since KoJen didn't know whether odd or even was more likely, he couldn't bias the outcome by assigning one player or the other to odd or even." Correction: he couldn't *intentionally* bias the outcome. No one is claiming he did. But was his picking either (Swann odd, Chuck even) or (Swann even, Chuck odd) out of thin air truly random? It was not, as we cannot make truly random decisions without some external random device. Objection 5. "But weren't KoJen's assignments close to random?" I'm not saying there was a huge, 90-10 bias in KoJen's assignments. But it seems to me not unreasonable that there might be a 60-40 bias. Objection 6. "Don't the combined near-randomness of KoJen's assignments and the cereal boxes make the selection random?" They make it better, but still not close enough. If KoJen's assignments were biased 60-40 (not an unreasonable assumption, IMO) and KoJen's cereal boxes were biased 60-40 (not an unreasonable assumption, IMO), then the final selection is biased 52-48 (detailed explanation of this can be provided upon request), an unacceptable deviation from 50-50. Thus, it is reasonably likely that KoJen's selection was nonrandom, and thus, the office of Notary has remained vacant. Objection 7: "You haven't proved that KoJen's selection was nonrandom; the burden of proof is on you." I will grant that I cannot prove that KoJen's selection was nonrandom, but neither has anyone proven that the selection was random. The assertion that the burden of proof lies on me is simply untrue. In a CFJ, neither side has the burden of proof--the caller is not required to prove anything! Rather, the burden is on the Judge to search out any relevant information not included in the CFJ and arrive at the correct conclusion emself, regardless of what the caller has or has not "proven." If e is unable to gather information which is relevant to the truth of the CFJ, e must Judge UNKNOWN. (See Rule 591.) ============================================================ Arguments of Judge (Steve): I am reluctant to deliver this Judgement, since I regard it as desirable that there should be a clear cut answer to the question of whether Swann is the Notary. However, careful consideration of the facts and arguments presented have led me inexorably to the conclusion that I am unable to obtain the information necessary to determine the truth or falsity of the Statement. Hence I must, by Rule 591, Judge UNKNOWN. There seem to me to be two issues to consider: (i) was KoJen's 'coin' fair? That is, did KoJen's method of *selection* distribute probability equally between its two possible outcomes? (ii) was KoJen's *assignment* fair? That is, was his method of assigning Chuck to even and Swann to odd a fair one? Now, if the answer to *either* of these questions were 'yes', then that would suffice, in my opinion, to prove the fairness of KoJen's method as a whole. In that case, the Statement would be FALSE. To see this, consider the following two extreme and opposite cases: 1. KoJen uses a completely biased method of selection, whose bias is known to him prior to making the selection, eg, "if today's date is even-numbered then Chuck is the Notary, otherwise Swann is the Notary", when KoJen already knows what today's date is. However, KoJen uses a completely fair method (such as flipping a fair coin) to make the assignment of Chuck to even-numbered days and Swann to odd-numbered days. 2. KoJen uses a completely biased method to make the *assignment*, but a completely fair method to make the selection. I think it's clear that in both these cases, the method as a whole is a fair one. Consider now the actual methods of assignment and selection employed by KoJen. His method of selection is by now infamous - he looked at a cereal box he happened to have with him to see if the number of ingredients listed on it was odd or even. Less attention has been paid to his method of assignment, but it appears that KoJen simply picked his assignment of Chuck to even and Swann to odd out of his head. The question is: are either of these methods demonstrably fair, in the sense given above (which is the sense of Rule 1079)? If either of them are demonstrably fair, the Statement is FALSE. But neither of the methods is demonstrably fair. Considering first KoJen's method of selection, we should need to know much more about which breakfast cereals KoJen buys, and about how the numbers of ingredients listed on them are distributed among the even and odd integers. (And why stop at breakfast cereals? Might not KoJen equally have employed some other foodstuff that happened to be at hand? Even, god forbid, a can of Nile Spice Black Bean Soup?) In the absence of this information, we cannot know whether KoJen's 'coin' was fair. Of course, all this would not matter if it could be demonstrated that KoJen's *assignment* was fair. That's the point of the argument I gave above. But was KoJen's assignment fair? Once again we seem to be confronted with insurmountable epistemological obstacles. It is apparently a part of widely accepted scientific wisdom that human beings are not particularly reliable generators of random numbers, (although I cannot cite specific scientific studies which confirm this). But what this implies for a given human being's ability to choose randomly and fairly between two alternatives on a given occasion is entirely unclear. It seems to me that we should need to know a great deal not only about the neurophysiological mechanisms which underpin the making of such choices generally, but also about how they were operating in this specific instance. And once again, this is information which it seems we cannot have. So we cannot know that KoJen's assignment was fair, either. So, given that we cannot definitively answer 'yes' to either of the two questions above, the Statement cannot be FALSE. But it seems to follow relatively straightforwardly that the Statement also cannot be TRUE. For all we know, KoJen's method as a whole *might* have been fair. It also might not have been. We should need to know a great deal more than we do now - more, indeed, than we're ever likely to know - to determine whether or not it was. Since this crucial information is unobtainable, I must Judge that the Statement is UNKNOWN. ============================================================ Evidence provided by Caller (Chuck): 1. Rule 591 2. Rule 790 3. Rule 1079 4. KoJen's announcement of vacancy of the Office of Notary, Jun. 30 (some header information deleted) 5. KoJen's "selection" of the Notary, Jul. 7 (some header information deleted) 6. Registrar's Report of Jul. 12 (excerpts) The complete text of documents excerpted in 4, 5, and 6 are available upon request. ======1. Rule 591 Rule 591/2 (Mutable, MI=1) Legal Judgements A legal Judgement is either TRUE, FALSE, UNDECIDABLE, or UNKNOWN. The Judgement of UNDECIDABLE is reserved for those statements which are logically neither TRUE nor FALSE. The Judgement of UNKNOWN is for those statements for which the Judge is unable to obtain information necessary to determine whether the statement is TRUE, FALSE, or UNDECIDABLE. The Judge must make a reasonable effort to obtain all information necessary to determine whether the statement is TRUE, FALSE, or UNDECIDABLE. The Judgement must be accompanied by reasons and arguments, which include, but are not necessarily limited to, citations of deciding Rules, past Judgements, and game custom. A Judgement delivered without reasons and/or arguments is completely invalid. Such reasons and arguments form no part of the Judgement itself. However, the Clerk of the Courts must distribute the reasons and arguments along with the Judgement. Any evidence which is used to justify the Judgement, other than appeals to Game Custom or to common sense, must be presented by the Judge. If the Judge introduces evidence beyond that submitted in the Call for Judgement, e must include this evidence in eir Judgement. All such added evidence must be distributed as part of the reasons and arguments by the Clerk of the Courts. History: .. Amended(1) by Proposal 1320, Nov. 21 1994 Amended(2) by Proposal 1487, Mar. 15 1995 ======2. Rule 790 Rule 790/0 (Mutable, MI=1) Filling Vacant Offices If, for any reason, an Office is vacant, that fact shall be announced by the Electioneer. The Electioneer shall be the Registrar; or in eir absence, the Speaker. All Players willing to hold the Office shall notify the Electioneer of that fact within three days of eir announcement of the vacancy. At the end of the three day period, the Electioneer shall randomly choose one player from those who indicated a willingness to hold the Office, and that Player shall become that Officer. This rule applies to Offices in general, and thus defers to Rules for specific Offices. (*Was: 689*) ======3. Rule 1079 Rule 1079/0 (Mutable, MI=1) Definition of "Random" All occurrences of the word "random" or forms of it shall be taken to mean "any one of the choices with equally distributed possibility for each choice". ======4. KoJen's announcement of vacancy of the Office of Notary, Jun. 30 (some header information deleted) Date: Fri, 30 Jun 95 08:15:18 -0400 >From: cogen@ll.mit.edu (David Cogen) To: nomic-official@teleport.com Subject: OFF: vacancy of Notary Notary Office is Vacant. (yawn.) Anyone want it? Notify Registrar within 3 days. -- KoJen ======5. KoJen's "selection" of the Notary, Jul. 7 (some header information deleted) Date: Fri, 7 Jul 95 15:17:15 -0400 >From: cogen@ll.mit.edu (David Cogen) To: nomic-official@teleport.com Subject: OFF: Office of Notary Volunteers for the Vacant Office of Notary were Chuck and Swann. I will now randomly choose the Notary. I have a cereal box in my lunch bag. It is "Raisin Squares". I will now count the number of separate ingredients listed in the ingredients list. If it is even, Chuck is the new Notary. If it is odd, Swann is. The number is 13. The new Notary is Swann. -- KoJen ======6. Registrar's Report of Jul. 12 (excerpts) ===== Agora Nomic Registrar's Reports ================================= DATE OF LAST REPORT : 95.07.07 DATE OF THIS REPORT : 95.07.12 ===== 3.0 Officers (Blue Pages) ======================================= {Listing of Officers, the Speaker; etc. Please see the full listing (section 6) for email addresses.} SPEAKER : Kelly OFFICERS: Ambassador : Kelly Archivist : Vanyel Assessor : Steve Assistant : Vanyel Banker : Andre Clerk Of The Courts : Andre Distributor : Vanyel Herald : Swann Justiciar : Steve Notary : Swann Promotor : KoJen Registrar : Ian Rulekeepor : Chuck Scorekeepor : Kelly Tabulator : Ian ================================================================= End of CFJ 790 ================================================================= Steve Gardner | "Justice? You get justice in the next Dept. of Philosophy, Monash Uni. | world, in this world you get the law." gardner@aurora.cc.monash.edu.au | -- William Gaddis --