> To my surprise and delight, Chuck almost immediately discovered the germ
> of > an idea for a plausible Win By Paradox. I would have been very happy to > see > Chuck declared sole winner in this fashion. But Walker and Michael > patiently and ingeniously picked apart his argument. It was actually Steve's message which prompted me to look again at the Rules and current Proposals and see if I could find a paradox. This was at the time when 331 was still in its voting period. I hadn't noticed it at first, but looking at it again I realized the ambiguity if the proposal passed. But it would need different sets of voters on proposals distributed at the same time. I had already voted on 331-341, and doubted that I could rescind one of my votes. (Although it hadn't happened yet, the later CFJ ruling that a vote couldn't be changed suggests that I was right.) Had the same set of voters all voted on 331-341, I would have avoided voting on one proposal in a subsequent distribution to create the ambiguity myself--and I then would have had to wait for someone else to CFJ first; I wouldn't be able to attempt the Win by Paradox based on my own CFJ, since I'd be ineligible to judge my own CFJ and then there wouldn't be any ambiguity about the list of Players from which to select a judge. I was relieved to see that the sets of voters on 331-341 was not identical and so my attempt could proceed, even if it was ultimately unsuccessful. And kudos (or even Kudos) to Walker and Michael on their excellent judgements. > > In a fascinating sideline, which Michael pointed out to us in a private > message, the path to a win by paradox remained open even after Michael's > Judgement on Chuck's second CFJ. As Michael pointed out in his Judgement, > Chuck's idea was basically sound, it's just that Chuck had made his move > too early, when the relevant rule defining the end of voting periods was > the old 205, not the new 333. So a new CFJ, referring to the close of the > voting periods of proposals 348-362, might have worked. This segues into another complication: due to some travel I had this weekend, I had little to no chance to check email during the last ~20 hours of the game, and even in the ~24 hours before that I had little time to participate. It was during that period that Michael sent the message Steve references above. Steve suggested that either Michael or I attempt the Win by Paradox based on that reasoning; I replied that I wouldn't have time to put together the appropriate CFJ and deferred to Michael, if he wanted to. My timing issue was also why I cast my extra votes and made my points transfer fairly early in the voting period on 364; had I been able to, I would have done that much closer to the end of the voting period in hopes of hiding our strategy as long as possible. My biggest worry about my limited time for participation towards the end of the game was the possibility that I might be assigned a CFJ to judge, and I wouldn't have the time to give it the attention and analysis it deserved (especially given the high bar set by other judgements!). Fortunately, that didn't happen. My idea for the "Innocuous Proposals" strategy was inspired by the distribution of proposals 331-341, where 9 of the 11 proposals were by omd, and it occurred to me that e might be making proposals more for the points to be had than for the rule changes themselves. And that we could do that, too. My proposal 347 - removing the two points for voting AGAINST a successful proposal - was also made with an eye towards the Innocuous Proposal strategy. With that reward still in place, I had realized, Innocuous Proposals could also earn a lot of points (and resulting Extra Votes) for people voting against the Innocuous Proposals. I realized this with just hours to spare: removal of the two-point reward had to go out in the third-to-last proposal distribution, so the Innocuous Proposals could go out in the second-to-last proposal distribution, and the game-winning proposal in the last distribution. I came up with the name "Innocuous Proposals" as a parallel (or anti-parallel, if you like) to the "Terrible Proposals" scam from way back in Nomic World, which someone else had mentioned in passing in our discussions. The particular nature of Goethe's Innocuous Proposals were entirely his own invention, and nicely done, I must say. > My final comment on this intricate passage of play is that it also might > not have worked. It would have been open to the Speaker to try and > 'collapse the game state', a manouevre with a long history in Agora Nomic > going back to its early Platonic days, though I'm not sure it has been > needed for many years since pragmatism was written so deeply into Agora's > ruleset. The set of voters on proposals 348-362 was nearly identical for > each of those proposals; there were only minor variations. So the Speaker > could have tried identifying each of the different possible sets of Judges > for such a CFJ, and rolling a die for each such set. If the same Judge is > selected in each of the 'legally possible worlds', then voila! -- instant > gamestate collapse, and the legality of selecting that Judge could be > determined with finality after all. Alas, all this remained, as they say > in > chess, 'in the notes'. A very similar thought had occurred to me, except the Speaker could do even better than independently selecting a Judge for each possible set; e could link the sets in such a way to maximize the probability that the same Judge is selected for each set. I'll demonstrate with a simple case of two proposals and four voters; the actual situation would be more complex but the principle is the same. Suppose S is the Speaker, and A, B, C, and D are voters. Suppose also that Proposals 1001 and 1002 end simultaneously, and A, B, C, and D vote on 1001, and only A, B, and C vote on 1002. Player A makes the CFJ and is ineligible to judge. So, the set of possible judges is S, B, C, or D if based on Proposal 1001; or S, B, or C if based on Proposal 1002. The Speaker selects as Judge: S with probability 1/4; B with probability 1/4; C with probability 1/4; D (if 1001 is the appropriate proposal to use) or S (if 1002) with probability 1/12 D (if 1001) or B (if 1002) with probability 1/12 D (if 1001) or C (if 1002) with probability 1/12. This results in the judge being selected with the appropriate probability for either possible proposal; and also a 3/4 probability that a single judge is unambiguously selected. (Compared to a 1/4 probability if you just select from the 1001-list and the 1002-list independently.) Thanks to all the players, especially my fellow winners, and many many thanks to Fool for running such an enjoyable game. Like others have mentioned, I like the idea of a Nomic with a defined endpoint (being well aware, of course, that there is no guarantee that the endpoint will remain unchanged) in which I can most likely play for just a few weeks. I don't have time to participate in a long-term Nomic now, but would enjoy playing again for just a few weeks on occasion. I dropped a line to David Chess (favor), with whom I am casually in touch with on Facebook, about the Vigintennial celebrations; he responded positively but apparently was unable to participate. It looks like his email address in the Census may be out of date (he said he hadn't gotten the email to the old-timers); I'll invite him to update that if he so chooses. Chuck
