Hi folks, I've seen many references to "Hylland's theorem" in recent papers and other places, and yet, this theorem seems to be a partial mystery to the Internet, and no one has bothered to write a Wikipedia article about it: https://en.wikipedia.org/wiki/Hylland%27s_theorem Way back in 2005, I found a discussion of "Hylland's theorem" (and "May's theorem") on the EM-list: http://lists.electorama.com/pipermail/election-methods-electorama.com//2005-January/thread.html#79759 That led me to this paper: "Strategy Proofness of Voting Procedures with Lotteries as Outcomes and Infinite Sets of Strategies" -- Aanund Hyllund -- January 1980 ...which seems to be archived here (among other places, I hope): https://www.sv.uio.no/econ/personer/vit/aanundh/upubliserte-artikler-og-notater/Strategy%20Proofness%5B1%5D.pdf Am I following the breadcrumbs properly? Is there a different "Hylland" that deserves to have a theorem named after them? I would like to either flesh out the following wiki page, or delete it: https://electowiki.org/wiki/Hylland%27s_theorem I'm not sure what to do with the "Hylland free riding" section in the "Free riding" article, but that needs better citations: https://electowiki.org/wiki/Free_riding#Hylland_free_riding Rob

Hi Rob, Rob Lanphier <roblan@gmail.com> a écrit : >  > Hi folks, >  > I've seen many references to "Hylland's theorem" in recent papers and other places, and > yet, this theorem seems to be a partial mystery to the Internet, and no one has > bothered to write a Wikipedia article about it: > https://en.wikipedia.org/wiki/Hylland%27s_theorem >  > Way back in 2005, I found a discussion of "Hylland's theorem" (and "May's theorem") on > the EM-list: > http://lists.electorama.com/pipermail/election-methods-electorama.com//2005-January/thread.html#79759 >  > That led me to this paper: > "Strategy Proofness of Voting Procedures with Lotteries as Outcomes and Infinite Sets > of Strategies" -- Aanund Hyllund -- January 1980 >  > ...which seems to be archived here (among other places, I hope): >  > https://www.sv.uio.no/econ/personer/vit/aanundh/upubliserte-artikler-og-notater/Strategy%20Proofness%5B1%5D.pdf >  > Am I following the breadcrumbs properly?  Is there a different "Hylland" that deserves > to have a theorem named after them? All references seem to point to the 1980 paper, yes. Markus' description in 2005 seems to refer specifically to a two-candidate situation, and when he says "Hylland's theorem" it's possible to read it as only referring to the finding he mentions: >> However, Hylland proved that when there are only two candidates and >> the used single-winner election method is strategyproof then the >> result depends only on whether the individual voter strictly prefers >> candidate A to candidate B, strictly prefers candidate B to candidate A >> or is indifferent between candidate A and candidate B (Aanund Hylland, >> "Strategy Proofness of Voting Procedures with Lotteries as Outcomes >> and Infinite Sets of Strategies," University of Oslo, 1980). >>  >> Therefore, I interpret May's theorem in connection with Hylland's >> theorem as follows [...] The paper "Strategy-proof Cardinal Decision Schemes" (by Dutta, Peters, and Sen, 2007) has this in the abstract: >> We provide a new proof of Hylland's theorem which shows that the only strategy-proof >> cardinal decision scheme satisfying a weak unanimity property is the random >> dictatorship. and inside one version of it: (https://warwick.ac.uk/fac/soc/economics/staff/bdutta/publications/cardinalrev7.pdf) >> [...] Hylland [9], in an important and regrettably unpublished paper, showed that >> the random dictatorship result holds even if the decision scheme is allowed to use >> cardinal information. In this paper, we have two main objectives. First, we provide >> an alternative and considerably simpler proof of Hylland’s theorem. The reference is still to the 1980 paper. Wikipedia's discussion of it suggests another view of the significance: >> Gibbard's theorem is itself generalized by Gibbard's 1978 theorem and Hylland's >> theorem, which extend these results to non-deterministic processes, i.e. where the >> outcome may not only depend on the agents' actions but may also involve an element >> of chance. > I would like to either flesh out the following wiki page, or delete it: > https://electowiki.org/wiki/Hylland%27s_theorem I'm not sure what we would say it is. It seems like when people use this term they also clarify (at least somewhat) what they mean by it. > I'm not sure what to do with the "Hylland free riding" section in the "Free riding" > article, but that needs better citations: > https://electowiki.org/wiki/Free_riding#Hylland_free_riding The citations go to Markus' paper, in which the relevant reference is: >> Aanund Hylland, Proportional Representation without Party Lists, pp. 126-153, >> RATIONALITY AND INSTITUTIONS, eds. Raino Malnes and Arild Underdal, Scandinavian >> University Press, Oslo, 1992 Hylland free riding seems unrelated to the 1980 paper or the theorem. Kevin votingmethods.net

On 2023-12-25 05:32, Rob Lanphier wrote: > Hi folks, > > I've seen many references to "Hylland's theorem" in recent papers and > other places, and yet, this theorem seems to be a partial mystery to the > Internet, and no one has bothered to write a Wikipedia article about it: > https://en.wikipedia.org/wiki/Hylland%27s_theorem > <https://en.wikipedia.org/wiki/Hylland%27s_theorem> > > Way back in 2005, I found a discussion of "Hylland's theorem" (and > "May's theorem") on the EM-list: > http://lists.electorama.com/pipermail/election-methods-electorama.com//2005-January/thread.html#79759 <http://lists.electorama.com/pipermail/election-methods-electorama.com//2005-January/thread.html#79759> > > That led me to this paper: > "Strategy Proofness of Voting Procedures with Lotteries as Outcomes and > Infinite Sets of Strategies" -- Aanund Hyllund -- January 1980 > > ...which seems to be archived here (among other places, I hope): > https://www.sv.uio.no/econ/personer/vit/aanundh/upubliserte-artikler-og-notater/Strategy%20Proofness%5B1%5D.pdf <https://www.sv.uio.no/econ/personer/vit/aanundh/upubliserte-artikler-og-notater/Strategy%20Proofness%5B1%5D.pdf> > > Am I following the breadcrumbs properly?  Is there a different "Hylland" > that deserves to have a theorem named after them? My impression is that "Hylland's theorem" refers to one of the results in that paper, although which result it is may vary. For instance, Dutta et al. (http://dx.doi.org/10.1007/s00355-006-0152-9, https://ageconsearch.umn.edu/record/269616/files/twerp722.pdf) refer to the paper you linked to, and then say "Despite this difficulty, Hylland, in an important and regrettably unpublished paper,showed that the random dictatorship result holds even if the decision scheme is allowed to use cardinal information. In this paper, we have two main objectives. First, we providean alternative and considerably simpler proof of Hylland’s theorem. [...]" Schulze says that Hylland proved that "when there are only two candidates and the used single-winner election method is strategyproof then the result depends only on whether the individual voter strictly prefers candidate A to candidate B, strictly prefers candidate B to candidate A or is indifferent between candidate A and candidate B". This is implied by the actual results in the paper, as far as I understand, but not actually given as a main result. The paper deals with methods that are immune to every kind of strategy. Hylland free riding is a different concept: it's a particular kind of strategy, and methods may be immune to it without being fully strategyproof. So the different Hylland concepts aren't really related, apart from both dealing with how methods respond to strategy. -km