Ballots are ordinal rankings with equal rankings, truncations, and relative strength of rankings enabled. A>B>>>>C>>D=E>F>>>G for example is an allowed ballot expressing preferences A>B>C>D>E>F>G, but with added ordinal information about the order of intensity of the preferences ... the preference A>B is not as intense as C>>D, for example. Is it supposed to be half as intense? No, just less intense. Does B>>>>C on one ballot mean more than B>>C on another ballot? No, the intensity comparisons have meaning only within ballots. Here's an example of a method that makes use of this kind of information: Let X and Y be the two candidates that (for the greatest number of ballots) find themselves on opposite sides of a preference when only the max intensity preferences of each ballot are not suppressed. Then let BX and BY be the respective subsets of ballots that prefer X over Y and vice-versa. Elect the head-to-head preferred between the respective outcomes of the method applied recursively to BX and BY. I'm sure you can think of better versions of this basic idea! El lun., 20 de sep. de 2021 6:20 p. m., Forest Simmons < forest.simmons21@gmail.com> escribió: > Very thoughtful insights! > > Something you said reminds me that there is a ballot type that requires > only ordinal information ... no utilities, but is much more expressive than > Universal Domain allows .... because the order is not just a ranking of the > candidates but an order of the intensities of preference. > > The first time I heard of Ranked Pairs before reading further I thought > "Great idea, let the voters rank the pairwise preferences in order of > perceived importance!" > > This can be expressed by augmenting inequality symbols with more chevrons > to indicate relative strength of preference: > > A>B>C>D becomes A>>B>C>>>D, for example. > > How to make good use of the second order ordinal information contained in > these ranked rankings is fun to contemplate! > > Not likely to be a public proposal any time soon, unless VPR becomes > popular ... then we could have VPRR, vote for a public ranked ranking. > > El lun., 20 de sep. de 2021 3:52 p. m., Kristofer Munsterhjelm < > km_elmet@t-online.de> escribió: > >> On 9/20/21 8:55 PM, Forest Simmons wrote: >> > I know this is picky semantics to some people, but to me strategic >> > voting does not imply dishonest voting. >> >> Some ideas of how to formalize my three levels: >> >> Suppose that there exists a "reference method" where optimal behavior >> coincides with what we would consider honest, and that thus under >> honesty fixes some parameters of the ballot. (E.g. Random Ballot for >> Plurality, Random Pair for Condorcet matrices and full ranked ballots, >> and Hay for linear/affine scalings of utilities.) >> >> Then level one behavior is only strictly speaking possible in a method >> that has no free parameters once the fixed parameters are set according >> to the reference method: level one is just voting the way the reference >> method incentivizes. (Alternatively: if there are free parameters left >> over, choosing them in a way that doesn't depend on what candidates are >> running.) >> >> Level two is possible in a method that has free parameters left over >> once we're constrained to honest behavior over the (now fixed) >> parameters. E.g how to equal-rank or truncate (but not reverse >> preferences) in a method that allows for equal-rank or truncation; what >> linear (or affine) transformation to use when rendering utilities into >> Range scores; and where to put the Approval cutoff. Engaging in level >> two behavior is either setting these free parameters, (or if you chose >> the alternative definition above: setting them in a way that depends on >> who's running.) >> >> Level three is simply voting differently for the fixed parameters, i.e. >> not voting the ballot that you would under the reference method. >> (Preference reversal, etc.) >> >> The problem with this rough idea is that there's no way to delineate >> things so that equal-rank and truncation is honest (level one) while >> approval cutoff decisions are level two. The closest I can think of is >> to say that equal-rank is level one if it's done in a way that's >> independent of irrelevant candidates (e.g. I rank down to when I feel >> tired, or I equal-rank everyone who's some epsilon away from each other >> by utility). That's the alternative definition above. >> >> But I suspect that the levels are also about intent... and there's also >> something else (I don't know if it's the high stakes or some artificial >> aspect to being asked to boil everything down to yes or no) that makes >> approval much harder to decide than equal-rank. >> >> Just some thoughts :-) >> >